Particle dynamic characteristic simulation method and device based on multi-scale fluid-solid coupling

Abstract

The invention discloses a particle dynamic characteristic simulation method and device based on multi-scale fluid-solid coupling, and the method comprises the steps: generating a background grid according to a simulation flow field region, and generating a local grid according to the position of a target particle; inputting the solid domain parameter and the fluid domain parameter of the current time step into a fluid-solid coupling model, and outputting a target solid domain parameter and a target fluid domain parameter; judging whether a local grid needs to be regenerated or not; if yes, a new local grid is generated according to the target solid domain parameters, and solid domain parameters and fluid domain parameters of the new local grid are obtained to serve as input parameters of the next time step; if not, taking the target fluid domain parameter and the target solid domain parameter as input parameters of the next time step; and repeating the inputting and judging processes until the simulation duration is reached, and determining the dynamic characteristics of the solid particles according to the target solid domain parameters of each time step. According to the method, multi-scale fluid-solid coupling calculation can be accurately and efficiently carried out, so that dynamic characteristic simulation of target particles is effectively realized.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid-solid coupling simulation, and in particular to a particle dynamic characteristics simulation method and device based on multi-scale fluid-solid coupling. Background Art

[0002] Fluid-solid interaction (FSI) problems have a wide range of applications in engineering and science, such as biofluid mechanics, aerospace structural analysis, and microfluidic chip design. However, existing FSI simulation methods face the following challenges when dealing with three-dimensional multiscale problems (multi-scale problems, such as tiny solid particles interacting with large-scale flow regions in microfluidic chips, and three-dimensional structures, such as cylindrical obstacles within the flow region):

[0003] (1) Low computational efficiency: Traditional methods usually require global meshing and solving of the entire computational domain. The number of meshes is huge, and the number of equations that need to be solved is large. Especially when dealing with three-dimensional multi-scale problems, the equations are solved slowly, the computation is time-consuming, and the simulation cycle is long. (2) Insufficient interface accuracy: There are discontinuities in physical quantities (such as pressure) at the fluid-solid interface. Traditional decoupling solution methods are prone to introduce numerical errors, resulting in distortion of the calculation results at the interface, or even numerical divergence, which in turn affects the accuracy of multi-scale fluid-solid coupling calculations. (3) Limited applicability: Many algorithms are only applicable to two-dimensional or axisymmetric problems and are difficult to extend to three-dimensional complex geometric structures, limiting their engineering application value.

[0004] To address the above issues, no effective solutions have been proposed so far. Summary of the Invention

[0005] The embodiments of this specification provide a method and device for simulating particle dynamic characteristics based on multi-scale fluid-solid coupling to solve the problem that the existing technology cannot accurately and efficiently perform multi-scale fluid-solid coupling calculations, and thus cannot effectively realize the dynamic characteristics simulation of target particles.

[0006] In a first aspect, the embodiments of this specification provide a method for simulating particle dynamic characteristics based on multi-scale fluid-structure coupling, including:

[0007] Generate a background grid based on the simulated flow field area where the target particle is located, and generate a local grid based on the location of the target particle, wherein the background grid is used to provide a flow field domain boundary for the local grid, and the scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold;

[0008] Input the solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field boundary into the fluid-solid coupling model, and output the target solid domain parameters and target fluid domain parameters after fluid-solid coupling at the current time step;

[0009] Determining whether a local grid needs to be regenerated according to the target solid domain parameters;

[0010] If yes, generate a new local grid according to the target solid domain parameters and obtain the solid domain parameters and fluid domain parameters of the new local grid as fluid-solid coupling input parameters for the next time step; if no, use the target fluid domain parameters and target solid domain parameters as fluid-solid coupling input parameters for the next time step;

[0011] The input and judgment process is repeated until the cumulative value of each time step reaches the simulation duration. The dynamic characteristics of the target particles in the simulated flow field area are determined based on the target solid domain parameters after fluid-solid coupling at each time step. The dynamic characteristics include at least motion trajectory and stress distribution.

[0012] In some embodiments, generating a local grid according to the position of the target particle includes:

[0013] Generate an initial local grid based on the position of the target particles;

[0014] Identify sensitive areas and insensitive areas in the initial local grid, where the curvature of the sensitive area at the fluid-solid interface is greater than or equal to a preset curvature threshold, or the minimum distance from the fluid-solid interface to the boundary of the computational domain is a preset distance threshold;

[0015] The grid cells are subdivided in the sensitive area, and the adjacent grid cells are merged in the non-sensitive area. Then, the quality of the grid cells in the sensitive area and the non-sensitive area is optimized to obtain the local grid.

[0016] In some embodiments, the fluid-structure interaction model is composed of the following equations:

[0017]

[0018] Where u is the velocity field of the fluid domain and the solid domain; w t is the moving speed of the target particle; P s is the pressure field of the solid domain; P f is the pressure field of the fluid domain; Re is the Reynolds number; D is the symmetric gradient tensor of the velocity field; E is the Young's modulus of the target particle; B is the left Cauchy Green tensor, which is used to describe the deformation of the target particle; I is the identity matrix; T is the simulation time; The entire computational domain consists of the solid domain and the fluid domain; is a solid domain; is the fluid domain; Used to describe the spatial variation of physical quantities; Used to describe the diffusion process of physical quantities.

[0019] In some embodiments, the fluid-structure interaction model processes the input solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field domain boundary in the following manner:

[0020] Based on the solid domain parameters and the fluid domain parameters of the current time step, the solid domain intermediate parameters and the fluid domain intermediate parameters between the current time step and the next time step are determined by adjusting the time step by adjusting the parameters;

[0021] Linearly combine the solid domain intermediate parameters, the fluid domain intermediate parameters with the solid domain parameters and the fluid domain parameters of the current time step to obtain the corrected solid domain parameters and the corrected fluid domain parameters;

[0022] Based on the modified solid domain parameters and the modified fluid domain parameters, the time step is scaled to determine and output the target solid domain parameters and target fluid domain parameters after fluid-solid coupling at the current time step.

[0023] In some embodiments, the solid domain parameters include at least one of the following: the velocity field of the solid domain, the movement speed of the target particle, the pressure field of the solid domain, the Young's modulus of the target particle, and the left Cauchy Green tensor; the fluid domain parameters include at least one of the following: the velocity field of the fluid domain, the pressure field of the fluid domain, the fluid density, and the dynamic viscosity.

[0024] In some embodiments, determining whether to regenerate a local mesh according to the target solid domain parameters includes:

[0025] Determine the target position of the target particle according to the target movement speed of the target particle;

[0026] Determine the difference between the target position of the target particle and the initial position of the target particle as the displacement amplitude of the target particle, and determine the difference between the target left Cauchy Green tensor of the target particle and the left Cauchy Green tensor of the target particle as the deformation degree of the target particle;

[0027] Determining whether the displacement amplitude and the deformation degree exceed corresponding preset thresholds;

[0028] If so, it is determined that the local mesh needs to be regenerated; if not, it is determined that the local mesh does not need to be regenerated.

[0029] In some embodiments, generating a new local grid and obtaining solid domain parameters and fluid domain parameters of the new local grid include:

[0030] Generate a new local grid according to the new position of the target particle, and determine the overlapping area and non-overlapping area between the new local grid and the old local grid;

[0031] The target solid domain parameters and target fluid domain parameters are interpolated into the overlapping area, the background flow field in the background grid is interpolated into the non-overlapping area, and the interpolated parameters are used as the solid domain parameters and fluid domain parameters of the new local grid.

[0032] In some embodiments, determining the dynamic characteristics of the target particles in the simulated flow field region based on the target solid domain parameters after fluid-solid coupling at each time step includes:

[0033] Superimpose the target motion speed of the target particle at each time step to determine the motion trajectory of the target particle in the simulated flow field area of ​​the target microfluidic chip;

[0034] According to the target left Cauchy Green tensor at each time step, the stress distribution of the target particle in the simulated flow field area of ​​the target microfluidic chip is determined.

[0035] In a second aspect, the embodiments of this specification further provide a device for simulating particle dynamic characteristics based on multi-scale fluid-solid coupling, comprising:

[0036] A background and local grid generation module is used to generate a background grid based on the simulated flow field area where the target particle is located, and to generate a local grid based on the position of the target particle. The background grid is used to provide a flow field domain boundary for the local grid. The scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold.

[0037] The fluid-solid coupling simulation module is used to input the solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field boundary into the fluid-solid coupling model, and output the target fluid domain parameters and target solid domain parameters after fluid-solid coupling at the current time step;

[0038] A judgment module, configured to judge whether a local grid needs to be regenerated according to the target solid domain parameters;

[0039] an input parameter determination module for generating a new local grid according to the target solid domain parameters and obtaining the solid domain parameters and fluid domain parameters of the new local grid as fluid-solid coupling input parameters for the next time step; and if not, using the target fluid domain parameters and target solid domain parameters as fluid-solid coupling input parameters for the next time step;

[0040] The dynamic characteristics determination module is used to repeat the input and judgment process until the cumulative value of each time step reaches the simulation time. The dynamic characteristics of the target particles in the simulated flow field area are determined based on the target solid domain parameters after fluid-solid coupling at each time step. The dynamic characteristics include at least motion trajectory and stress distribution.

[0041] In a third aspect, an embodiment of this specification further provides a computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of the above-mentioned method for simulating particle dynamic characteristics based on multi-scale fluid-solid coupling.

[0042] The embodiments of this specification provide a method and device for simulating particle dynamic characteristics based on multi-scale fluid-solid coupling. First, a background grid is generated based on the simulated flow field area where the target particle is located, and a local grid is generated based on the position of the target particle. The background grid is used to provide a flow field domain boundary for the local grid, and the scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold. Then, the solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field domain boundary are input into the fluid-solid coupling model, and the target solid domain parameters and target fluid domain parameters after the fluid-solid coupling of the current time step are output. Then, it is determined whether the local grid needs to be regenerated based on the target solid domain parameters of the current time step. If so, a new local grid is generated based on the target solid domain parameters of the current time step and the solid domain parameters and fluid domain parameters of the new local grid are obtained as the fluid-solid coupling input parameters of the next time step; if not, the target fluid domain parameters and target solid domain parameters after the fluid-solid coupling of the current time step are used as the fluid-solid coupling input parameters of the next time step. Finally, the input and judgment process is repeated until the cumulative value of each time step reaches the simulation time. The dynamic characteristics of the target particles in the simulated flow field area are determined according to the target solid domain parameters of each time step. The dynamic characteristics include at least motion trajectory and stress distribution. In the embodiment of this specification, by generating a background grid and a local grid, the background grid provides a local flow field boundary for the local grid, and only the solid domain parameters in the local grid and the fluid domain parameters within the local flow field boundary are used on the local grid to perform fluid-solid coupling simulation, thereby avoiding the problems of low computational efficiency and long simulation cycle caused by global grid division and solution, and improving the computational efficiency of fluid-solid coupling in three-dimensional multi-scale fluid-solid coupling scenarios, thereby greatly saving computing resources. The fluid-solid coupling model can avoid the problem of discontinuity of physical quantities (such as pressure) at the fluid-solid interface, and improve the accuracy and efficiency of fluid-solid coupling calculations. By judging whether the local grid needs to be regenerated, it is suitable for complex three-dimensional multi-scale fluid-solid coupling scenarios, and the fluid-solid coupling simulation of the next time step can be performed accurately and efficiently. Finally, based on the target solid domain parameters at each time step, the motion trajectory and stress distribution of the target particles in the simulated flow field area are determined, which can provide reliable data support for engineering problems in the fields of microfluidic chip design, biofluid mechanics, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0044] Figure 1 This is a flow chart of a particle dynamic characteristics simulation method based on multi-scale fluid-solid coupling provided in an embodiment of this specification;

[0045] Figure 2 is a schematic diagram of a local grid provided in an embodiment of this specification;

[0046] Figure 3 Schematic diagram of the simulation of the motion trajectory of the target particles in the microfluidic chip provided in the embodiments of this specification;

[0047] Figure 4 is a schematic diagram of updating a local grid provided in an embodiment of this specification;

[0048] Figure 5 This is a schematic diagram of the structure of a particle dynamic characteristics simulation device based on multi-scale fluid-solid coupling provided in an embodiment of this specification;

[0049] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this specification. DETAILED DESCRIPTION

[0050] To help those skilled in the art better understand the technical solutions in this specification, the following will provide a clear and complete description of the technical solutions in the embodiments of this specification, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of this specification, not all of them. All other embodiments derived by those skilled in the art based on the embodiments in this specification without creative effort shall fall within the scope of protection of this specification.

[0051] As mentioned earlier, fluid-solid interaction (FSI) problems have a wide range of applications in engineering and science, such as biofluid mechanics, aerospace structural analysis, and microfluidic chip design. However, existing FSI simulation methods face the following challenges when dealing with three-dimensional multiscale problems (multi-scale problems, such as tiny solid particles interacting with the large-scale flow field in a microfluidic chip, and three-dimensional structures, such as cylindrical obstacles within the flow field):

[0052] (1) Low computational efficiency: Due to the large number of equations that need to be solved and the huge number of grids, especially when dealing with three-dimensional multi-scale structures (such as the coupling of small solid structures with large-scale fluid domains), the equations are solved slowly and the simulation cycle is long; (2) Difficulty in precision control: Traditional methods tend to decouple the control equations and solve them separately, which will easily lead to insufficient precision of the numerical results and a very limited role in engineering applications; (3) Difficulty in interface pressure matching: There is a discontinuity in the pressure at the fluid-solid interface, which makes many numerical algorithms have common error problems during calculation. Especially when the hardness of the solid (Young's modulus) is large, the numerical oscillation and physical quantity discontinuity at the interface will become more serious, resulting in distorted calculation results or even numerical divergence; (4) Some algorithms are only applicable to two-dimensional or axisymmetric problems, which makes it difficult to extend them to real three-dimensional complex geometric structures, greatly limiting the engineering application prospects of the algorithms.

[0053] In order to solve the above problems, the embodiments of this specification provide a method and device for simulating particle dynamic characteristics based on multi-scale fluid-solid coupling. First, a background grid is generated according to the simulated flow field area where the target particle is located, and a local grid is generated according to the position of the target particle. The background grid is used to provide a flow field domain boundary for the local grid, and the scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold. Then, the solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field domain boundary are input into the fluid-solid coupling model, and the target solid domain parameters and target fluid domain parameters after the fluid-solid coupling of the current time step are output. Then, it is determined whether the local grid needs to be regenerated based on the target solid domain parameters of the current time step. If so, a new local grid is generated based on the target solid domain parameters of the current time step and the solid domain parameters and fluid domain parameters of the new local grid are obtained as the fluid-solid coupling input parameters of the next time step; if not, the target fluid domain parameters and target solid domain parameters after the fluid-solid coupling of the current time step are used as the fluid-solid coupling input parameters of the next time step. Finally, the input and judgment process is repeated until the cumulative value of each time step reaches the simulation duration. The dynamic characteristics of the target particles in the simulated flow field area are determined based on the target solid domain parameters of each time step. The dynamic characteristics include at least motion trajectory and stress distribution.

[0054] The present invention generates a local grid and a background grid, and performs fluid-solid coupling simulation on the local grid, which can significantly reduce the amount of calculation and improve the calculation efficiency. The scale difference between the simulated flow field area and the target particle is set to be greater than the preset scale threshold, and then the target solid domain parameters and target fluid domain parameters after fluid-solid coupling are output through the fluid-solid coupling model, which can improve the calculation efficiency of multi-scale fluid-solid coupling and solve the problems of low multi-scale calculation efficiency, poor fluid-solid interface accuracy and difficult interface pressure matching. By judging whether the local grid needs to be regenerated, the fluid-solid coupling input parameters of the next time step can be accurately determined, thereby ensuring the fluid-solid coupling accuracy of the next time step, and finally effectively realizing the motion trajectory and stress distribution simulation of the target particle in the simulated flow field area. The present invention is suitable for three-dimensional multi-scale fluid-solid coupling calculations and has a high engineering application prospect.

[0055] It should be noted that the "particles" in the present invention may include rigid particles, elastic particles, viscoelastic particles and solid particles with other mechanical characteristics. Both types of particles can be used for simulation calculations. "Dynamic characteristics" may refer to all physical quantities that change over time in the model, and may include the time-varying characteristics of the velocity field of the fluid and the solid, the time-varying characteristics of the position of the solid particles, the time-varying characteristics of the internal stress of the solid particles, the time-varying characteristics of the force on the solid particles, and so on. "Fluid-solid coupling" may refer to the process of combining the dynamic equations describing the flow of the fluid with the dynamic equations describing the motion and force of the solid in a mathematical modeling manner to solve them together, which can accurately simulate the interaction between the solid moving in the fluid and the fluid, as well as the dynamic evolution characteristics.

[0056] It is understood that the methods described in the embodiments of this specification can be applied to electronic devices, which can refer to electronic devices capable of data calculation, processing, and storage. Such electronic devices can be terminals such as PCs (personal computers), tablets, smartphones, wearable devices, and intelligent robots; they can also be servers. The server can be a standalone physical server, a server cluster or distributed system consisting of multiple physical servers, or a cloud server providing cloud computing services.

[0057] See Figure 1 As shown, the embodiment of this specification provides a method for simulating particle dynamic characteristics based on multi-scale fluid-structure coupling. In specific implementation, the method may include the following:

[0058] S101: Generate a background grid based on the simulated flow field area where the target particle is located, and generate a local grid based on the position of the target particle. The background grid is used to provide a flow field domain boundary for the local grid. The scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold.

[0059] Specifically, the target particle can be a solid particle, and the simulated flow field region can be the entire flow field region of the microfluidic chip, which serves as the simulated flow field region. The background grid can be a large, integrated background grid generated across the entire simulated flow field region, on which a corresponding finite element space can be established. The local grid can be a body-fitting local grid or a local body-fitting grid generated near the target particle's location. Variables describing the velocity field, pressure field, and solid structural state (such as the left Cauchy Green tensor) can be defined on this local grid. The target particle's scale must be significantly smaller than the simulated flow field region in which it resides, meaning the scale difference between the simulated flow field region and the target particle is greater than a preset scale threshold. By generating a background grid and a local grid, the background grid provides a local flow field boundary for the local grid. Based on this, accurate and efficient multiscale fluid-structure interaction calculations can be performed, significantly reducing the computational complexity of three-dimensional multiscale fluid-structure interaction problems while maintaining the physical accuracy of the target particle's local region. This effectively simulates the dynamic characteristics of the target particle in the simulated flow field region, resolving the problem of existing technologies' inability to accurately and efficiently perform multiscale fluid-structure interaction or three-dimensional multiscale fluid-structure interaction calculations.

[0060] In some embodiments, before the above S101, the specific implementation may also include:

[0061] Obtaining the inlet and outlet velocity fields and the inlet and outlet pressure fields of the target particles in the simulated flow field area, inputting the inlet and outlet velocity fields and the inlet and outlet pressure fields into the background flow field prediction model, and outputting the background flow field in the background grid, wherein the background flow field includes the background velocity field and the background pressure field;

[0062] Accordingly, the background grid in the above S101 is used to provide a flow field boundary for the local grid. In specific implementation, it may include:

[0063] The background velocity field is interpolated to the boundary of the local grid, and the interpolated boundary is used as the flow field boundary of the local grid.

[0064] Specifically, a background mesh covering the entire simulated flow region (e.g., a microfluidic chip channel) can be generated. This background mesh can be a global coarse mesh, typically using a non-body-fitting structured or unstructured mesh (e.g., hexahedral or tetrahedral elements) with a low mesh resolution to conserve computational resources. A corresponding finite element space is then established on the background mesh. By specifying the inlet and outlet velocity fields, inlet and outlet pressure fields, and no-slip boundary conditions on the remaining boundaries, a simple Navier-Stokes equation without solid interaction terms is solved using the P2-P1 finite element method. Given an appropriate time step and sufficient time, a stable background pure flow field is ultimately obtained, providing basic boundary information for subsequent local calculations. Specifically, the aforementioned background flow field prediction model can be constructed based on the Navier-Stokes equations with solid coupling terms neglected. The inlet and outlet velocity fields and inlet and outlet pressure fields of the target particle in the simulated flow region are input into the background flow field prediction model, which outputs the background flow field in the background mesh. The background velocity field in the background flow field is then interpolated to the boundaries of the local mesh to obtain the flow field domain boundary of the local mesh. The expression of the Navier-Stokes equation ignoring the solid coupling term can be as follows:

[0065] (1)

[0066] Among them, u f is the velocity field of the fluid domain; P f is the pressure field in the fluid domain; Re is the Reynolds number.

[0067] It should be noted that if the background flow field is significantly affected by solid motion (such as blocking effect), the background flow field can be solved periodically (such as updating once per time step), and accordingly, the flow field boundary of the local grid is periodically updated.

[0068] In some embodiments, generating a local grid according to the position of the target particle in S101 may include:

[0069] Generate an initial local grid based on the position of the target particles;

[0070] Identify sensitive areas and insensitive areas in the initial local grid, where the curvature of the sensitive area at the fluid-solid interface is greater than or equal to a preset curvature threshold, or the minimum distance from the fluid-solid interface to the boundary of the computational domain is a preset distance threshold;

[0071] The grid cells are subdivided in the sensitive area, and the adjacent grid cells are merged in the non-sensitive area. Then, the quality of the grid cells in the sensitive area and the non-sensitive area is optimized to obtain the local grid.

[0072] Specifically, an initial local mesh (second-order body-fitting mesh) can be generated near the position of the target particle (or a small local window of the target particle) using public mesh generation software to ensure that the initial local mesh has high geometric conformality at the fluid-solid interface and can accurately depict complex features such as interface curvature, convexity and concavity. The initial local mesh type generated in this process can be a second-order tetrahedron, which supports high-order solution under the finite element framework. Afterwards, sensitive areas and non-sensitive areas in the initial local mesh can be identified (only sensitive areas need to be identified, and the areas other than sensitive areas in the initial local mesh are regarded as non-sensitive areas). The identification method is as follows: determine the area where the curvature of the fluid-solid interface is greater than a preset curvature threshold, or determine the area where the minimum distance between the fluid-solid interface and the boundary of the computational domain is less than a preset distance threshold, or the area where there is a sharp change in slope or the area where the solid boundary is very close to the boundary of the computational domain. It is also possible to determine the area of ​​velocity gradient, pressure gradient, and stress concentration, and these areas are regarded as sensitive areas. The above-mentioned sensitive area determination method can be selected according to actual conditions. Of course, there can be other determination methods, which are not specifically limited in this specification. Afterwards, sensitive areas and non-sensitive areas can be marked in the local grid. In the sensitive areas, the original grid cells can be automatically subdivided to increase the number of grids. In the non-sensitive areas, the reconstruction algorithm can be used to merge adjacent grid cells to reduce the number of grids. Finally, the quality of the grid cells in the sensitive and non-sensitive areas can be optimized, such as topological consistency check and quality optimization (such as minimum cell angle, Jacobian positivity, etc.). The grid quality can be improved through algorithms such as Laplacian smoothing to ensure the stability of the numerical solution. Finally, a high-quality local grid is obtained, which not only meets the geometric fitting accuracy requirements but also has good numerical stability. You can refer to Figure 2 As shown, Figure 2 The darker areas in the figure are the fluid regions (fluid domains) of the local mesh, and the lighter areas are the solid regions (solid domains) of the local mesh.

[0073] Through the above process, while ensuring the mesh accuracy of key physical areas, the number of degrees of freedom required for simulation can be effectively controlled, the memory and computational burden can be reduced, and an efficient and feasible mesh generation foundation can be provided for large-scale three-dimensional multi-scale flow coupling simulation.

[0074] In some embodiments, a small local window of the target particle can be adaptively positioned and adjusted according to changes in physical quantities (such as velocity, pressure, stress, and particle spatial position). During the time advancement process, the update step is only performed on the nodes and units within the window, and the non-critical areas (non-overlapping areas) maintain the state of the previous time step. This local update mechanism significantly reduces the computational scale of each time step, especially in large-scale three-dimensional structure scenarios, which can effectively compress the amount of calculation and accelerate convergence. Compared with the traditional global coupling method, the local update algorithm described in the present invention not only ensures the overall solution accuracy, but also makes it possible for the simulation program to run in parallel with a low number of cores (10 to 20 cores) on a single node, greatly saving computing resources. At the same time, it can also reduce the total simulation time by more than 98%, and is particularly suitable for multi-scale fluid-solid interaction problems with strong local change characteristics.

[0075] S102: Input the solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field domain boundary into the fluid-solid coupling model, and output the target solid domain parameters and target fluid domain parameters after the fluid-solid coupling of the current time step.

[0076] Specifically, the solid domain parameters in the local grid at the current time step and the fluid domain parameters within the flow field boundary can be determined by assigning initial values ​​to the function space of the velocity field, pressure field, displacement field, and deformation field established on the local grid. The fluid-structure interaction model can be composed of multiple equations and is a dynamic mesh three-dimensional fast fluid-structure interaction calculation model. At the current time step, the solid domain parameters and fluid domain parameters can be input into the fluid-structure interaction model, which outputs the velocity field, pressure field, left Cauchy Green tensor, and the moving mesh or target particle velocity after fluid-structure interaction or three-dimensional interaction at the current time step. The target particle's velocity causes the local grid position to shift, thus affecting the input parameters (or fluid-structure interaction input parameters) input to the fluid-structure interaction model in the next time step. The dynamic mesh enables multi-scale fluid-structure interaction calculations at multiple time steps, ultimately providing a data foundation for simulating the dynamic characteristics of the target particle in the simulated flow field region.

[0077] In some embodiments, the fluid-structure coupling model in S102 may be composed of the following equations:

[0078] (2)

[0079] Where u is the velocity field of the fluid domain and the solid domain; w t is the moving speed of the target particle; P s is the pressure field of the solid domain; P fis the pressure field of the fluid domain; Re is the Reynolds number; D is the symmetric gradient tensor of the velocity field; E is the Young's modulus of the target particle; B is the left Cauchy Green tensor, which is used to describe the deformation of the target particle; I is the identity matrix; T is the simulation time; The entire computational domain consists of the solid domain and the fluid domain; is a solid domain; is the fluid domain; Used to describe the spatial variation of physical quantities; Used to describe the diffusion process of physical quantities.

[0080] in, (3).

[0081] Specifically, the equations in equation (2) above, from top to bottom, can be called the momentum equation (describing the coupling between fluid and solid), the continuity equation (describing the incompressible fluid), the solid deformation equation (describing the evolution of the left Cauchy Green tensor), and the last two equations are collectively called the mesh motion equations. Equation (2) constitutes the above-mentioned fluid-solid coupling model (fluid-solid coupling equations). By constructing the fluid-solid coupling model through the above-mentioned equations, the following technical effects can be achieved:

[0082] It can be seen from equation (2) that in order to adapt to the discontinuity of pressure at the interface, the present invention adopts a spatial splitting method to split the original continuous pressure function space into solid parts P s and the liquid portion P f The two spaces overlap at the fluid-solid interface, but because they belong to different function spaces, they do not affect each other and each satisfies the equations in its own region, thus avoiding the problem of fluid-solid coupling calculation distortion caused by pressure discontinuity.

[0083] Furthermore, by coupling Equation (2), with the initial and boundary conditions complete, a fully coupled discrete format and finite element weak form can be constructed, ultimately assembling a large matrix containing all the information in the model. Regardless of the situation, only a single solution to this large matrix is ​​required to obtain all the physical quantity outputs within a unit time step, meaning that all equations can be solved in a single calculation, resulting in high computational accuracy and efficiency.

[0084] In the fluid-solid model, the target particle velocity w can be directly solved t . According to the target particle's moving speed w t By moving the target particle, we can directly obtain the position of the target particle at that moment, which affects the calculation of the next time step. This method can achieve the rapid generation of local grids between different moments and the detailed tracking of the target particle's trajectory.

[0085] In some embodiments, the fluid-solid coupling model in S102 processes the input solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field domain boundary in the following manner:

[0086] Based on the solid domain parameters and the fluid domain parameters of the current time step, the solid domain intermediate parameters and the fluid domain intermediate parameters between the current time step and the next time step are determined by adjusting the time step by adjusting the parameters;

[0087] Linearly combine the solid domain intermediate parameters and the fluid domain intermediate parameters with the solid domain parameters and the fluid domain parameters of the current time step to obtain the corrected solid domain parameters and the corrected fluid domain parameters;

[0088] Based on the modified solid domain parameters and the modified fluid domain parameters, the time step is scaled to determine and output the target solid domain parameters and target fluid domain parameters after fluid-solid coupling at the current time step.

[0089] In some embodiments, the above-mentioned solid domain parameters may include at least one of the following: the velocity field of the solid domain, the movement speed of the target particle, the pressure field of the solid domain, the Young's modulus of the target particle, and the left Cauchy Green tensor; the fluid domain parameters may include at least one of the following: the velocity field of the fluid domain, the pressure field of the fluid domain, the fluid density, and the dynamic viscosity.

[0090] Specifically, the solution process for each time step of the fluid-structure interaction model (the process of processing the input parameters at each time step) can all be implemented using a time discretization approach. This means that the fluid-structure interaction model can be a model optimized for time discretization. This approach effectively improves time accuracy by introducing an intermediate prediction step at each time step, allowing for more efficient determination of the input parameters for the next time step. Compared to traditional first-order methods, this approach offers superior time evolution performance within the same error tolerance. The specific steps are as follows:

[0091] At each time step t n →t n+1 Inside (i.e. the current time step t n and the next time step t n+1 First, a predictive calculation is performed with the input parameters of the current time step (such as the velocity field of the solid domain, the pressure field of the solid domain, the velocity field of the fluid domain, the pressure field of the fluid domain, etc.) as the initial value to obtain the intermediate state t (1) Then, based on this intermediate state, another correction step is performed to obtain a higher precision t n+1 Time solution.

[0092] Specifically, the specific process of the fluid-solid coupling model processing the solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field boundary is as follows:

[0093] First, based on the solid domain parameters and fluid domain parameters of the current time step, the time step can be scaled to determine the solid domain intermediate parameters and fluid domain intermediate parameters between the current time step and the next time step according to the following formula (4):

[0094] (4)

[0095] Among them, U (1) are the intermediate parameters of the solid domain and the intermediate parameters of the fluid domain (collectively referred to as intermediate parameters) between the current time step and the next time step; U n are the solid domain parameters and fluid domain parameters of the current time step (collectively referred to as input parameters); is the scaled time step; To adjust the parameters, ; is the time step; F represents the solution process of the equation group corresponding to the fluid-structure coupling model (it can represent the solver of the fluid-structure coupling model).

[0096] Secondly, according to the following formula (5), the solid domain intermediate parameters, the fluid domain intermediate parameters and the solid domain parameters and fluid domain parameters of the current time step can be linearly combined to obtain the corrected solid domain parameters and corrected fluid domain parameters:

[0097] (5)

[0098] Among them, U * To correct the solid domain parameters and fluid domain parameters (collectively referred to as correction parameters); U n are the solid domain parameters and fluid domain parameters of the current time step; U (1) These are the intermediate parameters of the solid domain and the fluid domain between the current time step and the next time step.

[0099] Finally, based on the modified solid domain parameters and the modified fluid domain parameters, the time step can be scaled to determine and output the target solid domain parameters and target fluid domain parameters after fluid-solid coupling at the current time step according to the following formula (10):

[0100] (6)

[0101] Among them, U n+1 are the target solid domain parameters and target fluid domain parameters after fluid-solid coupling at the current time step (collectively referred to as output parameters); U * To correct the solid domain parameters and fluid domain parameters; is the scaling time step; F represents the solution process of the equation group corresponding to the fluid-structure coupling model.

[0102] Among them, Un It can include: velocity field of fluid domain and solid domain at the current time step, pressure field of fluid domain, pressure field of solid domain, solid deformation tensor (i.e. left Cauchy Green tensor), motion speed of target particles, etc. n+1 It can include: the target velocity field of the fluid domain and the solid domain after the fluid-solid coupling of the current time step, the target fluid domain pressure field, the target solid domain pressure field, the target solid deformation tensor (i.e., the left Cauchy Green tensor), the target motion speed of the target particle, etc., which can be used as the input parameters of the fluid-solid coupling in the next time step.

[0103] The present invention optimizes the fluid-solid coupling model through time discretization, and achieves the appropriate amplification of the time step while keeping the order of error unchanged, thereby significantly reducing the total number of cycles and saving overall calculation time. Numerical experiments have shown that after adopting the above-mentioned time discretization optimization strategy, the computational efficiency can be improved by 50% to 80% while maintaining the stable coupling of the solid-fluid interface and the accuracy of the solution. In addition, since the local body-fitting grid introduces curved boundaries and non-orthogonal grid structures, the use of a lower-order time discretization format can easily lead to stability deterioration. After adopting the above-mentioned time discretization optimization strategy, it can provide a more stable and smooth interface force propagation path and improve the consistency of physical quantities at the fluid-solid interface. Through the above-mentioned method, the time discretization of the fluid-solid coupling equations is optimized from the first order to the second order, thereby allowing a larger time step while maintaining the same level of numerical error, thereby reducing the total number of time steps and significantly improving computational efficiency. The above method is suitable for three-dimensional simulation of multi-scale fluid-solid coupling problems.

[0104] In some embodiments, the fluid density and dynamic viscosity can be used to calculate the Reynolds number.

[0105] S103: Determine whether a local grid needs to be regenerated based on the target solid domain parameters.

[0106] Specifically, by determining whether the local grid needs to be regenerated, the fluid-structure coupling input parameters for the next time step can be accurately determined, thereby ensuring the calculation accuracy of the multi-scale fluid-structure coupling for the next time step.

[0107] In some embodiments, the above-mentioned step S103 of determining whether to regenerate the local mesh according to the target solid domain parameters may include:

[0108] Determine the target position of the target particle according to the target movement speed of the target particle;

[0109] Determine the difference between the target position of the target particle and the initial position of the target particle as the displacement amplitude of the target particle, and determine the difference between the target left Cauchy Green tensor of the target particle and the left Cauchy Green tensor of the target particle as the deformation degree of the target particle;

[0110] Determining whether the displacement amplitude and the deformation degree exceed corresponding preset thresholds;

[0111] If so, it is determined that the local mesh needs to be regenerated; if not, it is determined that the local mesh does not need to be regenerated.

[0112] Specifically, after obtaining the target movement speed of the target particle, the moving position (target position) of the target particle can be determined according to the following formula:

[0113] (7)

[0114] Among them, x n+1 is the target position of the target particle; x n Can be the initial position of the target particle; w t n+1 is the target movement speed of the target particle; is the time step.

[0115] Afterwards, the difference between the target position of the target particle and its initial position can be determined as the target particle's displacement amplitude at the current time step. The difference between the target left Cauchy Green tensor of the target particle and its initial left Cauchy Green tensor can also be determined as the target particle's deformation degree at the current time step. If both the displacement amplitude and deformation degree at the current time step are greater than or equal to the corresponding preset thresholds, it can be determined that the local mesh where the target particle is located has been degraded or that the displacement of the target particle is too large, requiring the local mesh to be regenerated. If the displacement amplitude and deformation degree at the current time step are both greater than or equal to the corresponding preset thresholds, the calculation proceeds to the next time step.

[0116] By checking the degree of deformation and displacement, we can avoid numerical divergence or non-convergence caused by excessive mesh distortion, thereby ensuring the stability of the simulation process. If the preset threshold is not exceeded, there is no need to reconstruct the mesh and the next time step can be directly entered, reducing unnecessary computational overhead and improving overall efficiency. If the preset threshold is exceeded, that is, when the solid particles move significantly or the mesh quality degrades severely, reconstructing the local body-fitting mesh can accurately capture the new geometry and ensure the geometric fidelity of the simulation.

[0117] S104: If yes, generate a new local grid according to the target solid domain parameters of the current time step and obtain the solid domain parameters and fluid domain parameters of the new local grid as the fluid-solid coupling input parameters of the next time step; if no, use the target fluid domain parameters and target solid domain parameters after fluid-solid coupling in the current time step as the fluid-solid coupling input parameters of the next time step.

[0118] Specifically, if the displacement amplitude and deformation degree at the current time step are both greater than or equal to the corresponding preset thresholds, a new local mesh can be generated based on the target solid domain parameters of the current time step, and the solid domain parameters and fluid domain parameters of the new local mesh can be obtained. Among them, some of the solid domain parameters and fluid domain parameters of the new local mesh come from the target solid domain parameters and target fluid domain parameters output in the previous time step, and the remaining part comes from the solid domain parameters and fluid domain parameters defined by the background mesh. If the displacement amplitude and deformation degree at the current time step are both less than the corresponding preset thresholds, the target solid domain parameters and target fluid domain parameters output in the previous step can be directly used as the fluid-structure coupling input parameters for the next time step.

[0119] In some embodiments, generating a new local grid and obtaining solid domain parameters and fluid domain parameters of the new local grid in S104 may include:

[0120] Generate a new local grid according to the new position of the target particle, and determine the overlapping area and non-overlapping area between the new local grid and the old local grid;

[0121] The target solid domain parameters and target fluid domain parameters are interpolated into the overlapping area, the background flow field in the background grid is interpolated into the non-overlapping area, and the interpolated parameters are used as the solid domain parameters and fluid domain parameters of the new local grid.

[0122] Specifically, the target solid and fluid domain parameters calculated in the previous step can be interpolated into the overlapping region. For non-overlapping regions, the background flow field is interpolated to initialize the velocity field, and other variables are set to zero to reduce computational effort and maintain solution continuity. After interpolation, the new local mesh replaces the old one (which can be the one before the reconstruction), and the process restarts for the next round of calculations. This means that the solid and fluid domain parameters of the new local mesh can be input into the fluid-structure interaction model for further analysis and other operations.

[0123] By interpolating the calculation results of the previous step to the overlapping area of ​​the new local grid and initializing the variables in the non-overlapping area, the continuity of the physical quantity before and after the local grid update is guaranteed, avoiding numerical oscillation.

[0124] S105: Repeat the input and judgment process until the cumulative value of each time step reaches the simulation time. According to the target solid domain parameters after fluid-solid coupling at each time step, the dynamic characteristics of the target particles in the simulated flow field area are determined. The dynamic characteristics include at least motion trajectory and stress distribution.

[0125] Specifically, the cumulative value of each time step reaches the simulation duration, that is, , where n is the number of time steps; is the time step; T is the simulation duration (the total duration of the simulation calculation). When the target solid domain parameters output by the fluid-solid coupling model at each time step are superimposed, the motion trajectory and stress distribution of the target particles in the simulated flow field area are simulated. When , the calculation of the next time step will be continued, forming an iterative calculation process. For example: T = 1 second, = 0.01 seconds, n starts to increase from 0, step 0: when n = 0, the current time Seconds are less than T, step 100: when n=100, the current time seconds, reaches T, and stops the simulation.

[0126] In some embodiments, the above-mentioned S105, based on the target solid domain parameters after fluid-solid coupling at each time step, determines the dynamic characteristics of the target particles in the simulated flow field area. In specific implementation, it may include:

[0127] Superimpose the target motion speed of the target particle at each time step to determine the motion trajectory of the target particle in the simulated flow field area of ​​the target microfluidic chip;

[0128] According to the target left Cauchy Green tensor at each time step, the stress distribution of the target particle in the simulated flow field area of ​​the target microfluidic chip is determined.

[0129] Specifically, the target motion speed of the target particle at each time step can be superimposed to determine the motion trajectory of the target particle in the flow field of the target microfluidic chip (a microfluidic chip with cylindrical obstacles). Figure 3 As shown, Figure 3 There is an inflow from left to right in the image. The initial position of the target particle is on the far left. Every certain time step, the current position of the particle is saved and output. Finally, they are superimposed together to obtain the following: Figure 3 The particle trajectory shown in the flow field, where the circular structure obstacle in the flow field area and the light and dark changes in the flow field area represent the speed of the pure flow field in the chip. Figure 3 u-normed is the normalized velocity in the range of 0-1.93.

[0130] The stress distribution within the target particle can also be determined based on the target left Cauchy Green tensor (i.e., the target solid deformation tensor) at each time step. The target left Cauchy Green tensor output at each time step represents the current deformation of the target particle. Determining the stress distribution within the target particle facilitates a more detailed force analysis of the target particle in the flow field. The target solid domain pressure field and the target fluid domain pressure field can also be superimposed to assist in analyzing the force distribution of the target particle.

[0131] In some embodiments, the above-mentioned dynamic characteristics may also include velocity field distribution, stress distribution evolution, etc. The dynamic characteristic data may be selected according to actual needs, and this specification does not impose any specific limitations on this.

[0132] In some embodiments, after determining the motion trajectory of the target particles in the simulated flow field area of ​​the target microfluidic chip, the target microfluidic chip structure design can be optimized based on the motion trajectory of the target particles. For example, check whether the particles are trapped or their speed is significantly reduced in certain areas (such as near cylindrical obstacles). These areas may cause blockage or reduced efficiency. Analyze whether the particle trajectory deviates from the expected path, such as whether asymmetric movement occurs when bypassing obstacles, which may affect separation or detection accuracy. Subsequently, the cylindrical obstacles can be changed to streamlined shapes (such as elliptical or aerodynamic shapes) to reduce eddy currents and drag. The positions of the obstacles can also be rearranged to avoid excessive bending or intersection of the particle paths. The channel width or height can also be modified, the flow velocity distribution can be adjusted, and so on, ultimately achieving the goal of optimizing the chip structure.

[0133] In some embodiments, to further enhance the stability and robustness of three-dimensional multiscale solid-fluid coupling calculations, the present invention introduces a self-correcting method based on a breakpoint-resume mechanism. Key breakpoints can be set during the fluid-solid coupling calculation process, and at each breakpoint, information is automatically saved, including the current grid, time step, and variables defined on that grid, such as the velocity field, pressure field, and deformation field. If an abnormal interruption occurs during program execution (such as a memory overflow, convergence failure, or system failure), the system automatically restarts the calculation based on the most recent breakpoint status, avoiding full recalculation. This significantly reduces resource waste and saves simulation program monitoring costs. Furthermore, an anomaly detection module can be incorporated to automatically locate the source of the error and make adjustments after an error occurs, providing a certain degree of adaptive repair capability, thereby enhancing the stability and reliability of the entire solution process. Experiments have shown that in multiple complex three-dimensional coupled simulations, this breakpoint-resume and self-correcting mechanism can reduce resource waste caused by failures by over 80% and significantly improve the overall stability of the simulation task.

[0134] Based on the above embodiments, the present invention can achieve the following beneficial technical effects:

[0135] The computational efficiency of multi-scale solid-fluid coupling simulations has been significantly improved. Specifically, a "background-local" two-layer nested grid structure is adopted to divide the global computational domain into a stable background area and a dynamic local high-precision solution area (i.e., the generated background grid and local grid mentioned above). A small window local update strategy is introduced (i.e., the movement position of the target particle changes at each time step, and the corresponding local grid will move or reconstruct accordingly, thereby affecting the input parameters of the next time step). High-frequency updates are only performed in areas with drastic physical changes. At the same time, the time discretization of the fluid-solid coupling model is optimized, which can significantly relax the time step while ensuring numerical accuracy, further reducing the computational cost. This combination of multi-level structure, local space-time refinement, and high-order time discretization effectively avoids the waste of resources caused by global recalculation, making it possible to complete three-dimensional high-precision coupling simulations even on low-core computing platforms, breaking the bottleneck of traditional reliance on high-performance clusters and demonstrating significant engineering practical value.

[0136] The problem of numerical discontinuity of pressure at the fluid-solid interface is innovatively solved. By decomposing the function space of pressure on the basis of local grid, the inside and outside of the fluid-solid interface are assigned independent pressure spaces and calculated and solved separately, thus avoiding numerical oscillation and error accumulation caused by pressure jumps, ensuring the numerical stability of the fluid-solid interface area, and providing a new paradigm for multi-physical field strong coupling calculations.

[0137] The method of the present invention is highly versatile and engineering-adaptable. Its core mechanism supports unified modeling of fluid-structure coupling problems at different physical scales (such as microscale biofluid domains and macroscale structural domains) and different types of deformations (such as elastic deformation and large-displacement rigid body motion). In addition, for complex boundary conditions (such as inflow disturbances, wall slip, structural contact, etc.), the present invention designs a modular boundary processing strategy to ensure the accurate transmission and dynamic adaptation of boundary information (such as using the background grid to provide the flow field boundary for the local grid). Relying on the above-mentioned universal coupling framework, this method can be widely applied to key scenarios such as biofluid mechanics, aerospace structural response analysis, and precision manufacturing process modeling, and has significant technological advancement and cross-industry promotion potential.

[0138] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments. For details, please refer to the description of the aforementioned related processing embodiments, and no further description is given here.

[0139] The above describes the present invention. However, it is worth noting that this specific embodiment is only intended to better illustrate the present application and to describe specific embodiments of the specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims can be performed in an order different from that described in the embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order shown or the sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0140] The above-mentioned particle dynamic characteristics simulation method based on multi-scale fluid-solid coupling is described below with reference to specific embodiments.

[0141] refer to Figure 4 As shown, M bg is the background grid, M local 、M * local is the local grid established based on the current position of the solid particles. Among them, the background grid M bg It can be a local grid M local 、M * local Provides the flow field boundary. local Specifically, it can be the old local grid that has not been reconstructed, M * local Specifically, it can be the reconstructed new local grid. * local It is necessary to determine the area where it overlaps with the old local grid and the area where it does not overlap with the old local grid, and * local The overlapping and non-overlapping areas are marked in the figure. In the overlapping area, the latest time step of the old local grid can be directly interpolated, such as t n The target solid domain parameters and target fluid domain parameters output by the time step can be used to initialize the velocity field by interpolating the background flow field in the background grid in the non-overlapping area. Other variables are set to zero to reduce the amount of calculation and maintain the continuity of the solution. Each local grid involves the fluid-solid coupling solution under multiple time steps and the process of moving the local grid after the solution. local With M * local The process involves creating a new grid (or reconstructing the grid) and interpolation.

[0142] Specifically, the process of solving the old local grid and moving the grid is as follows:

[0143] At time step t n-1 Inside:

[0144] Calculation solution: Set the time step t n-1The fluid-structure coupling input parameters under are input to the fluid-structure coupling model, and the output time step t n-1 Target fluid domain parameters and target solid domain parameters under ;

[0145] Moving mesh: Move solid particles according to the solid particle moving speed in the target solid domain parameters and update the moving position of the solid particles;

[0146] The next time step input parameters are determined: solid particles or M local If the displacement amplitude and deformation degree do not exceed the preset threshold, the time step t n-1 The target fluid domain parameters and target solid domain parameters under the time step t n The fluid-structure interaction input parameters under .

[0147] At time step t n Inside:

[0148] Calculation solution: Set the time step t n The fluid-structure coupling input parameters under are input to the fluid-structure coupling model, and the output time step t n Target fluid domain parameters and target solid domain parameters under ;

[0149] Moving mesh: Move solid particles according to the solid particle moving speed in the target solid domain parameters and update the moving position of the solid particles;

[0150] The next time step input parameters are determined: solid particles or M local The displacement amplitude and deformation degree exceed the preset threshold, and a new local grid M is created. * local , and the time step t n The target fluid domain parameters and target solid domain parameters under the new local grid M are interpolated to * local The overlapping area of ​​the background grid M bg The background flow field in is interpolated to the new local grid M * local In the non-overlapping area, the interpolated parameters are used as the new local grid time step t n The fluid-structure interaction input parameters under .

[0151] The process of solving the new local mesh and moving the mesh is as follows:

[0152] At time step t n Inside:

[0153] Calculation solution: Set the time step t n The fluid-structure coupling input parameters under are input to the fluid-structure coupling model, and the output time step t n Target fluid domain parameters and target solid domain parameters under ;

[0154] Moving mesh: Move solid particles according to the solid particle moving speed in the target solid domain parameters and update the moving position of the solid particles;

[0155] The next time step input parameters are determined: solid particles or M * local If the displacement amplitude and deformation degree do not exceed the preset threshold, the time step t n The target fluid domain parameters and target solid domain parameters under the time step t n+1 The fluid-structure interaction input parameters under .

[0156] At time step t n+1 Inside:

[0157] Calculation solution: Set the time step t n+1 The fluid-structure coupling input parameters under are input to the fluid-structure coupling model, and the output time step t n+1 Target fluid domain parameters and target solid domain parameters under ;

[0158] Moving mesh: Move solid particles according to the solid particle moving speed in the target solid domain parameters and update the moving position of the solid particles;

[0159] The next time step input parameters are determined: solid particles or M * local The displacement amplitude and deformation degree exceed the preset threshold, and the above process is repeated until the cumulative value of each time step reaches the simulation duration.

[0160] The specific steps of the multi-scale fluid-structure interaction method are as follows:

[0161] (1) Global background flow field construction: Generate a large background grid in the entire simulated flow channel area and establish the corresponding finite element space. By setting the velocity at the inlet and outlet, as well as the no-slip boundary conditions on the remaining boundaries, use the P2-P1 finite element to solve a simple Navier-Stokes equation system without solid interaction terms. Given an appropriate time step, after sufficient time, a stable background pure flow velocity field is finally obtained, providing basic boundary information for subsequent local calculations.

[0162] (2) Local body-fitting grid generation and variable initialization: A body-fitting local grid is generated near the current position of the solid particle being studied, and variables used to describe the velocity, pressure, and solid structural state are defined on this local grid. In the initial state, these variables are assigned values ​​according to the physical properties.

[0163] (3) Background flow field interpolation to local boundary: The background velocity field is interpolated to the boundary of the local grid as the boundary condition of the fluid region of the local grid.

[0164] (4) Solving the local coupling equations: After inputting the velocity, pressure and deformation field of the solid at the current moment, the Newton iteration method is used to solve the local fluid-solid coupling equations under the velocity boundary conditions given in (3) to obtain the structural responses such as the velocity, pressure and deformation field of the solid particles and the surrounding flow field at the current time step.

[0165] (5) Structural displacement and grid update: Use the calculated grid velocity field to move the grid points (i.e., move the target particles according to the movement speed of the solid particles) and update the positions of the solid particles.

[0166] (6) Mesh quality check and iterative judgment: Check the displacement amplitude of the solid particles and the degree of mesh deformation at the current time step. If they do not exceed the preset threshold, proceed to the next time step and repeat the above coupling calculation process. If it is judged that the mesh quality is seriously degraded or the solid particle displacement is too large, perform the following mesh reconstruction operation.

[0167] (7) Local body-fitting mesh reconstruction and variable mapping: If the solid particles move significantly or the mesh quality degrades, the system will regenerate a body-fitting mesh at the new position of the solid particles and interpolate the previous calculation results to the overlapping area of ​​the new mesh. For non-overlapping areas, the background flow field is interpolated to initialize the velocity field, and other variables are set to zero to reduce the computational effort and maintain solution continuity.

[0168] (8) Grid update and iteration continue: After the interpolation is completed, the new grid replaces the old grid and the process re-enters the next round of calculation.

[0169] Although this specification provides examples such as the following examples or the accompanying Figure 5 The method operation steps or device structure shown, but based on routine or no creative labor, the method or device may include more or fewer operation steps or module units after partial merger. In the steps or structures that do not logically have a necessary causal relationship, the execution order of these steps or the module structure of the device is not limited to the execution order or module structure shown in the embodiments or drawings of this specification. When the method or module structure described is applied to an actual device, server or terminal product, it can be executed sequentially or in parallel according to the method or module structure shown in the embodiments or drawings (for example, a parallel processor or multi-threaded processing environment, or even a distributed processing or server cluster implementation environment). Based on the above-mentioned particle dynamic characteristics simulation method based on multi-scale fluid-solid coupling, the embodiment of this specification also proposes an embodiment of a particle dynamic characteristics simulation device based on multi-scale fluid-solid coupling. As Figure 5 As shown, the device may specifically include the following modules:

[0170] The background and local grid generation module 501 can be used to generate a background grid based on the simulated flow field area where the target particle is located, and generate a local grid based on the location of the target particle. The background grid is used to provide a flow field boundary for the local grid. The scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold.

[0171] The fluid-solid coupling simulation module 502 can be used to input the solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field domain boundary into the fluid-solid coupling model, and output the target fluid domain parameters and target solid domain parameters after the fluid-solid coupling at the current time step;

[0172] A judgment module 503 may be used to judge whether a local grid needs to be regenerated according to the target solid domain parameters;

[0173] The input parameter determination module 504 may be configured to, if yes, generate a new local grid based on the target solid domain parameters and obtain the solid domain parameters and fluid domain parameters of the new local grid as fluid-structure coupling input parameters for the next time step; if no, use the target fluid domain parameters and target solid domain parameters as fluid-structure coupling input parameters for the next time step;

[0174] The dynamic characteristics determination module 505 can be used to repeat the input and judgment process until the cumulative value of each time step reaches the simulation time. The dynamic characteristics of the target particles in the simulated flow field area are determined based on the target solid domain parameters after fluid-solid coupling at each time step. The dynamic characteristics include at least motion trajectory and stress distribution.

[0175] In some embodiments, the above-mentioned background and local grid generation module 501 can be specifically used to generate an initial local grid according to the position of the target particle; identify sensitive areas and insensitive areas in the initial local grid, where the curvature of the sensitive area at the fluid-solid interface is greater than or equal to a preset curvature threshold, or the minimum distance between the fluid-solid interface and the boundary of the calculation domain is a preset distance threshold; subdivide the grid cells in the sensitive area, merge adjacent grid cells in the insensitive area, and then perform quality optimization processing on the grid cells in the sensitive area and the insensitive area to obtain a local grid.

[0176] In some embodiments, the fluid-structure coupling model in the fluid-structure coupling simulation module 502 is composed of the following equations:

[0177]

[0178] Where u is the velocity field of the fluid domain and the solid domain; w t is the moving speed of the target particle; P s is the pressure field of the solid domain; P fis the pressure field of the fluid domain; Re is the Reynolds number; D is the symmetric gradient tensor of the velocity field; E is the Young's modulus of the target particle; B is the left Cauchy Green tensor, which is used to describe the deformation of the target particle; I is the identity matrix; T is the simulation time; The entire computational domain consists of the solid domain and the fluid domain; is a solid domain; is the fluid domain; Used to describe the spatial variation of physical quantities; Used to describe the diffusion process of physical quantities.

[0179] In some embodiments, the above-mentioned fluid-solid coupling simulation module 502 can be specifically used to determine the solid domain intermediate parameters and fluid domain intermediate parameters between the current time step and the next time step based on the solid domain parameters and fluid domain parameters of the current time step, and the scaled time step is determined by adjusting the time step by adjusting the parameters; linearly combine the solid domain intermediate parameters and fluid domain intermediate parameters with the solid domain parameters and fluid domain parameters of the current time step to obtain corrected solid domain parameters and corrected fluid domain parameters; based on the corrected solid domain parameters and corrected fluid domain parameters, the time step is scaled to determine and output the target solid domain parameters and target fluid domain parameters after fluid-solid coupling in the current time step.

[0180] In some embodiments, the solid domain parameters in the above-mentioned fluid-solid coupling simulation module 502 may include at least one of the following: the velocity field of the solid domain, the movement velocity of the target particles, the pressure field of the solid domain, the Young's modulus of the target particles, and the left Cauchy Green tensor; the fluid domain parameters may include at least one of the following: the velocity field of the fluid domain, the pressure field of the fluid domain, the fluid density, and the dynamic viscosity.

[0181] In some embodiments, the above-mentioned judgment module 503 can be specifically used to determine the target position of the target particle based on the target movement speed of the target particle; determine the difference between the target position of the target particle and the initial position of the target particle as the displacement amplitude of the target particle, and determine the difference between the target left Cauchy Green tensor of the target particle and the left Cauchy Green tensor of the target particle as the deformation degree of the target particle; determine whether the displacement amplitude and the deformation degree exceed the corresponding preset threshold value; if so, determine that the local grid needs to be regenerated; if not, determine that the local grid does not need to be regenerated.

[0182] In some embodiments, the above-mentioned input parameter determination module 504 can be specifically used to generate a new local grid according to the new position of the target particle, determine the overlapping area and non-overlapping area between the new local grid and the old local grid; interpolate the target solid domain parameters and the target fluid domain parameters to the overlapping area, interpolate the background flow field in the background grid to the non-overlapping area, and use the interpolated parameters as the solid domain parameters and fluid domain parameters of the new local grid.

[0183] In some embodiments, the above-mentioned dynamic characteristic determination module 505 can be specifically used to superimpose the target motion speed of the target particle at each time step to determine the motion trajectory of the target particle in the simulated flow field area of ​​the target microfluidic chip; determine the cumulative deformation of the target particle based on the target left Cauchy Green tensor at each time step, and determine the stress distribution of the target particle in the simulated flow field area of ​​the target microfluidic chip based on the cumulative deformation.

[0184] As can be seen from the above, a particle dynamic characteristics simulation device based on multi-scale fluid-solid coupling provided in the embodiments of this specification can solve the problems of low computational efficiency of multi-scale fluid-solid coupling, poor fluid-solid interface accuracy, and difficulty in matching interface pressure.

[0185] The embodiment of this specification also provides an electronic device based on the above-mentioned particle dynamic characteristics simulation method based on multi-scale fluid-solid coupling, including a processor and a memory for storing processor executable programs / instructions. When the processor is specifically implemented, it can perform the following steps according to the program / instructions: generating a background grid according to the simulated flow field area where the target particle is located, generating a local grid according to the position of the target particle, the background grid is used to provide a flow field domain boundary for the local grid, and the scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold; inputting the solid domain parameters in the local grid at the current time step and the fluid domain parameters within the flow field domain boundary into the fluid-solid coupling model, and outputting the fluid-solid domain parameters at the current time step. The target solid domain parameters and target fluid domain parameters after coupling are obtained; judging whether the local grid needs to be regenerated according to the target solid domain parameters; if so, generating a new local grid according to the target solid domain parameters and obtaining the solid domain parameters and fluid domain parameters of the new local grid as the fluid-solid coupling input parameters of the next time step; if not, using the target fluid domain parameters and target solid domain parameters as the fluid-solid coupling input parameters of the next time step; repeating the input and judgment process until the cumulative value of each time step reaches the simulation time, and determining the dynamic characteristics of the target particles in the simulated flow field area according to the target solid domain parameters after fluid-solid coupling at each time step, wherein the dynamic characteristics include at least motion trajectory and stress distribution.

[0186] In order to complete the above instructions more accurately, refer to Figure 6 As shown, the embodiment of this specification also provides another specific electronic device, wherein the electronic device includes a network communication port 601, a processor 602 and a memory 603, and the above structures are connected through internal cables so that each structure can perform specific data interaction.

[0187] wherein the processor 602 can be specifically used to generate a background grid according to the simulated flow field area where the target particle is located, and to generate a local grid according to the position of the target particle, wherein the background grid is used to provide a flow field domain boundary for the local grid, and the scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold; inputting the solid domain parameters in the local grid at the current time step and the fluid domain parameters within the flow field domain boundary into the fluid-solid coupling model, and outputting the target solid domain parameters and target fluid domain parameters after fluid-solid coupling at the current time step; judging whether it is necessary to regenerate the local grid according to the target solid domain parameters; if so, generating a new local grid according to the target solid domain parameters and obtaining the solid domain parameters and fluid domain parameters of the new local grid as the fluid-solid coupling input parameters for the next time step; if not, using the target fluid domain parameters and target solid domain parameters as the fluid-solid coupling input parameters for the next time step; repeating the input and judgment process until the cumulative value of each time step reaches the simulation time length, and determining the dynamic characteristics of the target particle in the simulated flow field area according to the target solid domain parameters after fluid-solid coupling at each time step, wherein the dynamic characteristics include motion trajectory, including at least motion trajectory and stress distribution;

[0188] The memory 603 may be specifically used to store corresponding instruction programs.

[0189] In this embodiment, the network communication port 601 can be a virtual port that is bound to different communication protocols, thereby being capable of sending or receiving different data. For example, the network communication port can be a port responsible for web data communication, a port responsible for FTP data communication, or a port responsible for email data communication. Furthermore, the network communication port can also be a physical communication interface or communication chip. For example, it can be a wireless mobile network communication chip, such as GSM or CDMA; it can also be a Wi-Fi chip; or it can be a Bluetooth chip.

[0190] In this embodiment, the processor 602 can be implemented in any suitable manner. For example, the processor can take the form of a microprocessor or a processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, an application-specific integrated circuit (ASIC), a programmable logic controller, an embedded microcontroller, etc. This specification is not intended to limit this.

[0191] In this embodiment, the memory 603 may include multiple levels. In a digital system, anything that can store binary data can be a memory. In an integrated circuit, a circuit with a storage function that has no physical form is also called a memory, such as RAM, FIFO, etc. In a system, a storage device with a physical form is also called a memory, such as a memory stick, TF card, etc.

[0192] The embodiment of this specification also provides a computer storage medium based on the above-mentioned particle dynamic characteristics simulation method based on multi-scale fluid-solid coupling, and the computer storage medium stores a computer program / instruction, which, when executed, realizes: generating a background grid according to the simulated flow field area where the target particle is located, generating a local grid according to the position of the target particle, the background grid is used to provide a flow field domain boundary for the local grid, and the scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold; inputting the solid domain parameters in the local grid at the current time step and the fluid domain parameters within the flow field domain boundary into the fluid-solid coupling model, and outputting the target solid domain parameters after fluid-solid coupling at the current time step. domain parameters and target fluid domain parameters; judging whether it is necessary to regenerate the local grid according to the target solid domain parameters; if so, generating a new local grid according to the target solid domain parameters and obtaining the solid domain parameters and fluid domain parameters of the new local grid as the fluid-solid coupling input parameters of the next time step; if not, using the target fluid domain parameters and the target solid domain parameters as the fluid-solid coupling input parameters of the next time step; repeating the input and judgment process until the cumulative value of each time step reaches the simulation time, and determining the dynamic characteristics of the target particles in the simulated flow field area according to the target solid domain parameters after fluid-solid coupling at each time step, wherein the dynamic characteristics include motion trajectory, including at least motion trajectory and stress distribution.

[0193] In this embodiment, the storage medium includes, but is not limited to, random access memory (RAM), read-only memory (ROM), cache, hard disk drive (HDD), or memory card. The memory can be used to store computer program instructions. The network communication unit can be an interface configured in accordance with a standard specified by a communication protocol and used for network connection and communication.

[0194] In this embodiment, the functions and effects specifically implemented by the program instructions stored in the computer storage medium can be explained in comparison with other implementations and will not be repeated here.

[0195] Although this specification provides method operation steps as described in the embodiments or flowcharts, more or fewer operation steps may be included based on conventional or non-creative means. The order of steps listed in the embodiments is only one way of executing the steps among many, and does not represent the only execution order. When the device or client product is actually executed, it can be executed in sequence or in parallel according to the method shown in the embodiments or the drawings (for example, in a parallel processor or multi-threaded processing environment, or even a distributed data processing environment). The terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, product or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, product or device. Without further restrictions, it is not excluded that there are other identical or equivalent elements in the process, method, product or device including the elements. Words such as first, second, etc. are used to indicate names and do not indicate any particular order.

[0196] Those skilled in the art will also appreciate that, in addition to implementing the controller in pure computer-readable program code, it is entirely possible to implement the same functionality by logically programming the method steps in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, embedded microcontrollers, and the like. Therefore, such a controller can be considered a hardware component, and the devices included therein for implementing various functions can also be considered structures within the hardware component. Alternatively, the devices for implementing various functions can be considered both software modules implementing the method and structures within the hardware component.

[0197] This specification may be described in the general context of computer-executable instructions, such as program modules, executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, classes, and the like that perform specific tasks or implement specific abstract data types. This specification may also be practiced in distributed computing environments where tasks are performed by remote processing devices connected through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media, including storage devices.

[0198] As can be seen from the above description of the embodiments, those skilled in the art will clearly understand that this specification can be implemented using software plus a necessary general-purpose hardware platform. Based on this understanding, the technical solution of this specification can essentially be embodied in the form of a software product. This computer software product can be stored in a storage medium such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for enabling a computer device (such as a personal computer, mobile terminal, server, or network device) to execute the methods described in various embodiments or portions of the embodiments of this specification.

[0199] The various embodiments in this specification are described in a progressive manner. References to the common or similar parts of the various embodiments are sufficient. Each embodiment focuses on the differences from the other embodiments. This specification can be used in a variety of general-purpose or specialized computer system environments or configurations. For example, personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable electronic devices, network PCs, minicomputers, mainframe computers, and distributed computing environments that include any of the above systems or devices.

[0200] Although the present specification has been described with reference to the embodiments, persons skilled in the art will appreciate that there are many variations to the present specification without departing from the spirit of the present specification, and it is intended that the appended claims encompass such variations without departing from the spirit of the present specification.

Claims

1. A particle dynamic characteristics simulation method based on multi-scale fluid-solid coupling, characterized in that: include: Generate a background grid based on the simulated flow field area where the target particle is located, and generate a local grid based on the location of the target particle, wherein the background grid is used to provide a flow field domain boundary for the local grid, and the scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold; Input the solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field boundary into the fluid-solid coupling model, and output the target solid domain parameters and target fluid domain parameters after fluid-solid coupling at the current time step; Determining whether a local grid needs to be regenerated according to the target solid domain parameters; If yes, generate a new local grid according to the target solid domain parameters and obtain the solid domain parameters and fluid domain parameters of the new local grid as fluid-solid coupling input parameters for the next time step; if no, use the target fluid domain parameters and target solid domain parameters as fluid-solid coupling input parameters for the next time step; The input and judgment process is repeated until the cumulative value of each time step reaches the simulation duration. The dynamic characteristics of the target particles in the simulated flow field area are determined based on the target solid domain parameters after fluid-solid coupling at each time step. The dynamic characteristics include at least motion trajectory and stress distribution.

2. The method according to claim 1, characterized in that Generating a local grid according to the position of the target particle includes: Generate an initial local grid based on the position of the target particles; Identify sensitive areas and insensitive areas in the initial local grid, where the curvature of the sensitive area at the fluid-solid interface is greater than or equal to a preset curvature threshold, or the minimum distance from the fluid-solid interface to the boundary of the computational domain is a preset distance threshold; The grid cells are subdivided in the sensitive area, and the adjacent grid cells are merged in the non-sensitive area. Then, the quality of the grid cells in the sensitive area and the non-sensitive area is optimized to obtain the local grid.

3. The method according to claim 1, characterized in that The fluid-structure interaction model consists of the following equations: Where u is the velocity field of the fluid domain and the solid domain; w t is the moving speed of the target particle; P s is the pressure field of the solid domain; P f is the pressure field of the fluid domain; Re is the Reynolds number; D is the symmetric gradient tensor of the velocity field; E is the Young's modulus of the target particle; B is the left Cauchy Green tensor, which is used to describe the deformation of the target particle; I is the identity matrix; T is the simulation time; The entire computational domain consists of the solid domain and the fluid domain; is a solid domain; is the fluid domain; Used to describe the spatial variation of physical quantities; Used to describe the diffusion process of physical quantities.

4. The method according to claim 1, wherein The fluid-structure interaction model processes the input solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field boundary in the following way: Based on the solid domain parameters and the fluid domain parameters of the current time step, the solid domain intermediate parameters and the fluid domain intermediate parameters between the current time step and the next time step are determined by adjusting the time step by adjusting the parameters; Linearly combine the solid domain intermediate parameters and the fluid domain intermediate parameters with the solid domain parameters and the fluid domain parameters of the current time step to obtain the corrected solid domain parameters and the corrected fluid domain parameters; Based on the modified solid domain parameters and the modified fluid domain parameters, the time step is scaled to determine and output the target solid domain parameters and target fluid domain parameters after fluid-solid coupling at the current time step.

5. The method according to claim 1, wherein The solid domain parameters include at least one of the following: the velocity field of the solid domain, the movement velocity of the target particle, the pressure field of the solid domain, the Young's modulus of the target particle, and the left Cauchy Green tensor; the fluid domain parameters include at least one of the following: the velocity field of the fluid domain, the pressure field of the fluid domain, the fluid density, and the dynamic viscosity.

6. The method according to claim 1, wherein The determining whether the local grid needs to be regenerated according to the target solid domain parameters includes: Determine the target position of the target particle according to the target movement speed of the target particle; Determine the difference between the target position of the target particle and the initial position of the target particle as the displacement amplitude of the target particle, and determine the difference between the target left Cauchy Green tensor of the target particle and the left Cauchy Green tensor of the target particle as the deformation degree of the target particle; Determining whether the displacement amplitude and the deformation degree exceed corresponding preset thresholds; If so, it is determined that the local mesh needs to be regenerated; if not, it is determined that the local mesh does not need to be regenerated.

7. The method according to claim 1, characterized in that The generating of a new local grid and obtaining solid domain parameters and fluid domain parameters of the new local grid include: Generate a new local grid according to the new position of the target particle, and determine the overlapping area and non-overlapping area between the new local grid and the old local grid; The target solid domain parameters and target fluid domain parameters are interpolated into the overlapping area, the background flow field in the background grid is interpolated into the non-overlapping area, and the interpolated parameters are used as the solid domain parameters and fluid domain parameters of the new local grid.

8. The method according to claim 1, characterized in that Determining the dynamic characteristics of the target particles in the simulated flow field region according to the target solid domain parameters after fluid-solid coupling at each time step includes: Superimpose the target motion speed of the target particle at each time step to determine the motion trajectory of the target particle in the simulated flow field area of ​​the target microfluidic chip; According to the target left Cauchy Green tensor at each time step, the stress distribution of the target particle in the simulated flow field area of ​​the target microfluidic chip is determined.

9. A particle dynamic characteristics simulation device based on multi-scale fluid-solid coupling, characterized in that: include: A background and local grid generation module is used to generate a background grid based on the simulated flow field area where the target particle is located, and to generate a local grid based on the position of the target particle. The background grid is used to provide a flow field domain boundary for the local grid. The scale difference between the simulated flow field area and the target particle is greater than a preset scale threshold. The fluid-solid coupling simulation module is used to input the solid domain parameters in the local grid of the current time step and the fluid domain parameters within the flow field boundary into the fluid-solid coupling model, and output the target fluid domain parameters and target solid domain parameters after fluid-solid coupling at the current time step; A judgment module, configured to judge whether a local grid needs to be regenerated according to the target solid domain parameters; an input parameter determination module for generating a new local grid according to the target solid domain parameters and obtaining the solid domain parameters and fluid domain parameters of the new local grid as fluid-solid coupling input parameters for the next time step; and if not, using the target fluid domain parameters and target solid domain parameters as fluid-solid coupling input parameters for the next time step; The dynamic characteristics determination module is used to repeat the input and judgment process until the cumulative value of each time step reaches the simulation time. The dynamic characteristics of the target particles in the simulated flow field area are determined based on the target solid domain parameters after fluid-solid coupling at each time step. The dynamic characteristics include at least motion trajectory and stress distribution.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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