Variable density low speed flow medium numerical calculation method and device

Abstract

The present application relates to the technical field of fluid mechanics, and discloses a numerical calculation method of variable-density low-speed flow medium, which comprises the following steps: determining a calculation region, dividing or reading grid information, fluid parameters and control parameters in the calculation region, opening an array according to the read information, initializing corresponding parameters of the calculation region, and entering a time step cycle after completion; setting a boundary condition, and assigning all boundary macro-quantities in a flow field; deriving a flow field numerical flux to solve a flow field Navier-Stokes equation according to a BGK equation under a finite volume framework; calculating pressure and velocity fluxes of a flow field unit interface, and updating boundary macro-quantity information through the flux information; judging whether there is an external force, and if yes, applying the external force through a splitting mode while updating the boundary macro-quantity; judging whether the time step meets a cycle condition; if yes, re-entering the setting of the boundary condition and assigning all boundary macro-quantities in the flow field; and if not, outputting flow field data and ending the simulation; and the method has the advantages of high algorithm precision and simple program.

Description

Technical Field

[0001] This invention relates to the field of fluid mechanics, and in particular to a method and apparatus for numerical calculation of mesoscopic flow at low speeds with varying density. Background Technology

[0002] Computational fluid dynamics (CFD) has been widely applied in various industrial fields, including automotive, shipbuilding, and aerospace. To solve problems in engineering, numerous commercial software programs have been developed both domestically and internationally for simulating fluid dynamic phenomena. Currently, most CFD methods are based on the macroscopic Navier-Stokes equations of traditional numerical schemes. These methods typically employ a computational strategy that decouples viscous and inviscid terms and struggle to account for tangential gradients within the finite volume method framework. However, the gas kinetic scheme (GKS) based on the mesoscopic Boltzmann equations can simultaneously couple viscous and inviscid terms while considering the influence of tangential gradients. The GKS method offers advantages such as clear object images, low dissipation, and applicability to high-speed flows, and has been widely applied to compressible flows. It has also been extended and applied to solving incompressible flows of constant density. However, in low-speed flow problems with significant spatial variations in density fields, such as the low-density regions caused by heat release during combustion, or in two-phase flows like cavitation and boiling where the density difference between the liquid and gas phases is large, the constant-density gas kinetic scheme is not suitable. This limits the application of this method in fields such as multi-component flow, multiphase flow, and turbulent combustion simulation.

[0003] Therefore, a method and apparatus for numerical calculation of mesoscopic flow with variable density at low speeds are provided to solve the above problems. Summary of the Invention

[0004] The main objective of this invention is to address the limitations of existing technologies in low-speed flow problems with significant density field variations, such as low-density regions caused by heat release during combustion, or in two-phase flows like cavitation and boiling where the density difference between the liquid and gas phases is substantial. These limitations restrict the application of this method in fields such as multi-component flow, multiphase flow, and turbulent combustion simulation.

[0005] The first aspect of this invention provides a method for numerically calculating the mesoscopic structure of variable-density low-speed flow, the method comprising:

[0006] Define the computational domain, and divide or read the mesh information, fluid parameters, and control parameters within the computational domain;

[0007] Based on the read information, an array is allocated, the corresponding parameters of the computation region are initialized, and then the time step loop is entered.

[0008] Set boundary conditions and assign values ​​to all macroscopic quantities at the boundaries of the flow field;

[0009] Solve the Navier-Stokes equations for the flow field to calculate the pressure and velocity flux at the interface of the flow field elements; update the macroscopic boundary quantity information using the flux information to determine whether there is an external force; if so, apply the external force through a splitting method and update the macroscopic boundary quantity simultaneously.

[0010] Determine if the time step meets the loop condition; if yes, re-enter the boundary condition setting process and assign values ​​to all macroscopic quantities at the boundaries of the flow field; if no, output the flow field data and end the simulation.

[0011] Furthermore, the process of dividing or reading the mesh information, fluid parameters, and control parameters within the computational region includes:

[0012] The computational domain is divided into different grids, and the grid information, fluid parameter information, and control parameter information of each grid in the computational domain are read.

[0013] Alternatively, it can read the mesh information, fluid parameter information, and control parameter information of the pre-defined mesh in the computational region.

[0014] Furthermore, the grid information includes grid length information, grid width information, number of grids information, unit grid length information, and grid coordinate information.

[0015] Furthermore, the fluid parameters include density information, velocity information, pressure information, and viscosity parameter information; the control parameter information includes time step information, CFL number information, and Mach number information.

[0016] Furthermore, the Navier-Stokes equations are as follows:

[0017]

[0018] in, For fluid density, For time, For fluid velocity, It is fluid dynamic pressure. For the deviatoric stress tensor, It is the external force term acting on the fluid;

[0019] The deviatoric stress tensor, which includes bulk viscosity, includes:

[0020]

[0021] In the formula, For fluid dynamics viscosity, The bulk viscosity coefficient, As a dimension, It is a unit vector.

[0022] Furthermore, the calculated pressure and velocity flux of the flow field includes:

[0023] The flux based on momentum is:

[0024]

[0025] The flux based on velocity is as follows:

[0026] .

[0027] Furthermore, the splitting method in applying external force through splitting includes:

[0028]

[0029] in, It is obtained by solving the Navier-Stokes equations.

[0030] A second aspect of the present invention provides a mesoscopic numerical calculation apparatus for variable density low-speed flow, comprising:

[0031] The data reading module is used to determine the computational domain and to divide or read the grid information, fluid parameters, and control parameters within the computational domain.

[0032] The time step loop enters the module, which is used to allocate an array based on the read information, initialize the corresponding parameters of the calculation area, and then enter the time step loop;

[0033] The boundary condition setting module is used to set boundary conditions and assign values ​​to all macroscopic quantities at the boundaries in the flow field;

[0034] The boundary macroscopic quantity update module is used to derive the numerical flux solution of the flow field Navier-Stokes equations based on the BGK equations within a finite volume framework; the Navier-Stokes equations are:

[0035]

[0036] in, For fluid density, For time, For fluid velocity, It is fluid dynamic pressure. For the deviatoric stress tensor, It is the external force term acting on the fluid;

[0037] The formula for the external force term is specifically expressed as follows:

[0038]

[0039] in, To simulate external forces, For fluid dynamic pressure, The overall parameter controls compressibility, and is taken as follows: . This represents the equilibrium distribution function. It can be represented as:

[0040] ;

[0041] Calculate the pressure and velocity flux at the interface of the flow field unit, update the boundary macroscopic quantity information using the flux information, determine whether there is an external force, and if so, apply the external force by splitting the flow field unit, while updating the boundary macroscopic quantity information.

[0042] The loop / end judgment module is used to determine whether the time step meets the loop condition; if yes, it re-enters the setting of boundary conditions and assigns values ​​to all macroscopic quantities of the boundary in the flow field; if no, it outputs the flow field data and ends the simulation.

[0043] A third aspect of the present invention provides an electronic device, the electronic device comprising a memory and at least one processor, wherein the memory stores instructions;

[0044] The at least one processor invokes the instructions in the memory to cause the electronic device to perform the various steps of the variable density low-speed flow mesoscopic numerical calculation method as described above.

[0045] A fourth aspect of the present invention provides a computer-readable storage medium storing instructions that, when executed by a processor, implement the various steps of the variable-density low-speed flow mesoscopic numerical calculation method as described above.

[0046] This invention starts from the continuous Boltzmann-BGK equations and constructs a low Mach approximation numerical flux within a finite volume framework. The flux constructed through Chapman-Enskog expansion analysis can be recovered to the macroscopic governing equations (Navier-Stokes equations). Based on the assumption of near-incompressible flow at constant density, the momentum-based flux can be simplified to a velocity-based flux form. After obtaining the flux form, a numerical algorithm based on gas kinetics can be constructed. This algorithm directly evolves and updates macroscopic quantities in the flow field, has a simple computational procedure, high computational accuracy, and can efficiently simulate low-speed flow physical processes numerically.

[0047] The innovation of the low Mach numerical algorithm of this invention lies in the construction of a low Mach numerical flux that can be recovered to the macroscopic governing equations using Chapman-Enskog analysis, the development of an algorithm based on the gas kinetics scheme, and the verification of the accuracy of the algorithm in solving unsteady flow processes. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the flux at the element interface under a finite volume scheme.

[0049] Figure 2 This is a flowchart of the mesoscopic numerical algorithm for variable density low-speed flow of the present invention;

[0050] Figure 3 This is a schematic diagram of the gas kinetics format interface;

[0051] Figure 4 A comparison diagram of the pressure and velocity fields of the Taylor Green vortex with the analytical solution;

[0052] Figure 5 The Taylor Green vortex pressure and velocity field contour plots are shown.

[0053] Figure 6 A schematic diagram of the Taylor Green vortex velocity field with high accuracy;

[0054] Figure 7 A schematic diagram of the structure of the variable density low-speed flow mesoscopic numerical calculation device provided in an embodiment of the present invention;

[0055] Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0056] This invention provides a method for mesoscopic numerical calculation of low-speed flow with variable density. The method includes: determining the computational domain; dividing or reading the grid information, fluid parameters, and control parameters within the computational domain; creating an array based on the read information; initializing the corresponding parameters of the computational domain; entering a time step loop after completion; setting boundary conditions and assigning values ​​to all boundary macroscopic quantities in the flow field; solving the Navier-Stokes equations for the flow field and calculating the pressure and velocity flux at the flow field unit interfaces; updating the boundary macroscopic quantity information using flux information; determining whether external forces exist; if so, applying external forces through a splitting method while simultaneously updating the boundary macroscopic quantities; determining whether the time step meets the loop conditions; if so, re-entering the process to set boundary conditions and assign values ​​to all boundary macroscopic quantities in the flow field; if not, outputting the flow field data and ending the simulation. This invention solves the problems in the prior art where, in low-speed flow problems with large spatial variations in density fields, such as low-density regions caused by heat release during combustion, or in two-phase flows such as cavitation and boiling where the density difference between the liquid and gas phases is large, the gas kinetic scheme based on constant density is not applicable; and it limits the application of this method in multi-component flow, multiphase flow, and turbulent combustion simulation.

[0057] The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0058] For ease of understanding, the specific process of the embodiments of the present invention is described below. Please refer to [link / reference]. Figure 1-6 The first embodiment of the mesoscopic numerical calculation method for variable density low-speed flow in this invention includes:

[0059] Define the computational domain, and divide or read the mesh information, fluid parameters, and control parameters within the computational domain;

[0060] Based on the read information, an array is allocated, the corresponding parameters of the computation region are initialized, and then the time step loop is entered.

[0061] Set boundary conditions and assign values ​​to all macroscopic quantities at the boundaries of the flow field;

[0062] Solve the Navier-Stokes equations for the flow field to calculate the pressure and velocity flux at the interface of the flow field elements; update the macroscopic boundary quantity information using the flux information to determine whether there is an external force; if so, apply the external force through a splitting method and update the macroscopic boundary quantity simultaneously.

[0063] Determine if the time step meets the loop condition; if yes, re-enter the boundary condition setting process and assign values ​​to all macroscopic quantities at the boundaries of the flow field; if no, output the flow field data and end the simulation.

[0064] Given that the method proposed in the current embodiment supports variable density low-speed flow in the GKS scheme within a finite volume framework, the GKS method is first introduced here, followed by an explanation of its modification and its connection with the macroscopic variable density incompressible Navier-Stokes equations, demonstrating that the mesoscopic scheme proposed in this embodiment can be used for low-speed variable density flow problems.

[0065] Current GKS methods are based on the original Boltzmann-BGK equations.

[0066]

[0067] in Indicates time Location The probability density function of the molecular velocity distribution at that location. The distribution function, The relaxation time is related to gas viscosity through pressure. This standard Boltzmann-BGK equation, through Chapman-Enskog expansion analysis, yields the standard compressible Navier-Stokes equation. If the temperature in the equilibrium distribution function... Alternatively, if the gas constant is chosen as a given fixed parameter, the velocity of sound in the fluid can be controlled; this is called a pseudo velocity of sound. In this case, the Chapman-Enskog analysis can be expanded to the weakly compressible Navier-Stokes equations. Within a finite volume framework, based on the equations and macroscopic information on both sides of the fluid mesh interface, the distribution function at the mesh interface can be analytically constructed. The spacetime integral solution,

[0068]

[0069] in Let represent the total derivative. Expanding and analyzing the above expression and the original BGK equation yields the Navier-Stokes equation.

[0070]

[0071] in For fluid density, For fluid density, For fluid pressure, This refers to fluid viscous stress.

[0072] The GKS method obtained using the above approach can be used to simulate low-speed flows. Its computational time step is not limited by the actual flow velocity, and it does not require solving energy / temperature equations, making it a mesoscopic artificial compression method. However, this method requires a small spatial variation in the actual fluid density, and therefore it is not suitable for multiphase flows with large differences in component density, or multi-component flows such as combustion.

[0073] The technical solution proposed in this embodiment is to modify the original Boltzmann-BGK equations by adding fictitious external force terms to ensure that the macroscopic equations obtained through Chapman-Enskog expansion correspond to the low Mach number approximation NS equations, i.e., the Low Mach Number Approximation (LMNA) method. Although the LMNA method is widely used in traditional NS equations, it is not supported by the standard GKS method. The modification method proposed in this embodiment is as follows: First, the BGK equations are extended, and external force terms are added:

[0074]

[0075] in, To simulate external forces, For fluid dynamic pressure, The overall parameter controls compressibility, and is taken as follows: . This represents the equilibrium distribution function. It can be represented as:

[0076]

[0077] Formula (6) above represents the normal distribution function. The moments of equilibrium are represented by formula (7).

[0078]

[0079] A numerical algorithm for mesoscopic flow with variable density at low speeds is presented in the following steps. Steps 1-6 first introduce the general flow for finite volume based on the traditional Navier-Stokes equations. Subsequent steps derive the GKS method, which can recover the above equations.

[0080] Step 1: Determine the computational domain, divide or read the mesh information, fluid parameters, and control parameters, and proceed to Step 2.

[0081] Step 2: Allocate an array based on the read information, initialize the corresponding parameters of the calculation area, and then enter the time step loop to proceed to Step 3.

[0082] Step 3: Set boundary conditions, assign values ​​to all macroscopic quantities at the boundaries of the flow field, and proceed to Step 4.

[0083] Step 4: Derive the numerical flux of the flow field based on the BGK equation within the finite volume framework, and use this to solve the Navier-Stokes equations for the flow field. First, calculate the pressure and velocity (or momentum) fluxes at the interface of the flow field unit. Then, update the macroscopic quantities within the unit using the flux information at the interface. If there is an external force, apply the external force through a splitting method, and update the macroscopic quantities simultaneously. Proceed to Step 5.

[0084] Step 5: Determine if the time step meets the loop condition. If it does, proceed to Step 3; otherwise, proceed to Step 6.

[0085] Step 6: Output the flow field data and end the simulation.

[0086] The mesh information in Step 1 includes mesh length, width, number of meshes, unit mesh length, and mesh coordinates; fluid parameters include density, velocity, pressure, and viscosity parameters at each mesh point; control parameters include dimensionless parameters such as time step, CFL number, and Mach number.

[0087] The Navier-Stokes equation in Step 4 above is:

[0088]

[0089] In equation (8), For fluid density, For time, For fluid velocity, It is fluid dynamic pressure. For the deviatoric stress tensor, This is the external force term acting on the fluid. The deviatoric stress tensor, which includes bulk viscosity, can be expressed as:

[0090]

[0091] In the formula, For fluid dynamics viscosity, The volume viscosity coefficient, As a dimension, It is a unit vector.

[0092] The interfacial flux in Step 4 includes the fluxes of pressure and velocity (or momentum), attached. Figure 1 The unit shown is The interface flux, where respectively represent and The flux in the direction can be used to update the macroscopic information within the cell using the flux at the cell interface.

[0093] The splitting method in Step 4 is implemented as follows:

[0094]

[0095] The velocity can be obtained by solving the first formula in equation (3). The velocity at the next time step is obtained by applying an external force according to the splitting method. .

[0096] Appendix Figure 2 The key to solving the Navier-Stokes equations in the finite volume framework is the solution of the flux at the flow field interface. The following will start from the BGK (Bhatnagar-Gross-Krook) equations, derive the flux at the flow field interface, and restore the macroscopic governing equations through the Chapman-Enskog approximation [3].

[0097] First, the BGK equation with force terms can be expressed as:

[0098]

[0099] in The distribution function, Represents the equilibrium distribution function. For microscopic speed, For the relaxation time, the gas density and momentum are: , It can be represented as:

[0100]

[0101] Force The expression is:

[0102]

[0103] in , For hydrodynamic pressure, the equilibrium moment is:

[0104]

[0105] The moment of the source term is:

[0106]

[0107] Using operators The BGK equation can be rewritten as follows:

[0108]

[0109] Therefore, the distribution function can be expressed in terms of equilibrium state and source term, and the Chapman-Enskog approximate expansion is also given:

[0110]

[0111] right Find the second moment:

[0112]

[0113] in Taking the zeroth and first moments of the BGK equations respectively, we obtain the following equations:

[0114]

[0115] Thus, the dynamic model can be used to derive the Navier-Stokes equations, which are the original BGK equations.

[0116] To further derive the expression for the interface flux, the numerical flux of the low Mach approximation is derived below.

[0117] First, define a new distribution function: ,in The expression is:

[0118]

[0119] The equilibrium expression for the above distribution function is:

[0120]

[0121] The BGK equation with source terms can be expressed as:

[0122]

[0123] The expression for the source term is:

[0124]

[0125] Take the moments of the equilibrium distribution function in equation (21):

[0126]

[0127] Moments of the source terms in equation (23):

[0128]

[0129] Rewriting the BGK equation in equation (22), we get the expression for the distribution function:

[0130]

[0131] The distribution function is expanded using the Chapman-Enskog approximation:

[0132]

[0133] Within a finite volume framework, the distribution function is... Moment A second-order time-precision Taylor expansion is performed at the point shown in the appendix. Figure 3 :

[0134]

[0135] For the distribution function of equation (27) and Find the first moment separately:

[0136]

[0137] For the distribution function of equation (27) and Find the second moments separately:

[0138]

[0139] Integrating the time-dependent distribution function in equation (28) with respect to velocity:

[0140]

[0141] For the above formula The pressure flux can be obtained by integrating over time:

[0142]

[0143] Find the second moment of the time-dependent distribution function in equation (28):

[0144]

[0145] For the above formula Integrating over time yields the flux of momentum:

[0146]

[0147] For near-incompressible flows at constant density: Pressure flux and velocity flux can be expressed as follows:

[0148]

[0149] Through the above derivation process, two types of low Mach numerical fluxes based on momentum and velocity were obtained. Applying these numerical fluxes to the mesoscopic numerical algorithm for variable density low-speed flow can enable numerical simulation of low-speed flow.

[0150] The Gas-Kinetic Scheme (GKS), as a mesoscopic method within a finite volume framework, offers several key advantages. Firstly, flow field information evolves and is updated through macroscopic quantities. Secondly, many effective processing techniques used in traditional numerical methods based directly on macroscopic quantities, such as the reconstruction of intra-cell or interfacial physical quantities, boundary conditions, and acceleration techniques in steady flow, can be directly applied. Thirdly, the GKS is constructed based on the continuous Boltzmann equations, eliminating the need for velocity space discretization and storage of distribution functions. This significantly reduces the computational and storage requirements, making it far less expensive than directly solving the BGK equations.

[0151] Please see Figure 1-6 The second embodiment of the mesoscopic numerical calculation method for variable density low-speed flow in this invention includes:

[0152] A numerical algorithm for mesoscopic flow with variable density at low speeds consists of the following steps:

[0153] Step 1: Determine the computational domain, divide or read the mesh information, fluid parameters, and control parameters, and proceed to Step 2.

[0154] Step 2: Allocate an array based on the read information, initialize the corresponding parameters of the calculation area, and then enter the time step loop to proceed to Step 3.

[0155] Step 3: Set boundary conditions, assign values ​​to the corresponding macroscopic quantities of all boundaries in the flow field, and proceed to Step 4.

[0156] Step 4: Derive the numerical flux of the flow field based on the BGK equation within the finite volume framework, and use this to solve the Navier-Stokes equations for the flow field. First, calculate the pressure and velocity (or momentum) fluxes at the interface of the flow field unit. Then, update the macroscopic quantities within the unit using the flux information at the interface. If there is an external force, apply the external force through a splitting method, and update the macroscopic quantities simultaneously. Proceed to Step 5.

[0157] Step 5: Determine if the time step meets the loop condition. If yes, proceed to Step 3; otherwise, proceed to Step 6.

[0158] Step 6: Output the flow field data and end the simulation.

[0159] To verify the correctness of the algorithm proposed in this invention, the following numerical examples are performed.

[0160] The implementation example is a two-dimensional Taylor Green vortex simulation. In a square cavity with four periodic boundaries, a time-dependent pressure field and velocity field are initialized. The pressure and velocity in the computational region will evolve with time. The correctness of the algorithm can be verified by comparing with the analytical solution.

[0161] The calculation parameters include the calculation area: ,Mach number fluid viscosity The CFL number is set to 0.01408, and the number of calculation steps is... The initialization of the pressure field and velocity field is as follows:

[0162]

[0163] Among them, speed .

[0164] For the near-incompressible flow with constant density in this example, an algorithm based on velocity flux can be used, with the pressure and velocity flux as follows:

[0165]

[0166] By deriving the velocity-based low Mach numerical flux, and applying the above numerical flux to the mesoscopic numerical algorithm for variable density low-speed flow, the flow process of this example can be numerically simulated.

[0167] As attached Figure 4 The comparison diagrams of the pressure and velocity fields with the analytical solutions shown demonstrate that the results of this algorithm agree well with the analytical solutions. Additionally, [the diagrams are attached]. Figure 5 The pressure and velocity field contour maps at the corresponding moments are given.

[0168] According to the appendix Figure 6 The double logarithmic curves show that the algorithm has higher than second-order spatial accuracy in calculating the velocity field.

[0169] The above describes the method for calculating the mesoscopic structure of variable-density low-speed flow in embodiments of the present invention. The following describes the apparatus for calculating the mesoscopic structure of variable-density low-speed flow in embodiments of the present invention. Please refer to [link to relevant documentation]. Figure 7 The variable density low-speed flow mesoscopic numerical calculation device in this embodiment of the invention includes, for the above embodiments:

[0170] The data reading module 701 is used to determine the computational region and divide or read the grid information, fluid parameters and control parameters in the computational region;

[0171] The time step loop enters module 702, which is used to allocate an array based on the read information, initialize the corresponding parameters of the calculation area, and then enter the time step loop.

[0172] Boundary condition setting module 703 is used to set boundary conditions and assign values ​​to all macroscopic quantities of the boundary in the flow field.

[0173] The boundary macroscopic quantity update module 704 is used to solve the Navier-Stokes equations for the flow field and calculate the pressure and velocity flux at the interface of the flow field unit. It updates the boundary macroscopic quantity information through flux information, determines whether there is an external force, and if so, applies the external force through a splitting method while updating the boundary macroscopic quantities.

[0174] The loop / end judgment module 705 is used to determine whether the time step meets the loop condition; if yes, it re-enters the setting of boundary conditions and assigns values ​​to all boundary macroscopic quantities in the flow field; if no, it outputs the flow field data and ends the simulation.

[0175] above Figure 7 The variable density low-speed flow mesoscopic numerical calculation device in the embodiments of the present invention will be described in detail from the perspective of modular functional entities. The electronic equipment in the embodiments of the present invention will be described in detail from the perspective of hardware processing.

[0176] Figure 8 This is a schematic diagram of the structure of an electronic device 700 provided in an embodiment of the present invention. The electronic device 700 can vary significantly due to different configurations or performance characteristics. It may include one or more central processing units (CPUs) 710 (e.g., one or more processors) and a memory 720, and one or more storage media 730 (e.g., one or more mass storage devices) for storing application programs 733 or data 732. The memory 720 and storage media 730 can be temporary or persistent storage. The program stored in the storage media 730 may include one or more modules (not shown in the diagram), each module including a series of instruction operations on the electronic device 700. Furthermore, the processor 710 may be configured to communicate with the storage media 730 and execute the series of instruction operations in the storage media 730 on the electronic device 700.

[0177] Electronic device 700 may also include one or more power supplies 740, one or more wired or wireless network interfaces 750, one or more input / output interfaces 750, and / or one or more operating systems 731, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art will understand that... Figure 8 The illustrated electronic device structure does not constitute a limitation on electronic devices and may include more or fewer components than illustrated, or combine certain components, or have different component arrangements.

[0178] The present invention also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when executed on a computer, cause the computer to perform the steps of a variable-density low-speed flow mesoscopic numerical calculation method.

[0179] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system, device, or unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0180] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0181] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for numerical calculation of mesoscopic flow at low speeds with varying density, characterized in that, The mesoscopic numerical calculation method for variable density low-speed flow includes: Define the computational domain, and divide or read the mesh information, fluid parameters, and control parameters within the computational domain; Based on the read information, an array is allocated, the corresponding parameters of the computation region are initialized, and then the time step loop is entered. Set boundary conditions and assign values ​​to all macroscopic quantities at the boundaries of the flow field; Within a finite volume framework, the Navier-Stokes equations for numerical flux solution of the flow field are derived based on the BGK equations; the Navier-Stokes equations are as follows: in, For fluid density, For time, For fluid velocity, It is fluid dynamic pressure. For the deviatoric stress tensor, It is the external force term acting on the fluid; The formula for the external force term is specifically expressed as follows: in, To simulate external forces, For fluid dynamic pressure, The overall parameter controls compressibility, and is taken as follows: , Represents the equilibrium distribution function. It can be represented as: Calculate the pressure and velocity flux at the interface of the flow field unit, update the boundary macroscopic quantity information using the flux information, determine whether there is an external force, and if so, apply the external force by splitting the flow field unit, while updating the boundary macroscopic quantity information. Determine if the time step meets the loop condition; if yes, re-enter the boundary condition setting process and assign values ​​to all macroscopic quantities at the boundaries of the flow field; if no, output the flow field data and end the simulation.

2. The method for numerical calculation of mesoscopic flow at low speeds with varying density according to claim 1, characterized in that, The division or reading of grid information, fluid parameter information, and control parameter information within the computational region includes: The computational domain is divided into different grids, and the grid information, fluid parameter information, and control parameter information of each grid in the computational domain are read. Alternatively, it can read the mesh information, fluid parameter information, and control parameter information of the pre-defined mesh in the computational region.

3. The method for numerical calculation of mesoscopic flow at low speeds with varying density according to claim 2, characterized in that, The grid information includes grid length information, grid width information, number of grids information, unit grid length information, and grid coordinate information.

4. The method for numerical calculation of mesoscopic flow at low speeds with varying density according to claim 2, characterized in that, The fluid parameter information includes density information, velocity information, pressure information, and viscosity parameter information; the control parameter information includes time step information, CFL number information, and Mach number information.

5. The method for numerical calculation of mesoscopic flow at low speeds with varying density according to claim 1, characterized in that, The deviatoric stress tensor that includes bulk viscosity is: In the formula, For fluid dynamics viscosity, The bulk viscosity coefficient, As a dimension, It is a unit vector.

6. The method for numerical calculation of mesoscopic flow at low speeds with varying density according to claim 5, characterized in that, The pressure and velocity flux at the interface of the computational flow field unit include: Under conditions of near-incompressible flow at constant density; exist Always Integrating over a time step yields the flux based on momentum in the following form: Under near-incompressible flow conditions at constant density, Therefore, the flux based on velocity can be obtained as follows: 。 7. The method for numerical calculation of mesoscopic flow at low speeds with varying density according to claim 6, characterized in that, The splitting method in applying external force through splitting includes: in, It is obtained by solving the Navier-Stokes equations.

8. A numerical calculation device for mesoscopic flow of variable density at low speeds, characterized in that, include: The data reading module is used to determine the computational domain and to divide or read the grid information, fluid parameters, and control parameters within the computational domain. The time step loop enters the module, which is used to allocate an array based on the read information, initialize the corresponding parameters of the calculation area, and then enter the time step loop; The boundary condition setting module is used to set boundary conditions and assign values ​​to all macroscopic quantities at the boundaries in the flow field; The boundary macroscopic quantity update module is used to derive the numerical flux solution of the flow field Navier-Stokes equations based on the BGK equations within a finite volume framework; the Navier-Stokes equations are: in, For fluid density, For time, For fluid velocity, It is fluid dynamic pressure. For the deviatoric stress tensor, It is the external force term acting on the fluid; The formula for the external force term is specifically expressed as follows: in, To simulate external forces, For fluid dynamic pressure, The overall parameter controls compressibility, and is taken as follows: ; Represents the equilibrium distribution function; It can be represented as: ； Calculate the pressure and velocity flux at the interface of the flow field unit, update the boundary macroscopic quantity information using the flux information, determine whether there is an external force, and if so, apply the external force by splitting the flow field unit, while updating the boundary macroscopic quantity information. The loop / end judgment module is used to determine whether the time step meets the loop condition; if yes, it re-enters the setting of boundary conditions and assigns values ​​to all macroscopic quantities of the boundary in the flow field; if no, it outputs the flow field data and ends the simulation.

9. An electronic device comprising a memory and at least one processor, wherein the memory stores instructions; The at least one processor invokes the instructions in the memory to cause the electronic device to perform the steps of the variable density low-speed flow mesoscopic numerical calculation method as described in any one of claims 1-7.

10. A computer-readable storage medium storing instructions thereon, characterized in that, When the instructions are executed by the processor, they implement the various steps of the variable density low-speed flow mesoscopic numerical calculation method as described in any one of claims 1-7.

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