A kinetic solution method and system for multi-scale particle transport simulation

Abstract

This invention belongs to the technical field of multi-scale particle transport simulation, and discloses a kinetic solution method and system for multi-scale particle transport simulation. The method includes: a particle kinetic model based on discrete velocity form; selecting discrete points in velocity space; calculating the distribution function along the direction of the discrete points in velocity space at the center of the grid according to a compact scheme; accumulating the contribution values ​​of the distribution function to macroscopic physical quantities; scanning the downstream grid sequentially based on the direction of the discrete points in velocity space; changing the discrete points in velocity space and repeating the operation until the contribution values ​​of the grid at all discrete points in velocity space are accumulated, and obtaining the final macroscopic physical quantities; outputting the calculation results of macroscopic physical quantities when the convergence condition is met. This invention discloses a kinetic solution method and system for multi-scale particle transport simulation that balances computational memory, accuracy, and efficiency, and is particularly suitable for multi-scale particle transport simulation with a large number of discrete points in velocity space and strong heterogeneity.

Description

Technical Field

[0001] This invention belongs to the technical field of multi-scale particle transport simulation, and more specifically, relates to a kinetic solution method and system for multi-scale particle transport simulation, which is particularly suitable for discrete velocity type method simulation of multi-scale particle transport with large velocity space discrete points and strong heterogeneity. Background Technology

[0002] In scientific and engineering fields such as hypersonic vehicle aerodynamics in near-space, multi-scale heat and mass transfer in micro / nanoelectronic devices, and energy-carrying particle transport, multi-scale flow and particle transport phenomena are prevalent, such as non-equilibrium gas flow and multi-scale photon thermal radiation in near-space hypersonic vehicle aerodynamics. Kinetic methods based on the microscopic motion of particles provide a solid foundation for constructing numerical simulations of multi-scale particle transport and have become one of the important tools for studying such problems.

[0003] Currently, the discrete velocity or discrete coordinate method has become one of the commonly used kinetic methods for studying multi-scale particle transport. The discrete velocity method solves the particle kinetic model equations by simultaneously discretizing and solving them in both geometric and velocity spaces, updating the particle distribution function, and calculating macroscopic physical quantities of particles through numerical integration, thus accurately solving multi-scale particle transport problems. However, particle kinetic model equations, such as those for gas molecules and photon thermal radiation, are typically complex high-dimensional multiphase probability density distribution function equations involving geometric, velocity, and time spaces. Furthermore, the discrete velocity method requires simultaneous discretization in both geometric and velocity spaces, resulting in a high-dimensional geometric-velocity space-dependent distribution function. Explicitly storing and calculating this distribution function leads to significant memory consumption and computational costs, especially for multi-scale particle transport problems requiring large numbers of discrete points in the velocity space, such as hypersonic non-equilibrium flows. This severely limits the application and engineering computational capabilities of the discrete velocity method.

[0004] To optimize the computational cost and memory footprint of discrete velocity methods, existing research generally introduces unstructured or adaptive discrete velocity space structures, using different velocity space discrete points in different multi-scale regions to reduce storage pressure. However, this velocity space design optimization is complex, and the velocity space discrete points corresponding to the distribution functions of different geometric space grids are inconsistent, requiring frequent interpolation calculations and complicating program processing. In addition, some methods optimize memory footprint by introducing additional numerical iterations, such as discrete velocity methods based on the Delta-Form memory reduction technique. While this method can reduce memory usage, the introduced incremental form increases the number of iterations, raising computational costs and reducing computational efficiency.

[0005] While the methods described above can reduce the storage requirements caused by velocity space discretization to some extent for specific problems, they are usually accompanied by complex optimization calculations and additional computational costs. Furthermore, methods for optimizing discrete velocity space structures still cannot completely avoid explicitly storing high-dimensional distribution functions, especially when dealing with problems requiring a large number of discrete velocity space points, such as highly rarefied free molecular flows. Memory consumption remains difficult to control, and these methods are also difficult to generalize to efficient computations for large-scale complex multi-scale flows or particle transport.

[0006] On the other hand, existing discrete velocity method distribution function reconstruction is generally based on multi-point interpolation schemes. For multi-scale particle transport problems with strong heterogeneity and inhomogeneity, the computational accuracy is low, requiring finer grid division to further ensure accuracy, which also exacerbates the deterioration of memory usage and computational cost. Summary of the Invention

[0007] In view of the above-mentioned defects or improvement needs of the prior art, this invention provides a kinetic solution method that takes into account computational memory, accuracy and computational efficiency. Its purpose is to solve the problems of large memory consumption, high computational cost and low accuracy of the prior art.

[0008] To achieve the above objectives, according to one aspect of the present invention, a kinetic solution method for multi-scale particle transport simulation is provided, comprising the following steps:

[0009] S1, Discretize the particle transport model to be simulated in geometric space and velocity space, divide the geometric space into grids and velocity space into discrete points, and establish a particle kinetic model in discrete velocity form;

[0010] S2, Select discrete points in velocity space, and perform a single geometric space scan based on the selected discrete point directions: Starting from the boundary of the geometric space grid, perform distribution function scanning and temporary macroscopic physical quantity updates for each grid sequentially from upstream to downstream according to the direction of the discrete point, until all grids have completed the solution of the distribution function at the grid center and grid interface and the update of the temporary macroscopic physical quantities; the distribution function scanning operation and temporary macroscopic physical quantity update for each grid specifically include:

[0011] S21, For each grid, at the selected discrete points in velocity space, the particle kinetic model in discrete velocity form is solved based on a compact scheme to calculate the distribution function at the grid center; wherein a compact scheme for the distribution function at the grid center is constructed based on the distribution function at the interface of the geometric space grid.

[0012] S22, based on the calculated distribution function at the center of the grid, accumulate the contribution of the distribution function at the selected discrete points in velocity space to the macroscopic physical quantity; store the accumulated value as a temporary macroscopic physical quantity for grid update;

[0013] Based on the calculated distribution function at the center of the grid and the direction of the selected discrete points in the velocity space, the distribution function at the interface of the next grid to be calculated is updated using a compact format.

[0014] S3, change the velocity space discrete point, repeat S2, until the contribution value of the distribution function of all geometric space grids to the macroscopic physical quantity at all velocity space discrete points is accumulated, and the final macroscopic physical quantity of all geometric space grids is obtained.

[0015] S4 determines whether the final macroscopic physical quantity meets the convergence condition. If not, return to S2 to start the next iteration. If it meets the condition, end the iteration process and output the calculation result of the macroscopic physical quantity.

[0016] According to the kinetic solution method for multi-scale particle transport simulation provided by the present invention, the discrete velocity form of the particle kinetic model in S1 is specifically as follows:

[0017] ;

[0018] Among them, subscript For the specific geometric space mesh element used in the calculation; subscript This corresponds to the center of the geometric space grid; subscript For the corresponding geometric space mesh interface; subscript For specific indexes of discrete points in velocity space; superscript The iteration number; For the geometric space of the first The volume of each grid, For the first A discrete point in velocity space; This refers to the normal vector of the interface of the corresponding geometric space mesh. This represents the surface area of ​​the corresponding geometric space grid. This refers to the relaxation time; For the geometric space of the first The equilibrium state or source term of each grid; Calculate the function for a specific equilibrium state or source term; For the geometric space of the first Macroscopic physical quantities of a grid; Indicates the first At the center of the grid along the first The distribution function of the direction of discrete points in velocity space. For the corresponding grid interface along the first Distribution function of the direction of discrete points in velocity space.

[0019] According to the kinetic solution method for multi-scale particle transport simulation provided by this invention, the compact scheme of the distribution function at the center of the grid in S21 is obtained by difference based on the distribution function at the interface between the upstream and downstream boundaries of the grid, specifically:

[0020] ;

[0021] in, Indicates the first At the center of the grid along the first Distribution function of the direction of discrete points in velocity space; Indicates the first Along the first grid interface The incident distribution function of the direction of the i-th discrete point in velocity space is the i-th Distribution function at the interface of the upstream boundary of each grid; Indicates the first Along the first grid interface The emission distribution function at the i-th discrete point in velocity space is the i-th Distribution function at the interface of the downstream boundary of each grid; This is a weighting factor, and its value range is... .

[0022] According to the kinetic solution method for multi-scale particle transport simulation provided by the present invention, the incident and exit distribution functions along the direction of discrete points in velocity space at the mesh interface in the compact scheme are specifically as follows:

[0023] , ;

[0024] Among them, subscript and Indicates the first The interface of the grid.

[0025] According to the kinetic solution method for multi-scale particle transport simulation provided by this invention, in S21, the particle kinetic model in discrete velocity form is solved based on a compact scheme, and the distribution function at the grid center is calculated as follows:

[0026] .

[0027] According to the kinetic solution method for multi-scale particle transport simulation provided by the present invention, the specific steps in S22 for accumulating the contribution of the distribution function to macroscopic physical quantities at the selected discrete points in velocity space are as follows:

[0028] ;

[0029] in, It is an integral function. Discrete points in velocity space The weight, For temporary macroscopic physical quantities, Indicates accumulation The temporary macroscopic physical quantity is obtained by calculating the distribution function of discrete points in velocity space.

[0030] According to the kinetic solution method for multi-scale particle transport simulation provided by the present invention, S22, updating the distribution function at the interface of the next grid to be calculated through a compact scheme, specifically includes:

[0031] Based on the calculated distribution function at the center of the grid and the compact format, the distribution function at the interface of the downstream boundary of the grid is obtained. The distribution function at the interface of the downstream boundary of the grid is used as the distribution function at the interface of the upstream boundary of the next grid to be calculated, thereby updating the distribution function at the interface of the next grid to be calculated.

[0032] According to the kinetic solution method for multi-scale particle transport simulation provided by the present invention, in S22, the distribution function at the interface is updated through a compact scheme. Specifically, based on the calculated distribution function at the grid center, the outgoing distribution function at the grid interface is obtained as follows:

[0033] ;

[0034] Based on the continuity condition, the outgoing distribution function at the mesh interface is then used as the incoming distribution function at the mesh interface of the next downstream mesh to be calculated, specifically:

[0035] .

[0036] According to the kinetic solution method for multi-scale particle transport simulation provided by the present invention, the distribution function at the center of each grid and the distribution function at the interface in S2 and S3 will be used as temporary single variables and will be updated repeatedly. There is no need to explicitly retain and store the distribution function at discrete points in velocity space. In the final calculation process, only temporary macroscopic physical quantities are stored.

[0037] According to another aspect of the present invention, a kinetic solution system for multi-scale particle transport simulation is provided, the system comprising a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing a kinetic solution method for multi-scale particle transport simulation as described above.

[0038] In summary, compared with the prior art, the kinetic solution method for multi-scale particle transport simulation provided by this invention offers the following advantages:

[0039] 1. A memory-saving approach is disclosed. This approach accumulates the contribution of the distribution function to the macroscopic physical quantity and updates the macroscopic physical quantity at discrete points in velocity space. It does not require explicit retention and storage of the distribution function at discrete points in velocity space. Only the macroscopic physical quantity is stored and retained during the calculation process. Its memory consumption and computational cost are greatly reduced, far lower than the traditional discrete velocity type method that stores and retains all distribution functions.

[0040] 2. The distribution function can be accurately solved and updated directly in a single geometric space scan. Compared with existing improvement techniques that require additional iterative processes or complex velocity space designs, the process is simpler, effectively reducing computational costs and improving computational efficiency while significantly reducing memory consumption.

[0041] 3. Based on the compact scheme, high-precision reconstruction of the distribution function can be achieved in a single-grid compact space, overcoming the shortcomings of traditional discrete velocity method, which is generally based on multi-point interpolation reconstruction and has insufficient computational accuracy for multi-scale particle transport problems with strong heterogeneity and non-uniformity.

[0042] 4. This invention has good universality and can be applied to a variety of particle kinetic models and velocity space structures, especially to multi-scale particle transport problems with large discrete points in the velocity space and strong heterogeneity. Attached Figure Description

[0043] Figure 1 This is a flowchart of the kinetic solution method for multi-scale particle transport simulation provided by the present invention.

[0044] Figure 2 This is a schematic diagram of the compact format and geometric space scanning provided by the present invention.

[0045] Figure 3 This is a schematic diagram of the present invention applied to multi-scale radiation transport embodiment 1—flat plate radiation embodiment.

[0046] Figure 4 This is a comparison chart of the accuracy results of applying the present invention to Example 1 of multi-scale radiation transport.

[0047] Figure 5 This is a schematic diagram of Embodiment 2 of the present invention applied to a gas flow problem—a square cavity driven flow embodiment.

[0048] Figure 6 This is a comparison diagram of the iterative convergence of the present invention applied to the gas flow problem in Example 2 with the existing incremental form (Delta-Form) method.

[0049] Figure 7 This is a graph showing the calculation results of the present invention applied to the gas flow problem in Example 2. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0051] To address the problems of large memory footprint, high computational cost, and low accuracy when handling non-uniform multi-scale flow or particle transport problems, such as... Figure 1 As shown, this embodiment provides a kinetic solution method for multi-scale particle transport simulation, which includes:

[0052] S1, Discretize the particle transport model to be simulated in geometric space and velocity space, divide the geometric space into grids and velocity space into discrete points, and establish a particle kinetic model in discrete velocity form;

[0053] S2, Select discrete points in velocity space, and perform a single geometric space scan based on the selected discrete point directions: Starting from the boundary of the geometric space grid, perform distribution function scanning and temporary macroscopic physical quantity updates for each grid sequentially from upstream to downstream according to the direction of the discrete point, until all grids have completed the solution of the distribution function at the grid center and grid interface and the update of the temporary macroscopic physical quantities; the distribution function scanning operation and temporary macroscopic physical quantity update for each grid specifically include:

[0054] S21, For each grid, at the selected discrete points in velocity space, the particle kinetic model in discrete velocity form is solved based on a compact scheme to calculate the distribution function at the grid center; wherein a compact scheme for the distribution function at the grid center is constructed based on the distribution function at the interface of the geometric space grid.

[0055] S22, based on the calculated distribution function at the center of the grid, accumulate the contribution of the distribution function at the selected discrete points in velocity space to the macroscopic physical quantity; store the accumulated value as a temporary macroscopic physical quantity for grid update;

[0056] Based on the calculated distribution function at the center of the grid and the direction of the selected discrete points in the velocity space, the distribution function at the interface of the next grid to be calculated is updated using a compact format.

[0057] S3, change the velocity space discrete point, repeat S2, until the contribution value of the distribution function of all geometric space grids to the macroscopic physical quantity at all velocity space discrete points is accumulated, and the final macroscopic physical quantity of all geometric space grids is obtained.

[0058] S4 determines whether the final macroscopic physical quantity meets the convergence condition. If not, return to S2 to start the next iteration. If it meets the condition, end the iteration process and output the calculation result of the macroscopic physical quantity.

[0059] The purpose of this embodiment is to perform kinetic calculations on discrete velocity-form particle kinetic model equations, especially on multi-scale particle transport models with large discrete points in the velocity space and strong heterogeneity, while significantly reducing memory usage, lowering computational costs, and improving the accuracy of distribution function reconstruction, thus meeting the application and engineering computational needs of multi-scale particle transport. The specific steps and implementation process are as follows:

[0060] S1. Discretize the particle transport model to be simulated in both geometric and velocity spaces, divide the geometric space into grids and the velocity space into discrete points, and establish a particle kinetic model in discrete velocity form; specifically, the particle kinetic model equations are as follows:

[0061] (1);

[0062] in, The distribution function, Geometric spatial location, For velocity-space position. This refers to the relaxation time; For the collision term in the kinetic model; For gradient operators; For the equilibrium state or source term of the kinetic model, For a specific equilibrium state or source term, the calculation function can be derived from the macroscopic physical quantities of the kinetic model. Calculated. Macroscopic physical quantity. It can usually be obtained by multiplying the distribution function numerically, i.e. , For integral functions. Note that the Boltzmann-type kinetic equation model shown in (1) can represent various particle kinetic models by modifying specific terms, such as the gas molecule kinetic model, the photon thermal radiation model, and other particle kinetic models.

[0063] Based on the finite volume method and the discrete velocity method, the above kinetic model equations are discretized in geometric space and velocity space. By dividing the geometric space into a grid and the velocity space into discrete points, the particle kinetic model equations in discrete velocity form can be obtained, specifically:

[0064] (2);

[0065] Among them, subscript For the specific geometric space mesh element used in the calculation; subscript This corresponds to the center of the geometric space grid; subscript For the corresponding geometric space mesh interface; subscript For specific indexes of discrete points in velocity space; superscript The iteration number; For the geometric space of the first The volume of each grid, For the first A discrete point in velocity space; This refers to the normal vector of the interface of the corresponding geometric space mesh. This represents the surface area of ​​the corresponding geometric space grid. This refers to the relaxation time; For the geometric space of the first The equilibrium state or source term of each grid; Calculate the function for a specific equilibrium state or source term; For the geometric space of the first Macroscopic physical quantities of a grid; Indicates the first At the center of the grid along the first The distribution function of the direction of discrete points in velocity space. For the corresponding grid interface along the first Distribution function of the direction of discrete points in velocity space.

[0066] As can be seen, the distribution function is a high-dimensional geometric space-velocity space related quantity. Explicitly storing and computing the distribution function will result in extremely high memory consumption and computational costs, especially for multi-scale particle transport problems with large discrete points in the velocity space and strong heterogeneity.

[0067] S2, select discrete points in velocity space, and perform a single geometric space scan based on the direction of the selected discrete points. Starting from the boundary of the geometric space grid, perform the distribution function scan operation and temporary macroscopic physical quantity update for each grid sequentially from upstream to downstream according to the direction of the discrete points in velocity space, until all grids have completed the solution of the distribution function at the grid center and grid interface and the update of the temporary macroscopic physical quantities. The distribution function scan operation and temporary macroscopic physical quantity update for each grid specifically include:

[0068] S21, For each spatial grid, at the selected discrete velocity space points, solve the particle kinetic model in discrete velocity form based on the compact scheme, and calculate the distribution function at the grid center; wherein the compact scheme of the distribution function at the grid center is constructed based on the distribution function at the interface of the geometric space grid;

[0069] S22, based on the calculated distribution function at the center of the grid, accumulate the contribution of the distribution function at the selected discrete points in velocity space to the macroscopic physical quantity; store the accumulated value as a temporary macroscopic physical quantity for grid update;

[0070] Based on the calculated distribution function at the center of the grid and the direction of the selected discrete points in the velocity space, the distribution function at the interface of the next grid to be calculated is updated using a compact format.

[0071] Specifically, to achieve high-precision compact solutions to the particle kinetic model equations in discrete velocity form and simplify the computational process, a compact scheme that enables high-precision reconstruction of the distribution function within a single grid is adopted. Furthermore, "incident" and "outcry" distribution functions are introduced at the geometric grid interface along the direction of the discrete points in velocity space, such as... Figure 2 As shown, at a specific discrete point in velocity space In S21, the compact format of the distribution function at the center of the grid is obtained by difference from the distribution function at the interface between the upstream and downstream boundaries of the grid, specifically:

[0072] (3);

[0073] in, Indicates the first At the center of the grid along the first Distribution function of the direction of discrete points in velocity space; Indicates the first Along the first grid interface The incident distribution function of the direction of the i-th discrete point in velocity space is the i-th Distribution function at the interface of the upstream boundary of each grid; Indicates the first Along the first grid interface The emission distribution function at the i-th discrete point in velocity space is the i-th Distribution function at the interface of the downstream boundary of each grid; This is a weighting factor, and its value range is... .

[0074] The incident and exit distribution functions along the direction of the discrete points in velocity space at the introduced geometric space mesh interface are as follows:

[0075] , (4);

[0076] Among them, subscript and Indicates the first At the interface of each grid. Specifically, along a specific velocity space discrete point. The direction of particle motion and the "incident" distribution function of the mesh interface will be known quantities, derived from specific boundary conditions or based on continuity conditions, and equal to the "outcrystall" distribution function of the interface of its "upstream" mesh. This continuity condition becomes an important basis for the geometric scan in subsequent steps.

[0077] By substituting the compact scheme (3) into the discrete velocity form of the particle kinetic model equation (2) and rearranging terms to eliminate the "ejection" distribution function at the mesh interface, the distribution function at the center of the geometric mesh can be calculated. That is, in S21, the particle kinetic model in discrete velocity form is solved based on the compact scheme, and the distribution function at the center of the mesh is calculated as follows:

[0078] (5).

[0079] That is, the compact format of the distribution function at the center of the grid in S21 is obtained by difference from the distribution function at the interface of the upstream and downstream boundaries of the grid; then, based on the compact format, the distribution function at the center of the grid in the discrete velocity form of the particle kinetic model is transformed into a quantity related to the distribution function at the interface of the upstream boundary of the grid; thus, starting from the boundary of the geometric space grid, the distribution function scanning and physical quantity update operations are repeatedly performed on each grid from upstream to downstream according to the direction of the discrete points in the velocity space.

[0080] Furthermore, in S22, based on the distribution function at the center of the grid obtained by the above calculation, the contribution of the distribution function at the selected discrete points in velocity space to the macroscopic physical quantity is accumulated; the accumulated value is stored as a temporary macroscopic physical quantity for grid update; more specifically;

[0081] Macroscopic physical quantities corresponding to geometric space grids Its calculation process can be regarded as the distribution function of the corresponding geometric space grid. The process of accumulating the contributions to macroscopic physical quantities at all discrete points in velocity space is as follows:

[0082] (6);

[0083] in Discrete points in velocity space The weight, For the integral function. Considering that only the calculation results of macroscopic physical quantities are needed in the end, the memory-saving approach provided by this invention is to distribute the function at the center of the grid obtained based on step S21. Then, the contribution of the distribution function at the discrete points in the velocity space to the macroscopic physical quantity is accumulated. After this, the distribution function of the geometric grid... It will no longer be needed for calculations of macroscopic physical quantities.

[0084] In S22, the accumulation of the contribution of the distribution function to the macroscopic physical quantity at the selected discrete points in velocity space is specifically as follows: First, based on the calculated distribution function at the grid center, the contribution value of the distribution function at the selected discrete points in velocity space to the macroscopic physical quantity is calculated; then, the contribution values ​​corresponding to all calculated discrete points in velocity space are gradually accumulated to obtain the accumulated value as a temporary macroscopic physical quantity; the details are as follows:

[0085] (7);

[0086] in, It is an integral function. Discrete points in velocity space The weight, For temporary macroscopic physical quantities, Indicates accumulation The temporary macroscopic physical quantity is obtained by calculating the distribution function of each discrete point in velocity space. It can be seen that after the cumulative contribution of the distribution function of all discrete points in velocity space to the macroscopic physical quantity has been calculated, It can be equated to a true macroscopic physical quantity For example, suppose the discrete points in the velocity space are divided into... ,total For each discrete point in velocity space, then we have .

[0087] After completing the above steps, the "ejection" distribution function along the direction of discrete points in velocity space at the mesh interface can be updated according to the compact format of the present invention, specifically as follows:

[0088] (8);

[0089] like Figure 2 As shown, based on the principle of continuity, starting from the boundary and along the direction of the discrete points in velocity space, the "outgoing" distribution function at the interface of the corresponding geometric space grid can be directly used as the "incoming" distribution function at the interface of the next grid to be calculated "downstream". At this point, the distribution function at the interface of the next grid to be calculated can be directly updated, specifically as follows:

[0090] (9).

[0091] Specifically, in S22, updating the interface distribution function of the next grid to be calculated using a compact format includes: obtaining the interface distribution function of the downstream boundary of the grid based on the calculated distribution function at the grid center and the compact format; using the interface distribution function of the downstream boundary of the grid as the interface distribution function of the upstream boundary of the next grid to be calculated, thereby updating the interface distribution function of the next grid to be calculated.

[0092] It should be noted that the relationship between "upstream" and "downstream" is along discrete points in velocity space. The determined grid adjacency relationship, such as Figure 2 As shown, for , The grid is Downstream of the grid. Similarly, for , The grid is Downstream of the grid.

[0093] Based on the selected discrete points in velocity space, after completing steps S21 to S22 for a specific geometric grid, the distribution function calculation for that geometric grid is complete, and the "incident" distribution function conditions for its downstream grids are obtained. At this point, the downstream grids can be further calculated until all geometric grids have completed step S2 according to the direction of the selected discrete points in velocity space. This process, starting from the boundary of the geometric space and calculating from upstream to downstream geometric grids according to the direction of the discrete points in velocity space, until all geometric grids are completed, is called a geometric space scan. Its calculation order strictly follows the direction of the discrete points in velocity space from "upstream" to "downstream." Mathematically, this geometric scan is a direct Gaussian elimination solution to the particle kinetic model equation (2) in discrete velocity form, and the accurate solution to the equation can be obtained directly through a single complete geometric space scan.

[0094] S3, change the velocity space discrete point, repeat S2, until the contribution values ​​of the distribution function of all geometric space grids to the macroscopic physical quantity at all velocity space discrete points are accumulated, and the final macroscopic physical quantity of all geometric space grids is obtained.

[0095] Specifically, assuming the discrete points in the velocity space are divided into: ,total For each discrete point in velocity space, an S2 geometric space scan step is performed, where the macroscopic contribution is accumulated. This process continues until the contributions of all discrete points in velocity space to the macroscopic physical quantity have been accumulated, yielding the final macroscopic physical quantity. .

[0096] It is worth noting that in S3, the distribution functions at the center and interface of each grid will be used as temporary single variables and updated repeatedly. There is no need to explicitly retain or store the distribution functions at discrete points in the velocity space. The final calculation process only stores temporary macroscopic physical quantities. It overcomes the shortcomings of traditional discrete velocity type methods, which require retaining or storing all distribution functions, resulting in large memory consumption and heavy computational burden.

[0097] S4 determines whether the final macroscopic physical quantity meets the convergence condition. If not, return to S2 to start the next iteration. If it meets the condition, end the iteration process and output the calculation result of the macroscopic physical quantity.

[0098] Specifically, it involves examining macroscopic physical quantities. Check if the error meets the convergence condition. If not, calculate the equilibrium state or source term and update the iteration counter. Then return to step S2 to perform the next round of iteration. If the convergence condition is met, output the calculation result and end the iteration process.

[0099] In one embodiment, a kinetic solution system for multi-scale particle transport simulation is provided. The system includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to perform the kinetic solution method for multi-scale particle transport simulation described above.

[0100] In some specific embodiments, in the field of engineering and scientific research related to multi-scale particle transport, existing kinetic discrete velocity methods suffer from problems such as large memory consumption, high computational cost, and low accuracy when handling non-uniform multi-scale particle transport problems, especially for multi-scale particle transport problems requiring large velocity space discrete points and those with strong heterogeneity. To verify the applicability and advantages of the method of this invention in such problems, several typical verification models and benchmark problems were constructed for verification tests using embodiments. Specifically, multi-scale particle transport can include photon transport, gas molecule transport, neutron transport, electron transport, etc., without specific limitations. For photon transport, macroscopic physical quantities can be radiation intensity and temperature; for gas molecule transport, macroscopic physical quantities can be density, temperature, and velocity; for neutron transport, macroscopic physical quantities can be neutron flux and power.

[0101] Specific Implementation Example 1: Figure 3 This paper presents an embodiment of a multiscale photon radiative transport problem in a plate of size L=1 with a constant heat source, where the velocity space is divided into 40 discrete points, and the extinction coefficient is given. The settings are as follows: The relaxation time corresponds to the equation (1):

[0102] (10);

[0103] Figure 4The figure demonstrates the accuracy advantages of this invention, specifically the radiation energy distribution of this multi-scale photon radiation problem. The traditional discrete velocity method shown in the figure employs a conventional multi-point interpolation scheme. As can be seen, compared to the multi-point interpolation scheme commonly used in the traditional discrete velocity method for distribution function reconstruction, the compact scheme of this invention effectively guarantees computational accuracy even on coarser grids. This effectively overcomes the problem of low accuracy in existing technologies when dealing with non-uniform multi-scale flows or particle transport problems.

[0104] Specific Implementation Example 2: Figure 5 An example of a classic square cavity driven gas flow problem in a free molecular flow region (Kn=10) is presented. Due to the rarefaction effect of the flow region, a large number of velocity space discrete points are required to ensure the accuracy of the calculation. The velocity space is divided into an 81×81 non-uniform trapezoidal integral velocity space, and the geometric space grid is divided into a 64×64 uniform grid.

[0105] Regarding memory advantages, the existing traditional discrete velocity method, which requires storing and preserving the distribution function, occupies 860.6 MB of memory in this embodiment, where MB is a unit of memory bytes. In contrast, the present invention only requires 0.68 MB, which is only 0.079% of the memory usage of the traditional method that stores the distribution function. The huge difference in memory usage is mainly due to the explicit storage of the distribution function.

[0106]

[0107] Regarding computational efficiency, based on this embodiment, the present invention was compared with the existing incremental (Delta-Form) memory reduction discrete speed method. The comparison results are shown in the table above.

[0108] As can be seen from the table above, this invention simplifies the solution process, reduces computational costs, and improves computational efficiency while saving memory. This is mainly because the Delta-Form memory reduction method requires the distribution function to be calculated starting from the equilibrium distribution function, thus necessitating a certain number of internal iterations for accurate calculation. Even with the use of some internal iteration convergence techniques to reduce the number of internal iterations, a significant amount of additional iterative computation work is still introduced. For example... Figure 6 As shown in the figure, this figure illustrates the inner iteration convergence curve of the existing Delta-Form method under the initial Delta-Form inner iteration in this embodiment 2.

[0109] This invention can solve the problem directly in one step, without the need for additional iterative calculations. The specific calculation results of this invention are as follows: Figure 7As shown, U and V represent the velocities along the X and Y axes, respectively, and Uw represents the velocity of the upper wall of the cavity-driven flow in this embodiment. This demonstrates the advantages of this invention compared to existing improved memory-saving discrete velocity methods, offering lower computational cost and higher computational efficiency when solving multi-scale flow or particle transport problems.

[0110] In summary, the above embodiments have verified the applicability and advantages of the present invention from different perspectives. Overall, the present invention provides a memory-saving approach, realizing the accumulation of the contribution of the distribution function to macroscopic physical quantities and the updating of macroscopic physical quantities at discrete points in velocity space. During the solution process, only macroscopic physical quantities are stored, without the need to explicitly retain and store the distribution function at discrete points in velocity space, resulting in a storage requirement far lower than traditional discrete velocity methods.

[0111] On the other hand, the compact scheme of the present invention can achieve high-precision reconstruction of the distribution function in a single-grid compact space, overcoming the shortcomings of the traditional discrete velocity method multi-point interpolation for multi-scale particle transport problems with strong heterogeneity and non-uniformity.

[0112] Furthermore, this invention can directly and accurately solve the distribution function in a single geometric space scan. Compared with the existing Delta-Form memory reduction method, which introduces additional iterative processes, this method is simpler, has lower computational costs, and is more computationally efficient. It is particularly suitable for multi-scale particle transport problems with large discrete points in the velocity space and strong heterogeneity.

[0113] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A kinetic solution method for multiscale particle transport simulation, characterized in that, The method comprises the following steps: S1, discretizing a particle transport model to be simulated in a geometric space and a velocity space, dividing a geometric space grid and a velocity space discrete point, and establishing a discrete velocity form of a particle kinetic model; S2, selecting a velocity space discrete point, performing a single geometric space scanning based on a selected velocity space discrete point direction: starting from a geometric space grid boundary, sequentially performing a distribution function scanning operation and a temporary macroscopic physical quantity update on each grid from upstream to downstream according to the velocity space discrete point direction, until all grids complete the solving of the distribution function at the grid center and the updating of the temporary macroscopic physical quantity at the grid interface; the distribution function scanning operation and the temporary macroscopic physical quantity update of each grid specifically comprise: S21, for each grid, based on a compact scheme, solving the discrete velocity form of the particle kinetic model at the selected velocity space discrete point to calculate the distribution function at the grid center; wherein the compact scheme of the distribution function at the grid center is constructed according to the distribution function at the interface of the geometric space grid; S22, based on the calculated distribution function at the grid center, accumulating the contribution of the distribution function at the selected velocity space discrete point to the macroscopic physical quantity; storing the accumulated value as the temporary macroscopic physical quantity of the grid update; based on the calculated distribution function at the grid center and the selected velocity space discrete point direction, updating the distribution function at the interface of the next to be calculated grid through the compact scheme; S3, replacing the velocity space discrete point, repeating S2 until the contribution value of the distribution function of all geometric space grids at all velocity space discrete points to the macroscopic physical quantity is accumulated, and the final macroscopic physical quantity of all geometric space grids is obtained; S4, judging whether the final macroscopic physical quantity meets a convergence condition, if not, returning to S2 to start the next iteration; if yes, ending the iteration process and outputting the macroscopic physical quantity calculation result; The discrete velocity form of the particle kinetic model in S1 is specifically: ； where subscript is the specific calculated geometric spatial grid cell; subscript is the corresponding geometric spatial grid center; subscript is the corresponding geometric spatial grid interface; subscript is the specific index of the velocity spatial discrete point; superscript is the iteration number; is the volume of the th grid in the geometric space, is the th velocity spatial discrete point; is the normal vector of the corresponding geometric spatial grid interface; is the surface area of the corresponding geometric spatial grid; is the relaxation time; is the equilibrium state or source term of the th grid in the geometric space; is the specific equilibrium state or source term calculation function; is the macroscopic physical quantity of the th grid in the geometric space; is the distribution function of the th grid center along the th velocity spatial discrete point direction, is the distribution function of the corresponding grid interface along the th velocity spatial discrete point direction.

2. The kinetic solving method of multiscale particle transport simulation of claim 1, wherein, The compact scheme of the distribution function at the grid center in S21 is obtained by difference according to the distribution functions at the interfaces of the upstream boundary and the downstream boundary of the grid, and is specifically: ； wherein, represents the distribution function at the center of the grid along the direction of the velocity space discretization point; represents the incident distribution function at the interface of the grid along the direction of the velocity space discretization point, which is the distribution function at the interface of the upstream boundary of the grid; represents the outgoing distribution function at the interface of the grid along the direction of the velocity space discretization point, which is the distribution function at the interface of the downstream boundary of the grid; is a weighting factor, which has a value range of .

3. The kinetic solving method of multiscale particle transport simulation of claim 2, wherein, The incident distribution function and the outgoing distribution function of the grid interface in the compact scheme along the velocity space discrete point direction are specifically: ， ； wherein the subscript with denotes the interface of the grid.

4. The kinetic solving method of multiscale particle transport simulation of claim 2, wherein, S21, based on the compact scheme, solving the discrete velocity form of the particle kinetic model to calculate the distribution function at the grid center is specifically: 。 5. The kinetic solving method of multiscale particle transport simulation of claim 1, wherein, S22, accumulating the contribution of the distribution function to the macroscopic physical quantity at the selected velocity space discrete point is specifically: ； wherein, is an integral function, is a weight of a velocity space discrete point , is a temporary macroscopic physical quantity, denotes a temporary macroscopic physical quantity calculated after accumulating distribution functions of the velocity space discrete points.

6. The kinetic solving method of multiscale particle transport simulation of claim 2, wherein, S22, updating the distribution function at the interface of the next to be calculated grid through the compact scheme specifically comprises: Based on the calculated distribution function at the grid center and the compact scheme, the distribution function at the interface of the downstream boundary of the grid is obtained, the distribution function at the interface of the downstream boundary of the grid is taken as the distribution function at the interface of the upstream boundary of the next to be calculated grid, and the updating of the distribution function at the interface of the next to be calculated grid is realized.

7. The kinetic solving method of multiscale particle transport simulations of claim 6, wherein, S22, updating the distribution function at the interface through the compact scheme specifically comprises: ； Further based on the continuity condition, the exit distribution function at the grid interface is taken as the incident distribution function at the grid interface of the next grid to be calculated downstream, specifically: 。 8. The kinetic solving method of multiscale particle transport simulations of claim 1, wherein, The distribution function at the center of each grid in S2 and S3 and the distribution function at the interface will be used as a temporary single variable and will be updated repeatedly, without the need to explicitly reserve and store the distribution function on the spatially discrete points, and the only temporary macroscopic physical quantity stored in the final calculation process is the macroscopic physical quantity.

9. A kinetic solver system for multiscale particle transport simulation, characterized in that, The system comprises a memory and a processor, the memory stores a computer program, and the processor executes the computer program to execute the kinetic solution method of the multi-scale particle transport simulation according to any one of claims 1-8.

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