A Three-Level Coarse Mesh Finite Difference Acceleration Method under a Domestic DCU Architecture

Abstract

The present invention proposes a three - level coarse - mesh finite - difference acceleration method for domestic DCU architecture, belonging to the cross - technical field of neutron physics and high - performance computing. The method includes: in the three - dimensional characteristic - line transport scanning stage, according to the domain - decomposition method, the computing tasks are sent to the device side (domestic DCU). Inside the DCU, according to the coarse - mesh vertices, edges and faces to which the trajectory segments belong, the neutron flux on the coarse - mesh surfaces to which the trajectory segments belong is stored, and the neutron flux that needs data transfer at the communication - domain boundary is stored; in the three - level coarse - mesh finite - difference method, the calculation results of the characteristic - line three - dimensional characteristic - line transport solution are transferred to the three - level coarse - mesh finite - difference solution module. Among them, the three - level coarse - mesh finite - difference performs multiple coarsening acceleration calculations in terms of energy groups and geometric structures, that is, a coarser mesh with a higher coarsening degree is used to accelerate the iterative calculation of the previous - level coarse mesh. The coarsening degrees of the three - level meshes from small to large are represented as the multi - energy - group cell - level mesh, the single - energy - group cell - level mesh and the single - energy - group assembly - level mesh. Then, the finite - difference equations of each level of the coarse mesh are constructed and solved using the successive over - relaxation iteration method. Finally, the fluxes in each flat - source region are updated according to the calculation results, and the effective neutron multiplication factor in the current iteration is calculated. The present invention relates to the cross - technical field of neutron physics and high - performance computing.

Description

Technical Field

[0001] The present invention relates to the cross - technical field of neutron physics and high - performance computing, and particularly refers to a three - level coarse - mesh finite - difference acceleration method for domestic DCU architecture. Background Art

[0002] The three - dimensional Method of Characteristics (MOC) is a high - precision numerical method used to solve the steady - state neutron transport equation, which describes the transport and interaction of neutrons in a reactor. By discretizing the neutron transport equation along characteristic lines in specific directions, this method can handle complex geometries, provide a high - precision neutron flux distribution, and is applicable to various core geometries, including pressurized water reactors and sodium - cooled fast reactors. Utilizing the powerful computing power of a supercomputer platform, the three - dimensional Method of Characteristics can achieve three - dimensional full - core simulations with pin - by - pin accuracy. However, this high - precision method requires fine mesh division and dense characteristic line generation, resulting in a significant increase in computational and storage requirements.

[0003] To improve the computational efficiency and accelerate the iterative process, the Coarse Mesh Finite - Difference (CMFD) method, due to its good acceleration performance, is widely used to accelerate the high - fidelity numerical solution of the three - dimensional Method of Characteristics neutron transport equation. Coarse Mesh Finite - Difference is an acceleration method for solving three - dimensional Method of Characteristics transport based on the multi - grid idea. Its main process is divided into coarsening and prolongation. In the coarsening process, using the equivalence theory, the fine - mesh fluxes, cross - sections, etc. in the Method of Characteristics are coarsened into the coarse mesh. In the prolongation process, by solving the coarse - mesh transport equation, the coarse - mesh calculation results are used to update the fine - mesh fluxes and other data.

[0004] Multiple studies have shown that, on the premise of ensuring computational accuracy, in order to reduce the number of iterations for solving the three - dimensional Method of Characteristics transport, usually one - level coarse - mesh finite - difference is used for iterative calculation. However, the scale of the single - level coarse - mesh matrix is large, which consumes a large amount of computing resources and the acceleration effect is not obvious. The multi - level coarse - mesh finite - difference method is an effective means to solve such problems.

[0005] The multi - level coarse - mesh finite - difference divides the computational granularity into multiple levels, and each level uses a different grid scale for calculation. By performing iterative calculations at each level, it can reduce the overall computational scale and time. By using coarser meshes to approximate the calculation results, the multi - level coarse - mesh finite - difference can significantly reduce the computational complexity while ensuring accuracy. Based on the above, the present invention proposes a three - level coarse - mesh finite - difference acceleration method for domestic DCU architecture. Summary of the Invention

[0006] The object of the present invention is to propose a three - level coarse - mesh finite - difference acceleration method for domestic DCU architectures to solve the problems raised in the background art. The present invention can, on the premise of ensuring calculation accuracy, further improve the parallelism of the method of characteristics and the multi - level coarse - mesh finite - difference method by using domestic DCUs. By using the three - level coarse - mesh finite - difference method, the scale of the coarse - mesh matrix is reduced, and the number of iterations and calculation time are further reduced, thereby improving the calculation efficiency.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A three - level coarse - mesh finite - difference acceleration method for domestic DCU architectures, including the following:

[0009] In the three - dimensional characteristic - line transport scanning stage, according to the domain - decomposition method, the calculation tasks are sent to the device side. Inside the device side, according to the coarse - grid vertices, edges and faces to which the divided trajectory segments belong, the neutron flux on the coarse - grid surfaces to which the trajectory segments belong and the neutron flux that needs data transfer at the communication - domain boundary are stored.

[0010] The calculation results of the three - dimensional characteristic - line transport solution of the characteristic lines are transferred to the three - level coarse - mesh finite - difference solution module, and multiple coarsening acceleration calculations are carried out on the energy groups and geometric structures by using the three - level coarse - mesh finite - difference method.

[0011] According to the calculation results of the three - level coarse - mesh finite - difference method, the fluxes of each flat - source region are updated, and the effective neutron multiplication factor in the current iteration is calculated.

[0012] Preferably, in the transport scanning stage, the scalar fluxes of each flat - source region are calculated based on each trajectory segment. The trajectory segments are further divided according to the maximum optical thickness, and the trajectories at the end of the divided segments are counted using the coarse grid. Then, according to the types of the coarse grids corresponding to the trajectory segments, the trajectories belonging to the coarse - grid faces and the trajectories belonging to the coarse - grid vertices and edges are stored separately. The trajectories located at the coarse - grid vertices and edges are subsequently split into each coarse - grid face.

[0013] Preferably, the multiple coarsening acceleration calculations carried out on the energy groups and geometric structures by using the three - level coarse - mesh finite - difference method specifically include the following:

[0014] A coarser - mesh is used to accelerate the iterative calculation of the previous - level coarse - mesh. The coarsening degrees of the three - level grids are represented from small to large as the multi - energy - group cell - level grid, the single - energy - group cell - level grid and the single - energy - group assembly - level grid. Then, the finite - difference equations of each level of the coarse - mesh are constructed, and the successive over - relaxation iteration method is used for solution.

[0015] Preferably, in the three - level coarse - mesh finite - difference method, the first - level multi - group pin - level coarse - mesh finite - difference (MG - Pin - CMFD) is used to accelerate the solution of the three - dimensional characteristic - line transport, and the second - level single - group pin - level coarse - mesh finite - difference (1G - Pin - CMFD) and the third - level single - group assembly - level coarse - mesh finite - difference (1G - ASY - CMFD) are used to accelerate the iterative speed of the previous level respectively to improve the overall solution efficiency.

[0016] Preferably, the equations for constructing the first - level multi - group pin - level coarse - mesh finite - difference are as follows:

[0017] Calculation of the average flux in the coarse mesh: Based on the characteristic - line method transport scanning process, combined with the fluxes in each flat - source region included in the coarse mesh, the average flux in the coarse mesh is obtained through volume homogenization calculation, and its corresponding calculation formula is:

[0018]

[0019] where, represents the average flux in the coarse mesh; represents the average flux in the flat - source region mesh; V k represents the volume of the flat - source region; the subscripts c, k, and g represent the coarse mesh, the flat - source region mesh, and the energy group used in the three - dimensional characteristic line respectively;

[0020] Calculation of the cross - section homogenization of the coarse mesh: Corresponding homogenization processing is carried out on each cross - section corresponding to each coarse mesh, and its corresponding calculation formula is:

[0021]

[0022] where, ∑ t,c,g and ∑ t,k,g represent the total cross - section of the coarse mesh and the total cross - section of the flat - source region mesh under this energy group respectively;

[0023] Calculation of the uniform diffusion coefficient corresponding to the coarse mesh: Before calculating the neutron current between adjacent coarse - mesh surfaces, first calculate and obtain the uniform diffusion coefficient corresponding to the coarse mesh, and its corresponding calculation formula is:

[0024]

[0025] where, D c,g represents the internal diffusion coefficient of the coarse mesh under this energy group;

[0026] Calculation of the effective diffusion coefficient, the net current term on the coarse - mesh surface, and the neutron - current correction coefficient, and its corresponding calculation formula is:

[0027]

[0028] where, represents the effective diffusion coefficient; Represents the net flow term on the coarse grid surface; Represents the neutron current correction coefficient; W c and W c+1 Represent the distance from the centroid of the current coarse grid and the current next adjacent grid to the surface respectively;

[0029] Calculation of the coarse mesh finite difference module, and its corresponding calculation formula is:

[0030]

[0031] where, w dir,c Represents the grid width of the coarse grid c in each direction of dir∈(x, y, z); Represents the average flux of the coarse grid after coarse mesh calculation; χ c,g Represents the neutron fission energy spectrum of the coarse grid; k eff Represents the effective neutron multiplication factor; v represents the average number of neutrons emitted per fission; Σ f,c,g Represents the fission cross section of this coarse mesh; ∑ s,c,g Represents the scattering cross section of this coarse mesh.

[0032] Preferably, the two - level single - energy - group cell - level coarse mesh finite difference is used to construct a single - energy - group linear system consistent with the first - level coarse mesh linear system, and calculate the single - group linear system to update the multi - group flux and eigenvalue. The specific calculation method is as follows:

[0033] Calculation of the flux of condensing one - energy - group from the multi - group average flux in the coarse grid, and its corresponding calculation formula is:

[0034]

[0035] where, the subscript e represents the single - energy - group unit of the coarse mesh finite difference after coarsening; G represents the number of all characteristic line energy groups;

[0036] Calculation of the net flow term of the surface of condensing one - energy - group from the multi - group neutron current in the coarse grid, and its corresponding calculation formula is:

[0037]

[0038] Calculation of the effective diffusion coefficient and the corrected diffusion coefficient of condensing one - energy - group at the cell - level in the coarse grid, and its corresponding calculation formula is:

[0039]

[0040] where, Represents the effective diffusion coefficient of condensing one - energy - group at the cell - level in the coarse grid; Represents the corrected diffusion coefficient.

[0041] Preferably, the three - group mono - energy component - level coarse - mesh finite - difference method is used to accelerate the calculation of the two - group mono - energy pin - cell - level coarse - mesh finite - difference method. The specific calculation method is as follows:

[0042] Calculation of the flux condensation of the mono - energy component - level coarse - mesh finite - difference method. The corresponding calculation formula is:

[0043]

[0044] where, represents the flux of the mono - energy component - level coarse - mesh finite - difference method; represents the coarse - mesh finite - difference grid at the component level; represents the coarse - mesh volume of the component;

[0045] Calculation of the surface net current term of the mono - energy component - level coarse - mesh finite - difference method. The corresponding calculation formula is:

[0046]

[0047] where, represents the surface net current term of the mono - energy component - level coarse - mesh finite - difference method; represents the surface area at the component level;

[0048] Calculation of the total cross - section of the mono - energy component - level coarse - mesh finite - difference method. The corresponding calculation formula is:

[0049]

[0050] where, represents the total cross - section of the mono - energy component - level coarse - mesh finite - difference method;

[0051] Calculation of the effective diffusion coefficient and the corrected diffusion coefficient of the mono - energy component - level coarse - mesh finite - difference method. The corresponding calculation formula is:

[0052]

[0053] where, represents the effective diffusion coefficient of the mono - energy component - level coarse - mesh finite - difference method; represents the corrected diffusion coefficient of the mono - energy component - level coarse - mesh finite - difference method; and respectively represent the distances from the centroid of the coarse - mesh at the component level and the current and the next adjacent grid to the surface ;

[0054] Preferably, according to the calculation results of the three - level coarse - mesh finite - difference method, updating the fluxes in each flat - source region and calculating the effective neutron multiplication factor in the current iteration specifically refers to:

[0055] The flux obtained by accelerating the solution of the first-level coarse mesh through the second-level and third-level coarse meshes is used to update the flux of the flat source region it contains, providing a more convergent flux for the iteration of the method of characteristics. The corresponding calculation formula is as follows:

[0056]

[0057] Among them, represents the flux obtained by accelerating the solution of the first-level coarse mesh through the second-level and third-level coarse meshes; represents the more convergent flux after update.

[0058] Compared with the prior art, the present invention provides a three-level coarse mesh finite difference acceleration method under a domestic DCU architecture, having the following beneficial effects:

[0059] The present invention proposes a three-level coarse mesh finite difference acceleration method under a domestic DCU architecture. In the transport sweep stage, according to the coarse grid points, edges, and faces to which the trajectory segments belong, the neutron flux on the surface of the coarse grid to which the trajectory segments belong is statistically calculated; the calculation results of the three-dimensional method of characteristics transport solution are transferred to the three-level coarse mesh finite difference solution module, where the three-level coarse mesh finite difference performs multiple coarsening acceleration calculations in terms of energy groups and geometric structures, divided into the first-level multi-energy group cell-level coarse mesh, the second-level single-energy group cell-level coarse mesh, and the third-level single-energy group assembly-level coarse mesh. Then, the finite difference equations of each level of coarse mesh are constructed and solved using the successive over-relaxation iteration method; finally, according to the calculation results of the three-level coarse mesh finite difference, the fluxes of each flat source region are updated, and the effective neutron multiplication factor in the current iteration is calculated. The present invention can further improve the parallelism of the method of characteristics and the coarse mesh finite difference method using a domestic DCU on the premise of ensuring the calculation accuracy. Using the three-level coarse mesh finite difference method, the scale of the coarse mesh matrix is reduced, the number of iterations is further reduced, and the calculation efficiency is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a schematic diagram of the overall flow of a three-level coarse mesh finite difference acceleration method for a domestic DCU architecture proposed in Embodiment 1 of the present invention;

[0061] Figure 2 is a schematic diagram of accelerating the three-dimensional method of characteristics transport solution of the method of characteristics using the three-level coarse mesh finite difference method under the idea of a multi-grid in Embodiment 1 of the present invention;

[0062] Figure 3 is a schematic diagram of the reactor geometric domain decomposition and coarse grid structure proposed in Embodiment 1 of the present invention;

[0063] Figure 4 is a schematic diagram of the coarsening of the three-level coarse mesh finite difference in terms of geometric structure (radial and axial) proposed in Embodiment 1 of the present invention;

[0064] Figure 5 Schematic diagram of sub - stream splitting in the trajectory located at the vertex of the coarse grid in Embodiment 1 of the present invention;

[0065] Figure 6 Schematic diagram of sub - stream splitting in the trajectory located on the edge of the coarse grid in Embodiment 1 of the present invention;

[0066] Figure 7 Schematic diagram of the coarse grid and the flat source region in the radial plane in Embodiment 1 of the present invention;

[0067] Figure 8 Schematic diagram of the net neutron current between the coarse grid c and the adjacent surface in the x and y directions in Embodiment 1 of the present invention. Detailed implementation manners

[0068] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0069] For a better understanding of the present invention, the terms related to the present invention are briefly described as follows:

[0070] 1) Trajectory

[0071] In the three - dimensional characteristic line method, a trajectory refers to the movement path of neutrons in the computational domain along a specific direction. By discretizing the neutron transport equation, the continuous neutron movement process is transformed into a discrete computational problem.

[0072] 2) Flat source region

[0073] A flat source region is a small region divided in the computational domain. In this region, from the time when the characteristic line enters the flat source region to the time when it leaves, the neutron source intensity is uniform, that is, the source term is constant. This means that within this region, the neutron source term is regarded as a constant, rather than a function that varies with spatial position, and it is also called the flat source approximation.

[0074] 3) Cross - section

[0075] In the characteristic line method, a cross - section is a measure used to describe the probability of neutrons interacting with atomic nuclei in matter. In addition to the flat source approximation, it is also assumed that the material properties in each flat source region are a certain constant. In each flat source region FSR with an area of A i the cross - section is averaged over the area. The cross - sections frequently used in steady - state neutron transport are the total neutron cross - section, the neutron scattering cross - section, the neutron fission cross - section, and the fission neutron energy spectrum. i

[0076] 4) Coarse grid

[0077] ​A coarse grid refers to a three-dimensional geometric grid created using constructive solid geometry methods. This coarse grid consists of union, intersection, and complement operations of half-spaces constructed by multiple planes such as the X-plane, Y-plane, and Z-plane, reflecting each coarse grid structure corresponding to the coarse mesh finite difference method and having attributes such as vertices, edges, and faces.

[0078] 5) Pin Cell

[0079] A pin cell is a computational unit in a reactor core, usually corresponding to a single fuel rod or the smallest unit of a fuel rod bundle. Each pin cell contains one or more fuel rods, as well as potentially coolant, cladding, and other materials. Calculations at the pin cell level provide high-resolution information on the detailed distribution within the reactor core and are also the basic units in coarse grid calculations.

[0080] 6) Assembly

[0081] An assembly is a larger unit composed of multiple pin cells, usually corresponding to a fuel assembly or a part of a fuel assembly. A fuel assembly contains multiple pin cells arranged in a specific geometry, and the reactor core is composed of multiple such assemblies. Calculations at the assembly level are carried out based on data at the pin cell level by combining the detailed information of multiple pin cells to obtain the distribution of physical quantities on a larger scale.

[0082] 7) Surface net current term

[0083] The surface net current term refers to the net flow of neutron current across the boundary of a coarse grid cell during calculations. It is the difference between the neutron current flowing out of and into the computational cell and is usually used to measure the net transport of neutrons between different computational cells.

[0084] Based on the above content, the present invention proposes a three-level coarse mesh finite difference acceleration method for domestic DCU architectures. Please refer to Figure 1 , the present invention includes the following:

[0085] During the three-dimensional characteristic line transport scanning stage, according to the domain decomposition method, the computational tasks are sent to the device side (domestic DCU). Within the DCU, based on the vertices, edges, and faces of the coarse grid to which the divided trajectory segments belong, the surface neutron currents of the coarse grids to which the trajectory segments belong are stored, and the neutron currents that need data transfer at the communication domain boundary are stored;

[0086] Transfer the calculation results of the three-dimensional characteristic line transport solution to the three-level coarse mesh finite difference solution module, where the three-level coarse mesh finite difference method accelerates the calculation by coarsening multiple times in energy groups and geometric structures, that is, uses a coarser mesh with a higher coarsening degree to accelerate the iterative calculation of the previous-level coarse mesh. The coarsening degrees of the three-level meshes are represented from small to large as the multi-energy group cell-level mesh, the single-energy group cell-level mesh, and the single-energy group assembly-level mesh. Then, establish the finite difference equations of the coarse meshes at each level and solve them using the successive over-relaxation iteration method;

[0087] According to the calculation results of the three-level coarse mesh finite difference, update the fluxes in each flat source region and calculate the effective neutron multiplication factor in the current iteration.

[0088] In the three-dimensional characteristic line transport scanning stage, according to the domain decomposition method, distribute the calculation tasks to the device side (domestic DCU). Inside the DCU, store the neutron currents on the coarse mesh surfaces to which the trajectory segments belong according to the vertices, edges, and faces of the coarse meshes to which the divided trajectory segments belong, and store the neutron currents that need data transfer at the communication domain boundary; transfer the calculation results of the three-dimensional characteristic line transport solution to the three-level coarse mesh finite difference solution module, then establish the finite difference equations of the coarse meshes at each level and solve them using the successive over-relaxation iteration method; finally, according to the calculation results of the three-level coarse mesh finite difference, update the fluxes in each flat source region and calculate the effective neutron multiplication factor in the current iteration. This can further improve the parallelism of the characteristic line method and the coarse mesh finite difference method using domestic DCU on the premise of ensuring the calculation accuracy. Use the three-level coarse mesh finite difference method to reduce the scale of the coarse mesh matrix and further reduce the number of iterations, thereby improving the calculation efficiency.

[0089] In this embodiment, when constructing the three-level coarse mesh finite difference solution module, transfer the calculation results of the three-dimensional characteristic line transport solution to the three-level coarse mesh finite difference solution module. Among them, the secondary single-energy group cell-level coarse mesh is the coarsening of the primary multi-energy group cell-level in energy groups. By pre-grouping the cross-sections and diffusion parameters of the primary coarse mesh, the calculation amount is further reduced; the tertiary single-energy group assembly-level coarse mesh is the coarsening of the secondary single-energy group cell-level coarse mesh in geometric structure to reduce the scale of the coarse mesh matrix; through the secondary single-energy group cell-level coarse mesh and the tertiary single-energy group assembly-level coarse mesh with a higher coarsening degree, accelerate the iterative speed of the previous level respectively, thereby improving the overall solution efficiency.

[0090] In this embodiment, the coarse mesh finite difference is an acceleration method for the three-dimensional characteristic line transport solution based on the multi-grid idea. Its main process is divided into coarsening and prolongation. In the coarsening process, the equivalent theory is used to ensure that the solution of the coarse mesh is consistent with the solution of the characteristic line, and coarsen the fine-grid fluxes, cross-sections, etc. in the characteristic line method into the coarse mesh. In the prolongation process, by solving the coarse mesh transport equation, use the calculation results of the coarse mesh to update the data such as the fine-grid fluxes. Please refer to Figure 2 , Figure 2A schematic diagram of the three-level coarse-grid finite difference accelerated characteristic line method calculation based on the multi-grid concept is shown.

[0091] In this embodiment, the transport equation of the coarse mesh finite difference method needs to be obtained by solving the three-dimensional characteristic line transport equation. First, the angular flux in the characteristic line method transport equation needs to be converted into a transport equation in the form of a diffusion theorem. In order to convert it into a form based on scalar flux rather than angular flux, the entire three-dimensional characteristic line transport equation needs to be integrated in the angular space, and its form is:

[0092]

[0093] Where r represents the spatial position vector, Ω represents the trajectory angular direction vector, g, g' represents the energy group index, ψ represents the neutron angular flux, and k eff represents the effective neutron multiplication factor, ∑ t represents the total neutron cross section, Σ s represents the neutron scattering cross section, Σ f represents the neutron fission cross section, χ represents the fission neutron energy spectrum, and v represents the average number of neutrons emitted in a single fission.

[0094] Convert the angular flux in 4π angular space into the net neutron flux form J g (r) is represented by:

[0095]

[0096] After the above-mentioned form conversion and the introduction of the divergence theorem, the transport equation corresponding to the grid c energy group g of the coarse mesh finite difference method is:

[0097]

[0098] Among them, the number of energy groups of the first-level coarse mesh finite difference corresponds to the number of characteristic line energy groups, and the boundary surface of the coarse mesh c is defined as S c , the surface normal (normal vector) is n.

[0099] In this embodiment, after domain decomposition is enabled, the communication domain and the coarse grid structure and DCU undertake the computing tasks within the domain. Figure 3 shown.

[0100] In this embodiment, in the three-level coarse-grid finite difference method, the first-level multi-energy group grid element level coarse-grid finite difference method is often used to accelerate the solution of three-dimensional characteristic line transport. However, the first-level coarse-grid finite difference method has problems such as large coarse-grid matrix size and unclear acceleration. A second-level single-energy group grid element level coarse-grid and a third-level single-energy group component level coarse-grid with higher mesh coarsening degree are proposed to respectively accelerate the iteration speed of the previous level, thereby improving the overall solution efficiency. Figure 4 The schematic diagram of the coarsening of the geometric structure (radial and axial) of the three-level coarse-grid finite difference is shown.

[0101] In this embodiment, during the transport scanning stage, the flux of each flat source region is calculated based on each trajectory segment. The trajectory segments need to be further segmented according to the maximum optical thickness. The coarse grid only counts the trajectories located at the end of the segmented section. According to the type of coarse grid corresponding to the trajectory segment, the trajectories belonging to the coarse grid surface and the trajectories belonging to the vertices and edges of the coarse grid are stored separately. The trajectories located at the vertices and edges of the coarse grid will be split into each coarse grid surface later.

[0102] In this embodiment, the method for splitting sub-streams in the trajectories of vertices and edges is as follows:

[0103] A1. For the sub-streams in the trajectories located at the vertices of the coarse grid, considering the geometric position of the vertices and according to the cubic geometry, there are a total of 8 types of vertex types. The sub-streams at the vertices are split into 3 adjacent edges, and the sub-streams in the adjacent edges are one-third of the original sub-streams at the vertex. This splitting method corresponds to Figure 5 the content shown.

[0104] A2. For the sub-streams in the trajectories of the coarse grid edges and the sub-streams in the edges after being split by A1, considering the cubic geometry, there are a total of 12 types of edge types. According to the coarse grid position and boundary conditions, the sub-streams in the edges are split into 2 adjacent faces, and the sub-streams in the adjacent faces are one-half of the original sub-streams in the edge. This splitting method corresponds to Figure 6 the content shown.

[0105] A3. The split sub-streams are superimposed on their respective corresponding coarse grid surfaces to achieve the statistics and storage of the sub-streams.

[0106] In this embodiment, the main calculation methods for each variable required to construct the coarse mesh finite difference equations at the first-level multi-energy group cell level include:

[0107] B1. The average flux in the first-level coarse grid needs to be obtained through volume homogenization calculation by combining the flux of each flat source region included in the coarse grid during the transport scanning process using the characteristic line method. Figure 7 The schematic diagram of the coarse grid and the flat source region in the radial plane is given, and the corresponding calculation formula for the volume homogenization average flux is:

[0108]

[0109] B2. In addition to the volume homogenization of the coarse grid flux, the corresponding homogenization treatment also needs to be carried out for each cross-section corresponding to each coarse grid. The corresponding calculation formulas for the total neutron cross-section, neutron fission cross-section, neutron scattering cross-section, and fission neutron energy spectrum are as follows:

[0110]

[0111] Among them, c represents the coarse grid in the coarse mesh finite difference method, g represents that a certain energy group in the coarse grid corresponds one-to-one with the characteristic line energy group, k represents the flat source region k contained in the coarse grid c, represents the average flux calculated by the characteristic line method for the energy group g of the coarse grid c, represents the average flux corresponding to the energy group g in the flat source region k, V k represents the volume of the flat source region k.

[0112] B3. Before calculating the neutron current between adjacent faces of the coarse grid, it is necessary to first calculate and obtain the uniform diffusion coefficient corresponding to the coarse grid, and its corresponding calculation formula is:

[0113]

[0114] B4. When obtaining the uniform diffusion coefficient D corresponding to each energy group g of the coarse grid c c,e , it is necessary to calculate the net neutron current, effective diffusion coefficient and neutron current correction coefficient between the coarse grid c and the adjacent faces in the x, y, and z directions. The calculation formula for the net neutron current between the coarse grid c and the adjacent face in the x and y directions is:

[0115]

[0116] Among them, represents the effective diffusion coefficient at the adjacent face between the coarse grid c and the adjacent grid c + 1, represents the neutron current correction coefficient at the adjacent face between the coarse grid c and the adjacent grid c + 1.

[0117] The net neutron current between the coarse grid c and the adjacent face in the x and y directions Figure 8 is shown as follows.

[0118] The calculation formulas for the effective diffusion coefficient and the neutron current correction coefficient are respectively:

[0119]

[0120] The equation form corresponding to the coarse mesh finite difference module is:

[0121]

[0122] Among them, w dir,c represents the grid width of the coarse grid c in each direction of dir ∈ (x, y, z), and g represents the corresponding number of energy groups of the coarse grid. After simplifying the above formula, the corresponding coarse mesh finite difference equation is:

[0123]

[0124] In this embodiment, the two - level single - energy - group cell - level coarse - mesh finite - difference method aims to construct a single - energy - group linear system consistent with the first - level coarse - mesh linear system and calculate the single - group linear system to update the multi - group flux and eigenvalue. Its basic principle is to condense the flux, neutron current, and cross - section of one energy group using multi - group flux, multi - group neutron current, and multi - group cross - section. The main calculation methods include:

[0125] C1. The multi - group average flux in the coarse mesh condenses the flux of one energy group, and its corresponding calculation formula is:

[0126]

[0127] where the subscript e represents the coarse - meshed finite - difference single - energy - group unit after coarsening, and G represents the number of all characteristic - line energy groups.

[0128] C2. The multi - group neutron current in the coarse mesh condenses the surface net - current term of one energy group, and its corresponding calculation formula is:

[0129]

[0130] C3. The multi - group cross - section in the coarse mesh condenses the cross - section data of one energy group, and its corresponding calculation formula is:

[0131]

[0132] The cell - level condensation in the coarse mesh of the diffusion coefficient, effective diffusion coefficient of one energy group and the corrected diffusion coefficient Its corresponding calculation formula is:

[0133]

[0134] Use the data of the multi - energy - group cell - level coarse - mesh finite - difference to construct the single - energy - group cell - level coarse - mesh finite - difference, and then the single - energy - group cell - level coarse - mesh finite - difference to accelerate the update of the multi - energy - group cell - level coarse - mesh finite - difference flux:

[0135]

[0136] where represents the coarse - mesh average flux calculated by the second - level energy - group compression coarse - mesh finite - difference, represents the single - energy - group coarse - mesh average flux calculated by the first - level coarse - mesh data accumulation, represents the coarse - mesh average flux calculated by the first - level coarse - mesh finite - difference, represents the single - energy - group cell - level coarse - mesh average flux after the second - level coarse - mesh iterative update.

[0137] In this embodiment, the scale of the coarse grid unit matrix at the pin level is too large, and there is potential for further acceleration of the single-energy-group pin-level coarse mesh. The assembly-level coarse grid is directly used to accelerate the iterative solution of the characteristic line. Although it is beneficial to reduce the scale of the coarse grid matrix, the effect of reducing the number of iterations of the three-dimensional characteristic line transport solution by the assembly-level coarse grid is not as good as that of the pin-level coarse grid. It is not suitable for directly accelerating the transport calculation. It can be used as the third-level coarse grid to accelerate the calculation of the second-level single-energy-group pin-level coarse grid. The main calculation methods include:

[0138] D1. Flux of the finite difference of the single-energy-group assembly-level coarse mesh Condensation, and its corresponding calculation formula is:

[0139]

[0140] Where represents the coarse grid finite difference grid at the assembly level, represents the volume of the assembly coarse grid.

[0141] D2. Surface net current term of the finite difference of the single-energy-group assembly-level coarse mesh Its corresponding calculation formula is:

[0142]

[0143] Where represents the surface area at the assembly level.

[0144] D3. Cross-section data of the finite difference of the single-energy-group assembly-level coarse mesh, and its corresponding calculation formula is:

[0145]

[0146]

[0147] D4. Diffusion coefficient, effective diffusion coefficient of the finite difference of the single-energy-group assembly-level coarse mesh and corrected diffusion coefficient Its corresponding calculation formula is:

[0148]

[0149] Where and respectively represent the distance from the centroid of the assembly-level coarse grid and the current next adjacent grid to the surface of.

[0150] Use the data of the single-energy-group pin-level coarse mesh to construct the finite difference equation of the single-energy-group assembly-level coarse mesh, and then use the single-energy-group assembly-level coarse mesh to accelerate the update of the finite difference flux of the single-energy-group pin-level coarse mesh:

[0151]

[0152] Among them, represents the coarse grid average flux calculated by the third-level geometric compression coarse grid finite difference, represents the component-level coarse grid average flux calculated by the second-level coarse grid data accumulation, represents the coarse grid average flux calculated by the second-level coarse grid finite difference, represents the single-energy group cell-level coarse grid average flux after the third-level coarse grid iteration update.

[0153] In this embodiment, the flux obtained by solving the first-level multi-energy group cell-level coarse grid after the second-level and third-level coarse grid acceleration will be used to update the flux of the flat source region it contains, so as to provide a more convergent flux for the iteration of the method of characteristics Its main calculation form is:

[0154]

[0155] Among them, represents the scalar flux corresponding to the coarse grid c energy group g obtained after the acceleration of the first two levels of coarse grid finite difference equations, represents the average flux corresponding to the coarse grid c energy group g obtained by using three-dimensional method of characteristics data. In the above formula, k ∈ c.

[0156] In this embodiment, taking the C5G7 benchmark as an example, the acceleration effects of the third-level coarse grid finite difference are carried out respectively. Through test verification, the third-level coarse grid finite difference calculation method proposed by the present invention can reduce the scale of the coarse grid matrix, further reduce the iteration times of the three-dimensional method of characteristics and improve the overall calculation efficiency on the premise of ensuring the accuracy.

[0157] As mentioned above, only the specific embodiments of the present invention are preferred, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and should be covered by the protection scope of the present invention.

Claims

1. A three - level coarse grid finite - difference acceleration method under a domestic DCU architecture, characterized in that, It includes the following content: In the three-dimensional characteristic line transport scanning stage, according to the domain decomposition method, the calculation tasks are sent to the device side. Inside the device side, according to the vertices, edges and faces of the coarse grid to which the divided trajectory segments belong, the neutron flux on the coarse grid surface to which the trajectory segments belong and the neutron flux that needs data transfer at the communication domain boundary are stored; The calculation results of the characteristic line three-dimensional characteristic line transport solution are transferred to the three-level coarse mesh finite difference solution module, and the three-level coarse mesh finite difference method is used to perform multiple coarsening acceleration calculations in the energy group and geometric structure; A coarser mesh with a higher coarsening degree is used to accelerate the iterative calculation of the previous level of coarse mesh. The coarsening degrees of the three-level meshes are represented from small to large as the multi-energy group cell-level mesh, the single-energy group cell-level mesh and the single-energy group assembly-level mesh. Then, the finite difference equations of each level of coarse mesh are constructed and solved using the successive over-relaxation iteration method; According to the calculation results of the three-level coarse mesh finite difference, the fluxes of each flat source region are updated, and the effective neutron multiplication factor in the current iteration is calculated.

2. A three-level coarse grid finite difference acceleration method under a domestic DCU architecture according to claim 1, characterized in that In the transport scanning stage, the standard fluxes of each flat source region are calculated based on each trajectory segment. The trajectory segments are further segmented according to the maximum optical thickness, and the trajectories located at the end of the segmented segments are statistically analyzed using the coarse grid; Then, according to the type of coarse grid corresponding to the trajectory segment, the trajectories belonging to the coarse grid surface and the trajectories belonging to the coarse grid vertices and edges are stored separately. The trajectories located at the coarse grid vertices and edges are subsequently split into each coarse grid surface.

3. A three - level coarse grid finite - difference acceleration method under a domestic DCU architecture according to claim 2, characterized in that, In the three-level coarse mesh finite difference method, the first-level multi-energy group cell-level coarse mesh finite difference is used to accelerate the three-dimensional characteristic line transport solution, and the second-level single-energy group cell-level coarse mesh finite difference and the third-level single-energy group assembly-level coarse mesh finite difference are used to accelerate the iterative speed of the previous level respectively to improve the overall solution efficiency.

4. A three - level coarse grid finite - difference acceleration method under a domestic DCU architecture according to claim 3, characterized in that, Construct the equations of the first-level multi-energy group cell-level coarse mesh finite difference. The specific calculation method is as follows: Calculation of the average flux in the coarse grid: Based on the transport scanning process of the characteristic line method, combined with the fluxes of each flat source region included in the coarse grid, the average flux in the coarse grid is obtained through volume homogenization calculation. The corresponding calculation formula is: Among them, represents the average flux in the coarse mesh; represents the average flux in the flat source region mesh; V k represents the volume of the flat source region; the subscripts c, k, and g respectively represent the energy groups used for the coarse mesh, the flat source region mesh, and the three-dimensional characteristic line; Calculation of the cross-section homogenization of the coarse grid: Corresponding homogenization processing is performed on each cross-section corresponding to each coarse grid. The corresponding calculation formula is: Among them, ∑ t,c,g and ∑ t,k,g respectively represent the total cross-section of the coarse mesh and the total cross-section of the mesh in the source region under this energy group; Calculation of the uniform diffusion coefficient corresponding to the coarse grid: Before calculating the neutron flux between adjacent coarse grid surfaces, the uniform diffusion coefficient corresponding to the coarse grid is first calculated. The corresponding calculation formula is: Among them, D c,g represents the coarse mesh internal diffusion coefficient under this energy group; Calculation of the effective diffusion coefficient, the net current term on the coarse grid surface and the neutron flux correction coefficient. The corresponding calculation formula is: Among them, represents the effective diffusion coefficient; represents the net flow term on the surface of the coarse grid; represents the neutron current correction coefficient; W c and W c+1 respectively represent the distance from the centroid of the current coarse grid and the current next adjacent grid to the surface; Calculation of the coarse mesh finite difference module. The corresponding calculation formula is: Among them, w dir,c represents the grid width of the coarse grid c in each direction of dir ∈ (x, y, z); represents the average flux of the coarse grid after coarse mesh calculation; χ c,g represents the neutron fission energy spectrum in the coarse grid; k eff represents the effective neutron multiplication factor; v represents the average number of neutrons emitted per fission; ∑ f,c,g represents the fission cross section of this coarse mesh; ∑ s,c,g represents the scattering cross section of this coarse mesh.

5. A three-level coarse grid finite difference acceleration method under a domestic DCU architecture according to claim 4, characterized in that The second-level single-energy group cell-level coarse mesh finite difference is used to construct a single-energy group linear system consistent with the first-level coarse mesh linear system, and calculate the single-group linear system to update the multi-group flux and eigenvalue. The specific calculation method is as follows: Calculation of the flux of condensing one energy group from the multi-group average flux in the coarse grid. The corresponding calculation formula is: Among them, the subscript e represents the single-energy group unit of the coarsened coarse mesh finite difference; G represents all the characteristic line energy group numbers; Calculation of the net current term of the surface of condensing one energy group from the multi-group neutron flux in the coarse grid. The corresponding calculation formula is: Calculation of the effective diffusion coefficient and the corrected diffusion coefficient of the one - energy - group condensation at the pin - cell level in the coarse mesh, and the corresponding calculation formula is as follows: Among them, represents the effective diffusion coefficient of the cell-level condensation one-energy group in the coarse mesh; represents the corrected diffusion coefficient.

6. A three - level coarse grid finite - difference acceleration method under a domestic DCU architecture according to claim 5, characterized in that The three - level single - energy - group assembly - level coarse - mesh finite - difference method is used to accelerate the calculation of the two - level single - energy - group pin - cell - level coarse - mesh finite - difference method. The specific calculation method is as follows: Calculation of the flux condensation of the single - energy - group assembly - level coarse - mesh finite - difference method, and the corresponding calculation formula is as follows: Among them, represents the flux of the coarse mesh finite difference at the single-energy group assembly level represents the coarse mesh finite difference grid at the assembly level, represents the coarse mesh volume of the assembly; Calculation of the surface net current term of the single - energy - group assembly - level coarse - mesh finite - difference method, and the corresponding calculation formula is as follows: Among them, represents the surface net current term of the coarse mesh finite difference at the single-energy group assembly level; represents the surface area at the assembly level; Calculation of the total cross - section of the single - energy - group assembly - level coarse - mesh finite - difference method, and the corresponding calculation formula is as follows: Among them, represents the total cross-section of the coarse mesh finite difference at the single-energy group component level; Calculation of the effective diffusion coefficient and the corrected diffusion coefficient of the single - energy - group assembly - level coarse - mesh finite - difference method, and the corresponding calculation formula is as follows: Among them, represents the effective diffusion coefficient of the coarse mesh finite difference at the single-energy group assembly level; represents the corrected diffusion coefficient of the coarse mesh finite difference at the single-energy group assembly level; and respectively represent the centroid of the coarse grid at the assembly level and the distances from the current and the next adjacent grids to the surface respectively.

7. A three - level coarse grid finite - difference acceleration method under a domestic DCU architecture according to claim 6, characterized in that, Updating the fluxes in each flat - source region according to the calculation results of the three - level coarse - mesh finite - difference method and calculating the effective neutron multiplication factor in the current iteration specifically refers to: Using the flux obtained by accelerating the solution of the first - level coarse mesh through the second - and third - level coarse meshes to update the fluxes in the flat - source regions it contains, providing a more convergent flux for the iteration of the characteristic - line method. The corresponding calculation formula is as follows: Among them, represents the flux obtained by accelerating the solution of the first-level coarse grid through the second-level and third-level coarse grids; represents the more convergent flux after updating.

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