Three-level coarse mesh finite difference acceleration method under domestic DCU architecture

Abstract

The invention provides a three-level coarse mesh finite difference acceleration method oriented to a domestic DCU architecture, and belongs to the cross technical field of neutron physics and high-performance calculation. The method comprises the following steps: a three-dimensional characteristic line transport scanning stage: issuing a calculation task to an equipment end (domestic DCU) according to a domain decomposition method, and in the DCU, according to a vertex, an edge and a surface of a coarse grid to which a track segment belongs, storing a neutron current on the surface of the coarse grid to which the track segment belongs, and storing a neutron current which is located at a communication domain boundary and needs data transmission; according to the three-level coarse mesh finite difference method, a three-dimensional feature line transport solution calculation result is transmitted to a three-level coarse mesh finite difference solving module, coarse mesh finite difference is subjected to multiple times of coarsening acceleration calculation on an energy group and a geometric structure, that is, a coarse mesh with the higher coarsening degree is used for accelerating iterative calculation of a previous-level coarse mesh, and the coarse mesh with the higher coarsening degree is used for accelerating iterative calculation of the previous-level coarse mesh. The coarsening degrees of the three-level grids are expressed as a multi-energy group lattice cell level grid, a single-energy group lattice cell level grid and a single-energy group component level grid from small to large, and then a coarse mesh finite difference equation set of each level is constructed and solved by using a successive super-relaxation iteration method; and finally, updating the flux of each flat source region according to a calculation result, and calculating an effective neutron multiplication factor in the current iteration. The invention relates to the cross technical field of neutron physics and high-performance calculation.

Description

Technical Field

[0001] The present invention relates to the cross-technical field of neutron physics and high performance computing, and in particular to a three-level coarse-net finite difference acceleration method for a 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 and describe the transmission and interaction of neutrons in the reactor. This method discretizes the neutron transport equation by characteristic lines along specific directions. It can handle complex geometric structures and provide high-precision neutron flux distribution. It is applicable to a variety of core geometries, including pressurized water reactors and sodium-cooled fast reactors. By leveraging the powerful computing power of supercomputing platforms, the three-dimensional characteristic line method can achieve three-dimensional full-reactor simulation with pin-by-pin accuracy. However, this high-precision method requires fine meshing and dense characteristic line generation, resulting in a significant increase in computing and storage requirements.

[0003] In order to improve computational efficiency and accelerate the iteration process, the coarse mesh finite difference (CMFD) method is widely used to accelerate the high-fidelity numerical solution of the three-dimensional characteristic line neutron transport equation due to its good acceleration performance. The coarse mesh finite difference is a three-dimensional characteristic line transport solution acceleration method based on the multi-grid concept. Its main process is divided into coarsening and extension. In the coarsening process, the fine grid flux, cross section, etc. in the characteristic line method are coarsened to the coarse grid using the equivalence theory. In the extension process, by solving the coarse mesh transport equation, the coarse mesh calculation results are used to update the fine mesh flux and other data.

[0004] Many studies have shown that, under the premise of ensuring the calculation accuracy, in order to reduce the number of iterations of the characteristic line three-dimensional characteristic line transmission solution, the first-level coarse mesh finite difference is usually used for iterative calculation. However, the single-level coarse mesh matrix is ​​large in size, consumes a lot of computing resources, and the acceleration effect is not obvious. The multi-level coarse mesh finite difference method is an effective means to solve this kind of problem.

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

[0006] The purpose of the present invention is to propose a three-level coarse-net finite difference acceleration method for the domestic DCU architecture to solve the problems raised in the background technology. The present invention can further improve the parallelism of the characteristic line method and the multi-level coarse-net finite difference method by using the domestic DCU under the premise of ensuring the calculation accuracy, and use the three-level coarse-net finite difference method to reduce the scale of the coarse-net matrix and further reduce the number of iterations and calculation time, thereby improving the calculation efficiency.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] A three-level coarse-net finite difference acceleration method under a domestic DCU architecture includes the following contents:

[0009] In the three-dimensional feature line transport scanning stage, the computing task is sent to the device end according to the domain decomposition method. In the device end, the neutron flow on the coarse grid surface to which the trajectory segment belongs and the neutron flow at the boundary of the communication domain that needs data transmission are stored according to the coarse grid vertices, edges and faces to which the trajectory segment belongs.

[0010] The calculation results of the three-dimensional characteristic line transport solution of the characteristic line 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 on the energy group and geometric structure;

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

[0012] Preferably, in the transport scanning stage, each flat source area standard flux is calculated based on each trajectory segment as basic data, the trajectory segment is further divided according to the maximum optical thickness, and the trajectories located at the tail end of the divided segment are counted using the coarse grid; then, according to the coarse grid type 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, and the trajectories located at the coarse grid vertices and edges are subsequently split into each coarse grid surface.

[0013] Preferably, the three-level coarse mesh finite difference method is used to perform multiple coarsening acceleration calculations on energy groups and geometric structures, specifically including the following contents:

[0014] A coarser coarse mesh is used to speed up the iterative calculation of the previous coarse mesh. The three-level grid coarsening degree is represented from small to large as multi-energy group cell-level grid, single energy group cell-level grid and single energy group component-level grid. Then, the coarse mesh finite difference equations of each level are constructed and solved using the successive super-relaxation iterative method.

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

[0016] Preferably, a system of equations of primary multi-energy group grid element-level coarse-grid finite difference is constructed, and the specific calculation method is as follows:

[0017] Calculation of the average flux in the coarse grid: Based on the characteristic line method transport scanning process, combined with the flux of each flat source area contained in the coarse grid, the average flux in the coarse grid is obtained by volume homogenization calculation. The corresponding calculation formula is:

[0018]

[0019] in, represents the average flux in the coarse grid; represents the average flux in the flat source area grid; V k represents the volume of the flat source region; the subscripts c, k, and g represent the energy groups used for the coarse grid, flat source region grid, and three-dimensional characteristic lines, respectively;

[0020] Calculation of homogenization of coarse grid sections: Perform homogenization processing on each section corresponding to each coarse grid. The corresponding calculation formula is:

[0021]

[0022] Among them, ∑ t,c,g and∑ t,k,g They represent the total cross section of the coarse grid and the total cross section of the flat source region grid under the energy group respectively;

[0023] Calculation of uniform diffusion coefficient corresponding to the coarse grid: Before calculating the neutron flux between adjacent coarse grid surfaces, first calculate and obtain the uniform diffusion coefficient corresponding to the coarse grid. The corresponding calculation formula is:

[0024]

[0025] Among them, D c,g represents the internal diffusion coefficient of the coarse network under this energy group;

[0026] The calculation formulas for the effective diffusion coefficient, the net flow term on the coarse grid surface and the neutron flux correction coefficient are as follows:

[0027]

[0028] in, represents the effective diffusion coefficient; represents the net flow term on the coarse grid surface; Indicates the neutron flux correction factor; W c and W c+1 Respectively represent the current coarse grid centroid and the current next adjacent grid to Distance of the surface;

[0029] The calculation formula of the coarse mesh finite difference module is:

[0030]

[0031] 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 grid calculation; χ c,g represents the coarse grid neutron fission energy spectrum; k eff represents the effective neutron multiplication factor; v represents the average number of neutrons emitted by a single fission; Σ f,c,g represents the fission cross section of the coarse mesh; ∑ s,c,g represents the scattering cross section of the coarse mesh.

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

[0033] The calculation of the flux of one energy group by condensing the average flux of multiple groups in the coarse grid is calculated as follows:

[0034]

[0035] Wherein, the subscript e represents the coarsened coarse-grid finite difference single energy group unit; G represents the number of all characteristic line energy groups;

[0036] The calculation of the surface net flow term of the condensation of multiple groups of neutron flows in the coarse grid into one energy group is calculated as follows:

[0037]

[0038] The calculation formula for the effective diffusion coefficient and the corrected diffusion coefficient of the grid element-level condensed energy group in the coarse grid is:

[0039]

[0040] in, represents the effective diffusion coefficient of the cell-level condensed energy group in the coarse grid; represents the corrected diffusion coefficient.

[0041] Preferably, the three-level single energy group component-level coarse-grid finite difference is used to accelerate the calculation of the two-level single energy group cell-level coarse-grid finite difference, and the specific calculation method is as follows:

[0042] The calculation of flux condensation of coarse-grid finite difference at the single energy group component level is as follows:

[0043]

[0044] in, Flux representing the coarse-grid finite difference at the component level of a single energy group Represents the component-level coarse-grid differential grid, Indicates the coarse mesh volume of the component;

[0045] The calculation formula for the surface net flow term of the coarse mesh finite difference at the single energy group component level is:

[0046]

[0047] in, The surface net flow term represents the coarse-grid finite difference at the level of the single energy group component; represents the surface area at the component level;

[0048] The calculation formula for the total cross section of the coarse mesh finite difference at the single energy group component level is:

[0049]

[0050] in, represents the total cross section of the coarse-grid finite difference at the component level of a single energy group;

[0051] The calculation formula for the effective diffusion coefficient and the corrected diffusion coefficient of the coarse-grid finite difference at the single-energy group component level is:

[0052]

[0053] in, represents the effective diffusion coefficient of the coarse-grid finite difference at the component level of the single energy group; represents the corrected diffusion coefficient of the coarse-grid finite difference at the component level of the single energy group; and Represents the component-level coarse grid centroid and the current next adjacent grid to the surface distance.

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

[0055] The flux obtained by accelerating the solution of the first-level coarse grid through the second-level and third-level coarse grids is used to update the flux of the flat source area contained in it, providing a more convergent flux for the iteration of the characteristic line method. The corresponding calculation formula is:

[0056]

[0057] in, It represents the flux obtained by accelerating the solution of the first-level coarse grid through the second-level and third-level coarse grids; Represents a more converged flux after the update.

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

[0059] The present invention proposes a three-level coarse-grid finite difference acceleration method under the domestic DCU architecture. In the transport scanning stage, according to the coarse-grid points, edges and faces to which the trajectory segment belongs, the neutron flow on the coarse-grid surface of the trajectory segment is counted; the characteristic line three-dimensional characteristic line transport solution calculation results are transferred to the three-level coarse-grid finite difference solution module, wherein the three-level coarse-grid finite difference performs multiple coarsening acceleration calculations on the energy group and the geometric structure, and is divided into a first-level multi-energy group grid element level coarse grid, a second-level single energy group grid element level coarse grid and a third-level single energy group component level coarse grid, and then constructs a coarse-grid finite difference equation group of each level, and uses the successive super-relaxation iteration method to solve; finally, according to the three-level coarse-grid finite difference calculation results, the flux of each flat source area is updated, and the effective neutron multiplication factor in the current iteration is calculated. Under the premise of ensuring the calculation accuracy, the present invention can further improve the parallelism of the characteristic line method and the coarse-grid finite difference method by using the domestic DCU, and use the three-level coarse-grid finite difference method to reduce the scale of the coarse-grid matrix, further reduce the number of iterations, and improve the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0061] Figure 2 It is a schematic diagram of accelerating the three-dimensional characteristic line transport solution of the characteristic line method using the three-level coarse grid finite difference method under the multi-grid concept proposed in Example 1 of the present invention;

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

[0063] Figure 4 Schematic diagram of the coarsening of the three-level coarse mesh finite difference in the geometric structure (radial and axial directions) proposed in Example 1 of the present invention;

[0064] Figure 5 A schematic diagram of sub-flow splitting in a trajectory at a vertex of a coarse grid proposed in Example 1 of the present invention;

[0065] Figure 6 A schematic diagram of subflow splitting in a trajectory at the edge of a coarse grid proposed in Example 1 of the present invention;

[0066] Figure 7 It is a schematic diagram of the coarse grid and the flat source area proposed in Example 1 of the present invention on a radial plane;

[0067] Figure 8 Schematic diagram of net neutron flow between the coarse grid c and adjacent surfaces in the x and y directions proposed in Example 1 of the present invention. DETAILED DESCRIPTION

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

[0069] In order to better understand the present invention, the terms involved in the present invention are briefly explained as follows:

[0070] 1) Trajectory

[0071] In the three-dimensional characteristic line method, the trajectory refers to the movement path of the neutron in a specific direction within the computational domain. The trajectory converts the continuous neutron motion process into a discrete computational problem by discretizing the neutron transport equation.

[0072] 2) Pingyuan District

[0073] The flat source region refers to a small area divided in the computational domain. In this region, the neutron source intensity is uniform from the characteristic line entering the flat source region to leaving it, that is, the source term is constant. This means that in this region, the neutron source term is regarded as a constant rather than a function that varies with spatial position. It is also called the flat source approximation.

[0074] 3) Cross section

[0075] In the characteristic line method, the 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 assumed that the material properties in each flat source region are constants. i FSR i In the analysis, the cross sections are averaged by area. The cross sections that are more 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.

[0076] 4) Coarse grid

[0077] A coarse grid refers to a three-dimensional geometric grid created using the constructive solid geometry method. The coarse grid is composed of half-space intersection and complement operations constructed by multiple planes such as the X plane, Y plane, and Z plane. Each coarse grid structure corresponding to the coarse grid finite difference method has properties such as vertices, edges, and faces.

[0078] 5) Pin Cell

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

[0080] 6) Assembly

[0081] An assembly is a larger unit composed of multiple cells, usually corresponding to a fuel assembly or part of a fuel assembly. A fuel assembly contains multiple cells arranged in a specific geometric shape, and the reactor core is composed of multiple such assemblies. Component-level calculations are performed on the basis of cell-level data, by merging the detailed information of multiple cells to obtain the distribution of physical quantities on a larger scale.

[0082] 7) Net surface flow

[0083] The surface net flow term refers to the net flow of neutrons passing through the boundary of the computational coarse grid unit. It is the difference between the neutron flow out of and into the computational unit, and is usually used to measure the net transmission of neutrons between different computational units.

[0084] Based on the above content, the present invention proposes a three-level coarse network finite difference acceleration method for the domestic DCU architecture, please refer to Figure 1 , the present invention includes the following contents:

[0085] In the three-dimensional feature line transport scanning stage, the computing task is sent to the device end (domestic DCU) according to the domain decomposition method. In the DCU, the neutron flow on the coarse grid surface to which the trajectory segment belongs is stored according to the coarse grid vertices, edges and faces to which the trajectory segment belongs, and the neutron flow at the boundary of the communication domain that needs data transmission is stored;

[0086] The calculation results of the characteristic line three-dimensional characteristic line transport solution are transferred to the three-level coarse-grid finite difference solution module, wherein the three-level coarse-grid finite difference method performs multiple coarsening acceleration calculations on the energy group and the geometric structure, that is, a coarse grid with a higher degree of coarsening is used to accelerate the iterative calculation of the previous level of coarse grid. The three-level grid coarsening degree is represented from small to large as a multi-energy group grid element level grid, a single energy group grid element level grid and a single energy group component level grid. Then, a coarse-grid finite difference equation group of each level is constructed and solved using a successive super-relaxation iteration method.

[0087] According to the three-level coarse-grid finite-difference calculation results, the flux of each flat source region is updated and the effective neutron multiplication factor in the current iteration is calculated.

[0088] In the three-dimensional characteristic line transport scanning stage, the calculation task is sent to the device end (domestic DCU) according to the domain decomposition method. In the DCU, according to the coarse grid vertices, edges and faces to which the trajectory segment belongs, the neutron flow on the coarse grid surface to which the trajectory segment belongs is stored, and the neutron flow at the boundary of the communication domain that needs data transmission is stored; the calculation results of the characteristic line three-dimensional characteristic line transport solution are passed to the three-level coarse grid finite difference solution module, and then the coarse grid finite difference equations of each level are constructed and solved using the successive super relaxation iteration method; finally, according to the three-level coarse grid finite difference calculation results, the flux of each flat source area is updated, and the effective neutron multiplication factor in the current iteration is calculated. In this way, under the premise of ensuring the calculation accuracy, the domestic DCU can be used to further improve the parallelism of the characteristic line method and the coarse grid finite difference method, and the three-level coarse grid finite difference method can be used to reduce the scale of the coarse grid matrix and further reduce the number of iterations, thereby improving the calculation efficiency.

[0089] In this embodiment, when constructing a three-level coarse-mesh finite difference solution module, the three-dimensional characteristic line transport solution calculation results are passed to the three-level coarse-mesh finite difference solution module, wherein the second-level single-energy group element-level coarse-mesh is a coarsening of the first-level multi-energy group element-level in terms of energy group, and the amount of calculation is further reduced by merging the first-level coarse-mesh cross-section and diffusion parameters in advance; the third-level single-energy group component-level coarse-mesh is a coarsening of the second-level single-energy group element-level coarse-mesh in terms of geometric structure to reduce the size of the coarse-mesh matrix; the second-level single-energy group element-level coarse-mesh and the third-level single-energy group component-level coarse-mesh with higher mesh coarsening can respectively accelerate the iteration speed of the previous level, thereby improving the overall solution efficiency.

[0090] In this embodiment, the coarse-grid finite difference is an accelerated method for solving three-dimensional characteristic line transport based on the multi-grid concept. Its main process is divided into coarsening and extension. In the coarsening process, the equivalence theory is used to ensure that the solution of the coarse grid is consistent with the solution of the characteristic line, and the fine grid flux, cross section, etc. in the characteristic line method are coarsened to the coarse grid. In the extension process, by solving the coarse grid transport equation, the coarse grid calculation results are used to update the fine grid flux and other data. 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, each trajectory segment is used as the basic data to calculate the standard flux of each flat source area. The trajectory segment needs to be further divided according to the maximum optical thickness, and the coarse grid only counts the trajectory located at the end of the segment. According to the coarse grid type corresponding to the trajectory segment, the trajectory belonging to the coarse grid surface and the trajectory belonging to the coarse grid vertex and edge are stored separately. The trajectory located at the coarse grid vertex and edge will be split into each coarse grid surface later.

[0102] In this embodiment, the sub-flow splitting method of vertex and edge trajectories is:

[0103] A1. For the neutron flow in the trajectory located at the vertex of the coarse grid, according to the geometric position of the vertex and the cube geometry, there are 8 types of vertices. The neutron flow in the vertex is split into 3 adjacent edges, and the neutron flow in the adjacent edge is one third of the neutron flow in the original vertex. This splitting method corresponds to Figure 5 Content shown.

[0104] A2. For the trajectory neutron flow of the coarse grid edge and the edge neutron flow after splitting in A1, there are 12 edge types according to the cube geometry. According to the coarse grid position and boundary conditions, the edge neutron flow is split into two adjacent faces, and the neutron flow of the adjacent face is half of the original edge neutron flow. This splitting method corresponds to Figure 6 Content shown.

[0105] A3. Superimpose the split neutron fluxes onto their corresponding coarse grid surfaces to achieve neutron flux statistics and storage.

[0106] In this embodiment, the variables required for constructing the coarse-grid finite difference equations at the level of the first-level multi-energy group grid element are mainly calculated by the following method:

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

[0108]

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

[0110]

[0111] Where c represents the coarse grid in the coarse grid finite difference method, g represents the one-to-one correspondence between a certain energy group in the coarse grid and the characteristic line energy group, k represents the flat source area k contained in the coarse grid c, represents the average flux of the coarse grid c energy group g calculated by the characteristic line method, represents the average flux corresponding to the flat source region k energy group g, V k Represents the volume of the flat source region k.

[0112] B3. Before calculating the neutron flux between adjacent coarse grid surfaces, it is necessary to first calculate the uniform diffusion coefficient corresponding to the coarse grid. The corresponding calculation formula is:

[0113]

[0114] B4. Obtain the uniform diffusion coefficient D corresponding to each coarse grid c energy group g c,e , it is necessary to calculate the net neutron flux, effective diffusion coefficient and neutron flux correction coefficient between the coarse grid c and the adjacent surface in the three directions of x, y and z. The net neutron flux between the coarse grid c and the adjacent surface in the x and y directions is calculated as follows:

[0115]

[0116] in, Indicates that the coarse grid c and the adjacent grid c+1 are on the adjacent surface The effective diffusion coefficient at Indicates that the coarse grid c and the adjacent grid c+1 are on the adjacent surface Neutron flux correction factor at .

[0117] Net neutron flow between the coarse grid c and adjacent surfaces in the x and y directions Figure 8 shown.

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

[0119]

[0120] The equation form corresponding to the coarse-grid 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 number of corresponding coarse grid energy groups. After simplification, the corresponding coarse grid finite difference equation is:

[0123]

[0124] In this embodiment, the secondary single energy group grid element level coarse mesh finite difference method aims to construct a single energy group linear system consistent with the primary coarse mesh linear system, and calculate the single group linear system to update the multi-group flux and eigenvalue. Its basic principle is to use multi-group flux, multi-group neutron flow, and multi-group cross section to condense the flux, neutron flow and cross section of an energy group. The main calculation methods include:

[0125] C1. The average flux of multiple groups in the coarse grid condenses the flux of an energy group, and the corresponding calculation formula is:

[0126]

[0127] Wherein, the subscript e represents the coarsened coarse-grid finite difference single energy group unit, and G represents the number of all characteristic line energy groups.

[0128] C2. The surface net flow term flow of multiple groups of neutron flows in the coarse grid condenses into one energy group, and the corresponding calculation formula is:

[0129]

[0130] C3. The cross-section data of multiple groups in the coarse grid are condensed into a cross-section data of one energy group, and the corresponding calculation formula is:

[0131]

[0132] Diffusion coefficient and effective diffusion coefficient of the grid-level condensed energy group in the coarse grid and corrected diffusion coefficient The corresponding calculation formula is:

[0133]

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

[0135]

[0136] in, represents the average flux of the coarse grid calculated by the coarse grid finite difference after the second-level energy group compression, It represents the average flux of the single energy group coarse grid calculated by accumulating the data of the first coarse grid. represents the average flux of the coarse grid calculated by the first-level coarse grid finite difference, It represents the average flux of the single energy group cell level coarse grid after the second-level coarse grid iterative update.

[0137] In this embodiment, the grid cell coarse grid unit matrix is ​​too large, and the single energy group grid cell coarse grid has the potential for further acceleration. The component level coarse grid is directly used to accelerate the iterative solution of the characteristic line. Although it is beneficial to reduce the size of the coarse grid matrix, the component level coarse grid is not as effective as the grid cell level coarse grid in reducing the number of iterations of the three-dimensional characteristic line transport solution. It is not suitable for directly accelerating the transport calculation. It can be used as a third-level coarse grid to accelerate the second-level single energy group grid cell level coarse grid calculation. The main calculation methods include:

[0138] D1. Flux of coarse-grid finite difference at the component level of a single energy group Condensation, the corresponding calculation formula is:

[0139]

[0140] in, Represents the component-level coarse-grid differential grid, Indicates the coarse mesh volume of the component.

[0141] D2. Surface net flow term of coarse mesh finite difference at the component level of single energy group The corresponding calculation formula is:

[0142]

[0143] in, Represents the surface area at the component level.

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

[0145]

[0146]

[0147] D4. Diffusion coefficient and effective diffusion coefficient of coarse-grid finite difference at the component level of single energy group and corrected diffusion coefficient The corresponding calculation formula is:

[0148]

[0149] in, and Represents the component-level coarse grid centroid and the current next adjacent grid to the surface distance.

[0150] Use the single energy group cell level coarse mesh data to construct the single energy group component level coarse mesh finite difference equation, and then the single energy group component level coarse mesh is used to accelerate the update of the single energy group cell level coarse mesh finite difference flux:

[0151]

[0152] in, represents the average flux of the coarse grid calculated by the third-level geometric compression coarse grid finite difference, It represents the average flux of the component-level coarse grid calculated by accumulating the data of the second-level coarse grid. represents the average flux of the coarse grid calculated by the secondary coarse grid finite difference method, It represents the average flux of the single energy group cell level coarse grid after three-level coarse grid iterative 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 is It will be used to update the flux of the flat source region it contains, thereby providing a more convergent flux for the iteration of the characteristic line method. Its main calculation form is:

[0154]

[0155] in, It 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, It represents the average flux corresponding to the coarse grid c energy group g obtained using the three-dimensional characteristic line data, where k∈c.

[0156] In this embodiment, the C5G7 benchmark is used as an example to perform three-level coarse mesh finite difference acceleration effects. Tests have shown that the three-level coarse mesh finite difference calculation method proposed in the present invention can reduce the size of the coarse mesh matrix while ensuring accuracy, further reduce the number of iterations of the three-dimensional characteristic line method, and improve the overall calculation efficiency.

[0157] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A three-level coarse-net finite difference acceleration method under a domestic DCU architecture, characterized in that: It includes the following: In the three-dimensional feature line transport scanning stage, the computing task is sent to the device end according to the domain decomposition method. In the device end, the neutron flow on the coarse grid surface to which the trajectory segment belongs and the neutron flow at the boundary of the communication domain that needs data transmission are stored according to the coarse grid vertices, edges and faces to which the trajectory segment belongs. The calculation results of the three-dimensional characteristic line transport solution of the characteristic line 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 on the energy group and geometric structure; According to the three-level coarse-grid finite-difference calculation results, the flux of each flat source region is updated and the effective neutron multiplication factor in the current iteration is calculated.

2. According to the three-level coarse network finite difference acceleration method under the domestic DCU architecture according to claim 1, it is characterized in that: In the transport scanning stage, each trajectory segment is used as the basic data to calculate the standard flux of each flat source area, and the trajectory segment is further divided according to the maximum optical thickness. The coarse grid is used to count the trajectories located at the end of the divided segment; then, according to the coarse grid type 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, and the trajectories located at the coarse grid vertices and edges are subsequently split into each coarse grid surface.

3. According to claim 1, a three-level coarse-net finite difference acceleration method under a domestic DCU architecture is characterized in that: The three-level coarse mesh finite difference method is used to perform multiple coarsening acceleration calculations on energy groups and geometric structures, specifically including the following contents: A coarser coarse mesh is used to speed up the iterative calculation of the previous coarse mesh. The three-level grid coarsening degree is represented from small to large as multi-energy group cell-level grid, single energy group cell-level grid and single energy group component-level grid. Then, the coarse mesh finite difference equations of each level are constructed and solved using the successive super-relaxation iterative method.

4. According to claim 3, a three-level coarse-net finite difference acceleration method under a domestic DCU architecture is characterized in that: In the three-level coarse-grid finite difference method, the first-level multi-energy group element-level coarse-grid finite difference is used to accelerate the solution of three-dimensional characteristic line transport, the second-level single-energy group element-level coarse-grid finite difference and the third-level single-energy group component-level coarse-grid finite difference are used to accelerate the iteration speed of the previous level respectively, so as to improve the overall solution efficiency.

5. According to the three-level coarse network finite difference acceleration method under the domestic DCU architecture according to claim 4, it is characterized in that: Construct a set of equations for the first-level multi-energy group grid element-level coarse-grid finite difference. The specific calculation method is as follows: Calculation of the average flux in the coarse grid: Based on the characteristic line method transport scanning process, combined with the flux of each flat source area contained in the coarse grid, the average flux in the coarse grid is obtained by volume homogenization calculation. The corresponding calculation formula is: in, represents the average flux in the coarse grid; represents the average flux in the flat source area grid; V k represents the volume of the flat source region; the subscripts c, k, and g represent the energy groups used for the coarse grid, flat source region grid, and three-dimensional characteristic lines, respectively; Calculation of homogenization of coarse grid sections: Perform homogenization processing on each section corresponding to each coarse grid. The corresponding calculation formula is: Among them, ∑ t,c,g and∑ t,k,g They represent the total cross section of the coarse grid and the total cross section of the flat source region grid under the energy group respectively; Calculation of uniform diffusion coefficient corresponding to the coarse grid: Before calculating the neutron flux between adjacent coarse grid surfaces, first calculate and obtain the uniform diffusion coefficient corresponding to the coarse grid. The corresponding calculation formula is: Among them, D c,g represents the internal diffusion coefficient of the coarse network under this energy group; The calculation formulas for the effective diffusion coefficient, the net flow term on the coarse grid surface and the neutron flux correction coefficient are as follows: in, represents the effective diffusion coefficient; represents the net flow term on the coarse grid surface; Indicates the neutron flux correction factor; W c and W c+1 Respectively represent the current coarse grid centroid and the current next adjacent grid to Distance of the surface; The calculation formula of the coarse mesh finite difference module 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 grid calculation; χ c,g represents the coarse grid neutron fission energy spectrum; k eff represents the effective neutron multiplication factor; v represents the average number of neutrons emitted by a single fission; Σ f,c,g represents the fission cross section of the coarse mesh; ∑ s,c,g represents the scattering cross section of the coarse mesh.

6. The three-level coarse-net finite difference acceleration method under the domestic DCU architecture according to claim 5 is characterized in that: The secondary single energy group grid element level coarse mesh finite difference is used to construct a single energy group linear system consistent with the primary 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: The calculation of the flux of one energy group by condensing the average flux of multiple groups in the coarse grid is calculated as follows: Wherein, the subscript e represents the coarsened coarse-grid finite difference single energy group unit; G represents the number of all characteristic line energy groups; The calculation of the surface net flow term of the condensation of multiple groups of neutron flows in the coarse grid into one energy group is calculated as follows: The calculation formula for the effective diffusion coefficient and the corrected diffusion coefficient of the grid element-level condensed energy group in the coarse grid is: in, represents the effective diffusion coefficient of the cell-level condensed energy group in the coarse grid; represents the corrected diffusion coefficient.

7. The three-level coarse-net finite difference acceleration method under the domestic DCU architecture according to claim 6 is characterized in that: The three-level single energy group component-level coarse-grid finite difference is used to accelerate the calculation of the two-level single energy group grid element-level coarse-grid finite difference. The specific calculation method is as follows: The calculation of flux condensation of coarse-grid finite difference at the single energy group component level is as follows: in, Flux representing the coarse-grid finite difference at the component level of a single energy group Represents the component-level coarse-grid differential grid, Indicates the coarse mesh volume of the component; The calculation formula for the surface net flow term of the coarse mesh finite difference at the single energy group component level is: in, The surface net flow term represents the coarse-grid finite difference at the level of the single energy group component; represents the surface area at the component level; The calculation formula for the total cross section of the coarse mesh finite difference at the single energy group component level is: in, represents the total cross section of the coarse-grid finite difference at the component level of a single energy group; The calculation formula for the effective diffusion coefficient and the corrected diffusion coefficient of the coarse-grid finite difference at the single-energy group component level is: in, represents the effective diffusion coefficient of the coarse-grid finite difference at the component level of the single energy group; represents the corrected diffusion coefficient of the coarse-grid finite difference at the component level of the single energy group; and Represents the component-level coarse grid centroid and the current next adjacent grid to the surface distance.

8. The three-level coarse-net finite difference acceleration method under the domestic DCU architecture according to claim 7 is characterized in that: The method of updating the flux of each flat source region and calculating the effective neutron multiplication factor in the current iteration according to the three-level coarse-grid finite difference calculation results specifically refers to: The flux obtained by accelerating the solution of the first-level coarse grid through the second-level and third-level coarse grids is used to update the flux of the flat source area contained in it, providing a more convergent flux for the iteration of the characteristic line method. The corresponding calculation formula is: in, It represents the flux obtained by accelerating the solution of the first-level coarse grid through the second-level and third-level coarse grids; Represents a more converged flux after the update.

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