A method for accelerating neutron transport calculation of three-dimensional characteristic lines based on domestic DCU architecture

Abstract

The present invention provides a method for accelerating neutron transport calculation of a three-dimensional characteristic line of a domestic DCU architecture, and belongs to the field of high-performance computing technology. The method includes: constructing uniform / non-uniform coarse-mesh finite difference grid geometric modeling according to the reactor geometric modeling and domain decomposition structure; in the trajectory generation and trajectory segmentation stage, recording the relationship between the flat source area and the coarse-mesh grid and the coarse-mesh grid and the communication domain, storing the trajectory segments reaching the vertices, edges and faces of the coarse-mesh grid, storing the trajectory segments located at the domain boundary, recording the trajectory connection sequence between adjacent communication domains, and the coarse-mesh grid surface adjacency relationship; in the transport scanning stage, according to the domain decomposition structure, sending the calculation task to the device end, storing the neutron flow on the surface of the coarse-mesh grid to which the trajectory segment belongs according to the coarse-mesh grid points, edges and faces to which the trajectory segment belongs, and storing the neutron flow at the communication domain boundary that needs information transmission; transmitting the transport solution calculation result to the coarse-mesh finite difference solution module, constructing a coarse-mesh finite difference equation group and solving it using the successive super-relaxation iteration method, updating the flux of each flat source area according to the calculation result and calculating the effective neutron multiplication factor in the current iteration.

Description

Technical Field

[0001] The present invention relates to the field of high performance computing technology, and in particular to a method for accelerating neutron transport calculations using a three-dimensional characteristic line of a domestic DCU architecture. Background Art

[0002] Compared with the high cost of nuclear tests, the use of supercomputing platforms for nuclear reactor numerical simulation has become one of the main experimental methods in the field of modern nuclear engineering. Using numerical simulation to calculate the power distribution of the reactor core at a specific time is one of the main goals of reactor numerical simulation. This type of problem is collectively referred to as the steady-state neutron transport problem.

[0003] For solving the problem of steady-state neutron transport, that is, solving the linear Boltzmann equation, various solutions have been derived in related fields at home and abroad. Among them, the most widely used and highly recognized methods are mainly the Monte Carlo (MC) method based on statistical experimental methods and the deterministic method. Using the deterministic method to solve the steady-state neutron transport equation usually requires discretization of energy groups and space. The most commonly used methods in the early days were the discrete ordinate method and the spherical harmonic function method, but the above methods have limitations when facing reactors with complex geometric structures. Due to the limitation of computing power in the early days, the method of characteristics (MOC) was not widely used in reactor numerical simulation. In recent years, with the support of the powerful computing power of supercomputing platforms, and the advantages of the method of characteristics itself in numerical accuracy, geometric adaptability, and potential parallelism, it has been widely used to solve the neutron transport equation under pressurized water reactors, sodium-cooled fast reactors and other special reactor types.

[0004] The high-precision three-dimensional characteristic line neutron transport calculation of the whole core can be supported by the powerful computing power of the supercomputing platform to perform pin-by-pin level precision three-dimensional full-core simulation. The high-precision characteristic line method requires fine grid division and dense characteristic line generation to support it, and the demand for computing and storage is also increasing. In order to improve the computing efficiency and the utilization of supercomputing resources, trajectory decomposition, domain decomposition, shared memory, axial extrusion, linear source approximation and other technologies are used to improve the computing efficiency.

[0005] In solving the steady-state neutron transport equation, the characteristic line method needs to achieve the target accuracy, that is, the convergence error is less than a certain threshold, and hundreds or even thousands of iterations are required. This is unacceptable in the engineering field, so some methods are needed to accelerate the iterative solution of the steady-state neutron transport equation. Coarse Mesh Finite Difference (CMFD) is an iterative acceleration method for the neutron transport equation 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 coarsen the fine grid flux, cross section, etc. in the characteristic line method to the coarse grid. 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.

[0006] At the same time, in order to solve some special cases in BEAVRS, such as the small water gaps between radial components and the inconsistent heights of axial grid element spacers, if the uniform coarse mesh finite difference grid is still used, the coarse mesh boundary cannot fit the flat source domain boundary, resulting in the flat source area being cut at the coarse mesh boundary, thus affecting the calculation accuracy. Summary of the invention

[0007] The purpose of the present invention is to propose a three-dimensional characteristic line neutron transport calculation acceleration method for a domestic DCU architecture to solve the problems raised in the background technology; under the premise of ensuring the calculation accuracy, the present invention uses the domestic DCU to further improve the parallelism between the characteristic line method and the coarse-grid finite difference method, improves the convergence speed of the three-dimensional characteristic line method and reduces the number of iterations and calculation time, and at the same time, through the non-uniform coarse-grid finite difference method, it is particularly suitable for processing special reactor geometric structures with inconsistent reactor radial component spacing and axial grid element spacers.

[0008] In order to achieve the above object, the present invention adopts the following technical solutions:

[0009] A method for accelerating neutron transport calculation of three-dimensional characteristic lines of a domestic DCU architecture, the method comprising the following steps:

[0010] According to the reactor geometry modeling and domain decomposition structure, uniform / non-uniform coarse mesh finite difference grid geometry modeling is constructed;

[0011] In the trajectory generation and trajectory segmentation stage, the relationship between the flat source area and the coarse mesh and between the coarse mesh and the communication domain is recorded, the trajectory segments reaching the vertices, edges and faces of the coarse mesh are stored, the trajectory segments located at the domain boundary are stored, and the trajectory connection sequence between adjacent communication domains and the adjacency relationship of the coarse mesh surface are recorded;

[0012] In the transport scanning stage, the computing tasks are sent to the device side (domestic DCU) according to the domain decomposition structure. In the device side, the neutron flow on the coarse mesh surface of the trajectory segment is stored according to the coarse mesh points, edges and faces to which the trajectory segment belongs, and the neutron flow at the boundary of the communication domain that needs to be transmitted is stored;

[0013] The transport solution calculation results are transferred to the coarse-grid finite difference solution module, and the coarse-grid finite difference equation system is constructed and solved using the successive super-relaxation iteration method;

[0014] According to the 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.

[0015] Preferably, the uniform / non-uniform coarse-grid finite difference geometric modeling method is constructed based on the reactor geometric modeling and domain decomposition structure, and specifically includes the following contents:

[0016] For different reactor geometry types, choose to use uniform or non-uniform geometry partitioning: for examples such as C5G7 and Takeda, where the geometry modeling is relatively uniform in the radial plane and the axial direction, a uniform coarse-mesh finite difference grid is constructed; for special problems in light water reactors, such as non-uniform fuel assemblies, thin water gaps between assemblies, and axial grids of different heights, a non-uniform coarse-mesh finite difference grid is constructed.

[0017] Preferably, in the trajectory generation and trajectory segmentation stage, the relationship between the flat source area and the coarse mesh and between the coarse mesh and the communication domain is recorded, and the trajectory segments reaching the vertices, edges and faces of the coarse mesh are stored, which specifically includes the following contents:

[0018] In the three-dimensional trajectory segment generation stage, the lengths of the trajectory segments of each axial layer at the same starting point are counted, the shortest trajectory segment is selected and a keyword corresponding to the flat source area is generated, and the X, Y, and Z numbers corresponding to the coarse mesh grid are added to the keyword;

[0019] For a trajectory segment whose starting point or end point is located at a vertex / edge / face of a coarse mesh, the number corresponding to the vertex, edge or face of the coarse mesh is added to the storage information of the current trajectory segment;

[0020] After the trajectory segmentation is completed, the flat source areas are renumbered and sorted according to the axial order of each trajectory segment in the trajectory chain, and the mapping record between the flat source area and the coarse mesh is completed. The mapping method satisfies:

[0021] Assume that the non-empty set FSR {fsr1, fsr2, ..., fsr n} and the non-empty set CMFD{cell1, cell2, ..., cell m}, each coarse grid cell contains at least one flat source region fsr, that is, there is a one-to-one mapping or many-to-one mapping between FSR and CMFD.

[0022] Preferably, the storage of the track segments located at the domain boundary, recording the track connection sequence between adjacent communication domains, and the coarse mesh surface adjacency relationship specifically includes the following contents:

[0023] After domain decomposition, when obtaining the number corresponding to the coarse network grid, the global number of the coarse network grid is converted into a local number in the communication domain according to the communication domain where the coarse network grid is located.

[0024] Preferably, the transport scanning stage specifically includes the following contents:

[0025] In the transport scanning stage, the standard flux of each flat source area is calculated based on each trajectory segment. The trajectory segment is further divided according to the maximum optical thickness, and the coarse mesh only counts the trajectories located at the end of the divided segment. According to the coarse mesh type corresponding to the trajectory segment, the trajectories belonging to the coarse mesh surface and the trajectories belonging to the vertices and edges of the coarse mesh are stored separately, and the neutron flow in the trajectories located at the vertices and edges of the coarse mesh is split into each coarse mesh surface.

[0026] Preferably, the sub-flow splitting method of the vertex and edge trajectory specifically includes:

[0027] For the trajectory neutron flow at the vertex of the coarse mesh, it is necessary to split the trajectory neutron flow at the vertex into three adjacent edges according to the geometric position of the vertex. Taking the cube geometry as an example, there are 8 types of vertices, each of which has three different adjacent edges and adjacent faces. According to the position of the coarse mesh (at the edge of the reactor geometry / at the non-edge) and the boundary conditions of the coarse mesh (periodic boundary / reflection boundary / vacuum boundary), the neutron flow at the vertex is split into three adjacent edges, and the neutron flow at the adjacent edge is one third of the neutron flow at the original vertex.

[0028] The trajectory neutron flow originally located at the edge of the coarse mesh and the edge neutron flow after splitting are further split. Taking the cube geometry as an example, there are 12 edge types in total, and each edge has two different adjacent faces. Similarly, according to the location of the coarse mesh (at the edge of the reactor geometry / not at the edge) and the boundary conditions of the coarse mesh (periodic boundary / reflection boundary / vacuum boundary), the trajectory neutron flow at the edge is split into 2 adjacent faces, and the neutron flow of the adjacent face is half of the original edge neutron flow.

[0029] The neutron fluxes after the above splitting process are respectively superimposed on the corresponding coarse mesh surfaces to realize the statistics and storage of neutron fluxes on each surface of the coarse mesh.

[0030] Preferably, the transport solution calculation results are transferred to the coarse-mesh finite difference solution module, a coarse-mesh finite difference equation group is constructed and solved using the successive super-relaxation iteration method, which specifically includes the following contents: the variables required for constructing the coarse-mesh finite difference equation group, the specific calculation method includes:

[0031] Combined with the characteristic line method transport scanning process, the average flux in the coarse mesh is obtained by volume homogenization calculation through the flux of each flat source area contained in the coarse mesh. The corresponding calculation formula is:

[0032]

[0033] Where c represents a coarse grid in CMFD, e represents an energy group in the coarse grid, k represents the MOC flat source domain k contained in the CMFD coarse grid c, g represents a MOC energy group contained in the CMFD coarse grid energy group e, l represents the result after the lth iteration of ANT-MOC calculation, l mid It represents the intermediate form of CMFD between the lth iteration and the l+1th iteration. represents the average flux of CMFD coarse grid c energy group e calculated by MOC, represents the average flux corresponding to the MOC fine grid k energy group g, V k represents the volume of the fine grid flat source domain k;

[0034] Each section corresponding to each coarse mesh is homogenized accordingly. Taking the total section as an example, the calculation formula for the homogenization of the coarse mesh section is:

[0035]

[0036] in, represents the uniform total cross section of the coarse grid c energy group e, Σ t,k,g represents the total cross section of energy group g for the fine grid k; the scattering cross section corresponding to energy group e for the coarse grid c Fission cross section Fission spectrum distribution The calculation is also performed according to the volume homogenization method;

[0037] Before calculating the neutron flux between adjacent coarse mesh surfaces, the uniform diffusion coefficient corresponding to the coarse mesh is first calculated and obtained. The corresponding calculation formula is:

[0038]

[0039] The calculation formulas for the effective diffusion coefficient and the neutron flux correction coefficient are:

[0040]

[0041] The equation form corresponding to the coarse-grid finite difference module is:

[0042]

[0043] in, represents the uniform diffusion coefficient corresponding to each coarse grid c energy group e, 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 The neutron flux correction factor at represents the net neutron flow between the coarse grid c and the adjacent surface in the x, y, and z directions, w dir,c It represents the grid width of the coarse grid c in each direction of dir∈(x,y,z), and E represents the number of coarse grid energy groups corresponding to the coarsening of the MOC energy group.

[0044] Preferably, the method of updating the flux of each flat source region and calculating the effective neutron multiplication factor in the current iteration by using the coarse grid finite difference calculation results specifically includes the following contents: It is used to update the flux of the flat source area it contains, thereby providing a more convergent flux for the iteration of the characteristic line method. The calculation formula is:

[0045]

[0046] in, represents the scalar flux corresponding to the coarse grid c energy group e obtained by solving the CMFD transport equation, It represents the average flux corresponding to the fine grid k energy group g after CMFD update, where k∈c,g∈e.

[0047] Compared with the prior art, the present invention provides a method for accelerating neutron transport calculation of three-dimensional characteristic lines of a domestic DCU architecture, which has the following beneficial effects:

[0048] The present invention proposes a method for accelerating the calculation of neutron transport of three-dimensional characteristic lines of a domestic DCU architecture. According to the geometric modeling of the reactor, a uniform / non-uniform coarse-mesh finite difference grid geometric modeling is constructed; in the trajectory generation and trajectory segmentation stage, the relationship between the flat source area and the coarse grid is recorded, and the trajectory segments reaching the vertices, edges and faces of the coarse grid are recorded; in the transport scanning stage, the neutron flow on the surface of the coarse grid to which the trajectory segment belongs is counted according to the coarse grid points, edges and faces to which the trajectory segment belongs; the transport solution calculation results are transferred to the coarse-mesh finite difference solution module, a coarse-mesh finite difference equation group is constructed and solved using the successive super-relaxation iteration method, and the flux of each flat source area is updated according to the calculation results and the effective neutron multiplication factor in the current iteration is calculated. Using the above design, the present invention can further improve the parallelism of the characteristic line method and the coarse-mesh finite difference method by using the domestic DCU under the premise of ensuring the calculation accuracy, improve the convergence speed of the three-dimensional characteristic line method and reduce the number of iterations and calculation time, and at the same time, through the non-uniform coarse-mesh finite difference method, it is particularly suitable for processing the special reactor geometry structure with inconsistent radial component spacing and axial grid element spacers of the reactor. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of a method for accelerating neutron transport calculation of three-dimensional characteristic lines of a domestic DCU architecture proposed in Example 1 of the present invention;

[0050] Figure 2 It is a schematic diagram of accelerating the transport solution of the characteristic line method by the coarse-grid finite difference method under the multi-grid concept proposed in Example 1 of the present invention;

[0051] Figure 3 It is a schematic diagram of the reactor geometric domain decomposition and the coarse mesh structure proposed in Example 1 of the present invention;

[0052] Figure 4 Schematic diagram of the uneven coarse mesh proposed in Example 1 of the present invention;

[0053] Figure 5 This is a schematic diagram of a trajectory segment start point or end point located at a vertex / edge / surface of a coarse mesh proposed in Embodiment 1 of the present invention;

[0054] Figure 6 Schematic diagram of the mapping relationship between the flat source area and the coarse mesh grid proposed in Example 1 of the present invention;

[0055] Figure 7 A schematic diagram of sub-flow splitting in a trajectory at a vertex of a coarse mesh proposed in Example 1 of the present invention;

[0056] Figure 8 It is a schematic diagram of the sub-flow splitting schematic diagram of the trajectory at the edge of the coarse mesh proposed in Example 1 of the present invention;

[0057] Fig. 9It is a schematic diagram of the coarse mesh grid and the flat source area proposed in Example 1 of the present invention on a radial plane;

[0058] Fig.10 Schematic diagram of net neutron flow between the coarse mesh c and adjacent surfaces in the x and y directions proposed in Example 1 of the present invention. DETAILED DESCRIPTION

[0059] 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.

[0060] In order to better understand the present invention, the terms involved in the present invention are briefly explained as follows:

[0061] 1) Trajectory

[0062] A trajectory is a ray with start coordinates, end coordinates and direction (forward and backward), generated at a certain angle.

[0063] 2) Boundary conditions

[0064] There are three main types of boundary conditions: total reflection, periodicity, and vacuum; among them,

[0065] Total reflection: The incident ray and the reflected ray always intersect at the boundary, and the azimuth angles satisfy different angular relationships according to the hexagonal edges they intersect;

[0066] Period: The incident angle and the outgoing angle are the same, the two rays are parallel, one is considered outgoing and the other is considered incident, because each ray has two directions;

[0067] Vacuum: The incident flux is 0 and the outgoing flux is treated as a missing item.

[0068] 3) Track chain

[0069] A trajectory chain refers to a ray loop formed by connecting trajectories end to end under corresponding boundary conditions. For example, a trajectory chain formed under total reflection boundary conditions is called a reflective trajectory chain.

[0070] 4) Pingyuan District

[0071] The commonly used approximation of the characteristic line method is called the flat source region approximation (or flat source approximation). It is assumed that the source term is constant in a discrete space unit. In this case, this discrete space unit is called a flat source region (FSRs), which means that the source term does not change from entering the flat source region to leaving it along the characteristic line.

[0072] 5) Cross section

[0073] In the characteristic line method, in addition to the flat source approximation, it is also 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.

[0074] 6) Axial extrusion geometry

[0075] Ray tracing is performed simultaneously on different radial planes. The planes that have completed ray tracing are superimposed together to obtain a plane containing all radial information, called an overlapping plane. The 2D geometric part on the overlapping plane is equivalent to the axial extrusion area, which has a corresponding unique identifier. It contains an axial grid and an FSRs array.

[0076] 7) Coarse mesh

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

[0078] Based on the above content, a three-dimensional characteristic line neutron transport calculation acceleration method for a domestic DCU architecture proposed in the present invention is described below with reference to specific examples.

[0079] Embodiment 1:

[0080] See also Figure 1 This embodiment proposes a method for accelerating neutron transport calculation of three-dimensional characteristic lines of a domestic DCU architecture, including:

[0081] According to the reactor geometry modeling and domain decomposition structure, uniform / non-uniform coarse mesh finite difference grid geometry modeling is constructed;

[0082] In the trajectory generation and trajectory segmentation stage, the relationship between the flat source area and the coarse mesh and between the coarse mesh and the communication domain is recorded, the trajectory segments reaching the vertices, edges and faces of the coarse mesh are stored, the trajectory segments located at the domain boundary are stored, and the trajectory connection sequence between adjacent communication domains and the adjacency relationship of the coarse mesh surface are recorded;

[0083] In the transport scanning stage, the computing tasks are sent to the device end (domestic DCU) according to the domain decomposition structure. In the domestic DCU, the neutron flow on the coarse mesh surface of the trajectory segment is stored according to the coarse mesh points, edges and faces to which the trajectory segment belongs, and the neutron flow at the boundary of the communication domain that needs information transmission is stored;

[0084] The transport solution calculation results are transferred to the coarse-grid finite difference solution module, and the coarse-grid finite difference equation system is constructed and solved using the successive super-relaxation iteration method;

[0085] According to the 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.

[0086] A method for accelerating neutron transport calculation of a three-dimensional characteristic line of a domestic DCU architecture described in an embodiment of the present invention constructs uniform / non-uniform coarse-mesh finite difference grid geometric modeling according to reactor geometric modeling and domain decomposition structure; in the trajectory generation and trajectory segmentation stage, records the relationship between the flat source area and the coarse-mesh grid and the coarse-mesh grid and the communication domain, stores the trajectory segments reaching the vertices, edges and faces of the coarse-mesh grid, stores the trajectory segments located at the domain boundary, records the trajectory connection sequence between adjacent communication domains, and the coarse-mesh grid surface adjacency relationship; in the transport scanning stage, according to the domain decomposition structure, sends the calculation task to the device end (domestic DCU), and in the domestic DCU, stores the neutron flow on the surface of the coarse-mesh grid to which the trajectory segment belongs according to the coarse-mesh grid points, edges and faces to which the trajectory segment belongs, and stores the neutron flow at the communication domain boundary that needs information transmission; transmits the transport solution calculation result to the coarse-mesh finite difference solution module, constructs a coarse-mesh finite difference equation group and solves it using the successive super-relaxation iteration method, updates the flux of each flat source area according to the calculation result, and calculates the effective neutron multiplication factor in the current iteration. In this way, under the premise of ensuring the calculation accuracy, the domestic DCU can be used to further improve the parallelism between the characteristic line method and the coarse-mesh finite difference method, improve the convergence speed of the three-dimensional characteristic line method and reduce the number of iterations and calculation time. At the same time, the non-uniform coarse-mesh finite difference method is particularly suitable for dealing with special reactor geometric structures with inconsistent reactor radial component spacing and axial grid element spacers.

[0087] In this embodiment, the coarse-grid finite difference acceleration method is a theoretical acceleration method based on the idea of ​​the multigrid method. The multigrid method is a common method in solving differential equations. Its principle is that the transmission speed of global information on the coarse-grid grid is faster than that on the fine-grid grid. The fine-grid grid in the characteristic line method refers to the flat source area. Using this principle, the equations to be solved are alternately solved in the coarse and fine grids. The coarse grid reduces the scale of solution and accelerates information transmission, while the fine grid ensures the calculation accuracy. In the three-dimensional characteristic line method, the coarse and fine grids need to be consistent when solving problems.

[0088] There are many structures of multi-grid methods, which generally involve two important steps, namely coarsening and extension. In the neutron transport problem, coarsening generally refers to transferring the calculation results of the fine grid to the coarse grid, while extension refers to the solution obtained through the coarse grid or to update the fine grid. Generally speaking, the multi-grid method can use grids of different scales to accelerate the calculation. In each layer, coarsening and extension will transfer the grid information to coarser and finer grids respectively. Two layers of grids are used in this patent, namely the fine grid calculated by the characteristic line method and the coarse grid used by the coarse grid finite difference method. There is an important difference between the coarse grid finite difference method and the multi-grid method, that is, in the coarse grid finite difference method, although the equation to be solved is consistent with the original problem, it essentially uses different equations to solve. Different from the characteristic line method's method of discretizing the trajectory angle space, the coarse grid finite difference method is based on the divergence theorem to describe the neutron transport equation. The neutron transport equation in this alternative form depends on the average quantity in each coarse grid grid, and is not related to the angular direction. Figure 2 A schematic diagram showing the coarse-grid finite difference acceleration of characteristic line method calculations based on the multi-grid concept is shown.

[0089] In this embodiment, the transport equation of the coarse-grid finite difference method needs to be obtained through the multi-energy group transport equation of the characteristic line method. First, the angular flux ψ in the transport equation of the characteristic line method needs to be g (r,Ω), into a transport equation in the form of a diffusion theorem, in order to convert it into a transport equation based on a scalar flux φ g (r) rather than the angular flux ψ g (r,Ω) form, it is necessary to integrate the entire characteristic line method transport equation in the angular space, and its form is:

[0090]

[0091] The angular flux in the 4π angular space is converted into the form of net neutron flow, which is expressed in the form of:

[0092]

[0093] After the above-mentioned form conversion and the introduction of the divergence theorem, the transport equation corresponding to the energy group e of the coarse mesh finite difference method grid c is:

[0094]

[0095] In this embodiment, according to the reactor geometry modeling and domain decomposition structure, uniform / non-uniform coarse mesh finite difference grid geometry modeling is constructed. For different reactor geometry types, uniform geometry partitioning or non-uniform geometry partitioning can be selected. In the reactor domain decomposition, the communication domain and the coarse mesh structure and DCU undertake the computing tasks in the domain. Figure 3 shown.

[0096] When performing transport calculations in the C5G7 benchmark example, the example geometry description files used all use a uniform distribution method, so the use of uniform coarse-mesh finite difference geometry modeling will not have any effect on the calculation results. However, in light water reactors, the arrangement of fuel assemblies is not completely uniform. For example, in BEAVRS, there are small water gaps between assemblies in the radial direction, and the heights of the grid element spacers in the axial direction are also different. In the face of the above situation, if the coarse mesh is still constructed in a uniform manner, the boundary of the coarse mesh will not be completely aligned with the boundary of the flat source area, causing some flat source areas to be cut by the coarse mesh boundary, thereby affecting the calculation accuracy. Therefore, in the face of the above-mentioned uneven construction of the reactor geometry, it is necessary to use non-uniform coarse-mesh finite difference geometry modeling to accelerate the transport calculation and ensure the accuracy of the calculation results.

[0097] Taking a single component, a grating pitch of 1.26cm, and a radial layout surrounded by a 0.5cm water gap as an example, the corresponding Figure 4 (a). If a uniform coarse mesh is used to divide the grid, the result after division is as follows Figure 4 As shown in (b), it can be seen from the figure that at the junction of the coarse mesh boundary and the flat source area, the flat source area will be cut by the coarse mesh boundary. Since the coarse mesh will not participate in the geometric construction of the reactor CSG, the flat source area passed by the coarse mesh boundary will be repeatedly calculated. After the introduction of non-uniform coarse mesh, the grid division method is as follows Figure 4 (c) shows that it avoids Figure 4 In the case of (b), the grid boundary is aligned with the flat source region boundary.

[0098] In this embodiment, in the trajectory generation and trajectory segmentation stage, the relationship between the flat source area and the coarse mesh is recorded, and the trajectory segment method of the points, edges and faces reaching the coarse mesh is recorded. In the three-dimensional trajectory segment generation stage, the length of each axial layer trajectory segment under the same starting point needs to be counted, the shortest trajectory segment is selected and the keyword corresponding to the flat source area is generated. The X, Y, and Z numbers corresponding to the coarse mesh need to be added to the keyword. The flat source area keyword, that is, the identification string, is generated as follows:

[0099] A flat source area is always associated with a local coordinate point. Once a local point finds its bottom-level Cell, it is constructed as a local point linked list. Each node in this linked list is at a certain level of constructed solid geometry, and it will save the pointer to the constructed solid geometry object at this level. If the intersection of all the constructed solid geometry objects corresponding to this linked list is calculated, a flat source area is obtained. Using this local point, an "identification string" (also called a keyword) is generated to uniquely identify each flat source area. In simple terms, the steps are as follows:

[0100] A1, take a local point and construct a linked list, each node corresponds to a certain layer of constructed entity geometry object (Universe / Lattice / Cell).

[0101] A2, put together the unique identifiers of the geometric objects of each layer of the local point to obtain a string, which uniquely identifies the flat source area where the point is located.

[0102] A3, adding the coarse grid number where the local point is located, that is, the X, Y, and Z coordinates corresponding to the coarse grid, to the identification string to form the flat source area identification string.

[0103] Therefore, a local point list corresponds to a flat source area (it is also the characteristic point of the flat source area), and a flat source area is uniquely identified by the constructed entity geometry level information of this local point list (the intersection of the constructed entity geometry levels).

[0104] In this embodiment, after domain decomposition is enabled, the numbering method corresponding to the coarse network grid needs to convert the global number of the coarse network grid into a local number in the communication domain according to the communication domain in which the coarse network grid is located. The specific local numbering method is:

[0105] Part Number:

[0106]

[0107] In this embodiment, if the starting point or end point of a trajectory segment is located at a vertex / edge / face of a coarse mesh, the corresponding number of the vertex, edge or face of the coarse mesh needs to be added to the storage information of the current trajectory segment. Figure 5 , Figure 5 The starting or ending points of the middle track segments are at the edge of the coarse mesh grid, which are track segments 1 and 7. The numbering of the vertices, edges, and faces of each coarse mesh grid is generated as follows:

[0108] B1. First, we need to design the basic numbers corresponding to each vertex, edge, and face in the coarse mesh. Taking a cube as an example, the basic numbers of vertices, edges, and faces are:

[0109]

[0110] The base numbers corresponding to the faces are as follows:

[0111]

[0112] The base numbers corresponding to the edges are as follows:

[0113]

[0114] The base numbers corresponding to the vertices are as follows:

[0115]

[0116] B2, because it is necessary to number and distinguish the vertices, edges and faces corresponding to each coarse mesh, the numbering is generated in the following way:

[0117] surface_id=NUM_SURFACES×cell+surface

[0118] In this calculation formula, cell represents the number corresponding to the coarse mesh, and its numbering method is cell = x + y × num_x + z × (num_x × num_y), where num_x and num_y represent the number of grids divided by the coarse mesh in the X direction and Y direction respectively. Surface represents the basic number of a vertex / edge / face in the coarse mesh.

[0119] In this embodiment, after the track segmentation is completed, the flat source areas need to be renumbered and sorted according to the axial order of each track segment in the track chain, and the mapping record between the flat source areas and the coarse mesh grid is completed. The mapping method is:

[0120] Assume that the non-empty set FSR {fsr1, fsr2, K, fsr n} and the non-empty set CMFD{cell1, cell2, K, cell m}, each coarse grid cell contains at least one flat source region fsr, that is, there is a one-to-one mapping or many-to-one mapping between FSR and CMFD, and the mapping method is as follows Figure 6 shown.

[0121] In this embodiment, during the transport scanning stage, each track segment is used as the basic data to calculate the standard flux of each flat source area. The track segment needs to be further divided according to the maximum optical thickness, and the coarse mesh only counts the tracks at the end of the divided segment. According to the coarse mesh type corresponding to the track segment, the tracks belonging to the coarse mesh surface and the tracks belonging to the vertices and edges of the coarse mesh are stored separately. The tracks located at the vertices and edges of the coarse mesh will be split into each coarse mesh surface later.

[0122] In this embodiment, the sub-flow splitting method of vertex and edge trajectories is:

[0123] C1, for the trajectory neutron flow at the vertex of the coarse mesh, it is necessary to split the trajectory neutron flow at the vertex into three adjacent edges according to the geometric position of the vertex. Taking the cube geometry as an example, there are 8 types of vertices, and each vertex has three different adjacent edges and adjacent faces. According to the location of the coarse mesh (at the edge of the reactor geometry / at the non-edge) and the boundary conditions of the coarse mesh (periodic boundary / reflection boundary / vacuum boundary), the neutron flow at the vertex is split into three adjacent edges. The neutron flow at the adjacent edge is one third of the neutron flow at the original vertex. This splitting method corresponds to Figure 7 Content shown.

[0124] C2, further splits the trajectory neutron flow originally located at the edge of the coarse mesh and the edge neutron flow after splitting by B1. Taking the cube geometry as an example, there are 12 edge types in total, and each edge has two different adjacent faces. Similarly, according to the location of the coarse mesh (at the edge of the reactor geometry / at the non-edge) and the boundary conditions of the coarse mesh (periodic boundary / reflection boundary / vacuum boundary), the trajectory neutron flow at the edge is split into 2 adjacent faces. The neutron flow of the adjacent face is half of the original edge neutron flow. This splitting method corresponds to Figure 8 Content shown.

[0125] C3, superimposes the neutron flux after the above splitting process on the corresponding coarse mesh surface respectively, so as to realize the neutron flux statistics and storage on each surface of the coarse mesh.

[0126] In this embodiment, the variables required for constructing the coarse-grid finite difference equation system are mainly calculated by the following method:

[0127] D1, the average flux in the coarse mesh, needs to be obtained by volume homogenization calculation through the flux of each flat source area contained in the coarse mesh in combination with the characteristic line method transport scanning process. Fig. 9 A schematic diagram of the coarse mesh and the flat source area on the radial plane is given, and the corresponding calculation formula for the volume homogenized average flux is:

[0128]

[0129] D2, in addition to the need for volume homogenization of the coarse mesh flux, each cross section corresponding to each coarse mesh 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:

[0130]

[0131]

[0132] c represents a coarse grid in the coarse grid finite difference method, e represents an energy group in the coarse grid, k represents the flat source region k contained in the coarse grid c, g represents the flat source region energy group contained in the coarse grid energy group e, l represents the result after the lth iteration of the transport iteration calculation, l mid represents the intermediate state between the lth iteration and the l+1th iteration, represents the average flux of energy group e of the coarse grid c 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.

[0133] D3, before calculating the neutron flux between adjacent coarse mesh surfaces, it is necessary to first calculate the uniform diffusion coefficient corresponding to the coarse mesh. The corresponding calculation formula is:

[0134]

[0135] D4, obtain the uniform diffusion coefficient corresponding to each coarse grid c energy group e It is necessary to calculate the net neutron flux, effective diffusion coefficient and neutron flux correction coefficient between the coarse mesh c and the adjacent surface in the x, y and z directions. The net neutron flux between the coarse mesh c and the adjacent surface in the x and y directions is calculated as follows:

[0136]

[0137] Indicates that the coarse mesh c and the adjacent mesh c+1 are on the adjacent surface The effective diffusion coefficient at Indicates that the coarse mesh c and the adjacent mesh c+1 are on the adjacent surface Neutron flux correction factor at .

[0138] Net neutron flow between the coarse mesh c and adjacent surfaces in the x and y directions Fig.10 shown.

[0139] The calculation formulas for the effective diffusion coefficient and the neutron flux correction coefficient are:

[0140]

[0141] The equation form corresponding to the coarse-grid finite difference module is:

[0142]

[0143] w dir,c represents the grid width of the coarse grid c in each direction of dir∈(x,y,z), and E represents the number of corresponding coarse grid energy groups. After simplification, the corresponding coarse grid finite difference equation is:

[0144]

[0145] In this embodiment, the flux obtained by solving each coarse grid is It will be used to update the flux of the flat source region it contains, thus providing a more convergent flux for the iteration of the characteristic line method. Its main calculation form is:

[0146]

[0147] It means solving the coarse-grid finite difference equation and obtaining the scalar flux corresponding to the energy group e of the coarse-grid grid c. Indicates the use The updated average flux corresponding to the energy group g in the flat source region k, in the above formula, k∈c, g∈e.

[0148] In this embodiment, a 3D C5G7 single component, a 3D C5G7 full stack, and a full stack with radial distribution and water gap added by modifying the 3D C5G7 are used as examples to respectively perform uniform and non-uniform coarse mesh finite difference acceleration effects. Tests have verified that the uniform and non-uniform coarse mesh finite difference calculation method constructed by the present invention can greatly reduce the number of characteristic line method iterations and shorten the total calculation time.

[0149] The three-dimensional characteristic line neutron transport calculation acceleration method of the domestic DCU architecture provided in this embodiment also provides a considerable reference scheme for the coarse-mesh finite difference acceleration method under other geometric structures. In addition, the naming rules of mesh vertices, edges, and faces in this patent, as well as the neutron flow splitting method, expand the application of coarse-mesh finite difference under other coarse-mesh mesh geometry construction; and this method can be successfully connected to the characteristic line method after the transport solution, providing a good foundation for the subsequent construction of a multi-level coarse-mesh finite difference method.

[0150] 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 method for accelerating neutron transport calculation based on three-dimensional characteristic lines of a domestic DCU architecture, characterized in that: The method comprises the following steps: According to the reactor geometry modeling and domain decomposition structure, uniform / non-uniform coarse mesh finite difference grid geometry modeling is constructed; In the trajectory generation and trajectory segmentation stage, the relationship between the flat source area and the coarse mesh and between the coarse mesh and the communication domain is recorded, the trajectory segments reaching the vertices, edges and faces of the coarse mesh are stored, the trajectory segments located at the domain boundary are stored, and the trajectory connection sequence between adjacent communication domains and the adjacency relationship of the coarse mesh surface are recorded; In the transport scanning phase, the computing tasks are sent to the device side according to the domain decomposition structure. In the device side, the neutron flow on the coarse mesh surface of the trajectory segment is stored according to the coarse mesh points, edges and faces of the trajectory segment, and the neutron flow at the boundary of the communication domain that needs to be transmitted is stored. The transport solution calculation results are transferred to the coarse-grid finite difference solution module, and the coarse-grid finite difference equation system is constructed and solved using the successive super-relaxation iteration method; According to the 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 claim 1, a method for accelerating neutron transport calculation based on three-dimensional characteristic lines of a domestic DCU architecture is characterized in that: The uniform / non-uniform coarse mesh finite difference geometric modeling method is constructed according to the reactor geometric modeling and domain decomposition structure, and specifically includes the following contents: For different reactor geometry types, choose to use uniform or non-uniform geometry partitioning: for examples with relatively uniform geometry modeling in the radial plane and axial direction, construct a uniform coarse-mesh finite difference grid; for light water reactors, where there are special problems such as non-uniform fuel assemblies, thin water gaps between assemblies, and axial grids with different heights, construct a non-uniform coarse-mesh finite difference grid.

3. According to claim 1, a method for accelerating neutron transport calculation based on three-dimensional characteristic lines of a domestic DCU architecture is characterized in that: In the trajectory generation and trajectory segmentation stage, the relationship between the flat source area and the coarse mesh and between the coarse mesh and the communication domain is recorded, and the trajectory segments reaching the vertices, edges and faces of the coarse mesh are stored, which specifically includes the following contents: In the three-dimensional trajectory segment generation stage, the lengths of the trajectory segments of each axial layer at the same starting point are counted, the shortest trajectory segment is selected and a keyword corresponding to the flat source area is generated, and the X, Y, and Z numbers corresponding to the coarse mesh grid are added to the keyword; For a trajectory segment whose starting point or end point is located at a vertex / edge / face of a coarse mesh, the number corresponding to the vertex, edge or face of the coarse mesh is added to the storage information of the current trajectory segment; After the trajectory segmentation is completed, the flat source areas are renumbered and sorted according to the axial order of each trajectory segment in the trajectory chain, and the mapping record between the flat source area and the coarse mesh is completed. The mapping method satisfies: Assume that the non-empty set FSR {fsr1, fsr2, ..., fsr n } and the non-empty set CMFD{cell1, cell2, ..., cell m }, each coarse grid cell contains at least one flat source region fsr, that is, there is a one-to-one mapping or many-to-one mapping between FSR and CMFD.

4. According to claim 1, a method for accelerating neutron transport calculation based on three-dimensional characteristic lines of a domestic DCU architecture is characterized in that: The storage of the track segments located at the domain boundary, recording the track connection sequence between adjacent communication domains, and the coarse mesh surface adjacency relationship specifically includes the following contents: After domain decomposition, when obtaining the number corresponding to the coarse network grid, the global number of the coarse network grid is converted into a local number in the communication domain according to the communication domain where the coarse network grid is located.

5. According to claim 1, a method for accelerating neutron transport calculation based on three-dimensional characteristic lines of a domestic DCU architecture is characterized in that: The transport scanning stage specifically includes the following contents: In the transport scanning stage, the standard flux of each flat source area is calculated based on each trajectory segment. The trajectory segment is further divided according to the maximum optical thickness, and the coarse mesh only counts the trajectories located at the end of the divided segment. According to the coarse mesh type corresponding to the trajectory segment, the trajectories belonging to the coarse mesh surface and the trajectories belonging to the vertices and edges of the coarse mesh are stored separately, and the neutron flow in the trajectories located at the vertices and edges of the coarse mesh is split into each coarse mesh surface.

6. According to claim 5, a method for accelerating neutron transport calculation based on three-dimensional characteristic lines of a domestic DCU architecture is characterized in that: The sub-flow splitting method of the vertex and edge trajectory specifically includes: For the neutron flow of the trajectory located at the vertex of the coarse mesh, according to the position of the coarse mesh and the boundary conditions of the coarse mesh, the neutron flow of the trajectory at the vertex is split into three adjacent edges, and the neutron flow of the adjacent edges is one third of the neutron flow of the original vertex; The trajectory neutron flow originally located at the edge of the coarse mesh and the edge neutron flow after splitting are further split. According to the position of the coarse mesh and the boundary conditions of the coarse mesh, the trajectory neutron flow located at the edge is split into two adjacent faces, and the neutron flow of the adjacent face is half of the original edge neutron flow; The neutron fluxes after the above splitting process are respectively superimposed on the corresponding coarse mesh surfaces to realize the statistics and storage of neutron fluxes on each surface of the coarse mesh.

7. According to claim 1, a method for accelerating neutron transport calculation based on three-dimensional characteristic lines of a domestic DCU architecture is characterized in that: The transport solution calculation results are transferred to the coarse-mesh finite difference solution module, a coarse-mesh finite difference equation group is constructed and solved using the successive super-relaxation iteration method, which specifically includes the following contents: the variables required for constructing the coarse-mesh finite difference equation group, the specific calculation method includes: Combined with the characteristic line method transport scanning process, the average flux in the coarse mesh is obtained by volume homogenization calculation through the flux of each flat source area contained in the coarse mesh. The corresponding calculation formula is: Where c represents a coarse grid in CMFD, e represents an energy group in the coarse grid, k represents the MOC flat source domain k contained in the CMFD coarse grid c, g represents a MOC energy group contained in the CMFD coarse grid energy group e, l represents the result after the lth iteration of ANT-MOC calculation, l mid It represents the intermediate form of CMFD between the lth iteration and the l+1th iteration. represents the average flux of CMFD coarse grid c energy group e calculated by MOC, represents the average flux corresponding to the MOC fine grid k energy group g, V k represents the volume of the fine grid flat source domain k; The cross sections corresponding to each coarse mesh are homogenized accordingly. For the total cross section, the calculation formula for the homogenization of the coarse mesh cross section is: in, represents the uniform total cross section of the coarse grid c energy group e, ∑ t,k,g represents the total cross section of energy group g for the fine grid k; the scattering cross section corresponding to energy group e for the coarse grid c Fission cross section Fission spectrum distribution The calculation is also performed according to the volume homogenization method; Before calculating the neutron flux between adjacent coarse mesh surfaces, the uniform diffusion coefficient corresponding to the coarse mesh is first calculated and obtained. The corresponding calculation formula is: The calculation formulas for the effective diffusion coefficient and the neutron flux correction coefficient are: The equation form corresponding to the coarse-grid finite difference module is: in, represents the uniform diffusion coefficient corresponding to each coarse grid c energy group e, 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 The neutron flux correction factor at represents the net neutron flow between the coarse grid c and the adjacent surface in the x, y, and z directions, w dir,c It represents the grid width of the coarse grid c in each direction of dir∈(x,y,z), and E represents the number of coarse grid energy groups corresponding to the coarsening of the MOC energy group.

8. According to claim 1, a method for accelerating neutron transport calculation based on three-dimensional characteristic lines of a domestic DCU architecture is characterized in that: The above method updates the flux of each flat source region through the coarse grid finite difference calculation results, and calculates the effective neutron multiplication factor in the current iteration, which specifically includes the following contents: the flux obtained by solving each coarse grid It is used to update the flux of the flat source area it contains, thereby providing a more convergent flux for the iteration of the characteristic line method. The calculation formula is: in, represents the scalar flux corresponding to the coarse grid c energy group e obtained by solving the CMFD transport equation, It represents the average flux corresponding to the fine grid k energy group g after CMFD update, where k∈c,g∈e.

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