A feature line based spatial region decomposition parallel acceleration method and system
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-10-25
- Publication Date
- 2026-08-11
AI Technical Summary
[0002]作为核反应堆系统分析计算的基础,反应堆物理分析计算通过求解中子输运方程,获得堆芯反应性和全堆精细功率分布,为快速开展先进核动力堆芯研发,需要研发先进的高精度反应堆物理设计软件;为模拟复杂结构堆芯,国内外正广泛开展基于精确物理模型和精细几何建模的“一步法”反应堆物理计算方法研究,三维中子输运方程的中子角通量包含7个因变量(空间3维、角度2维、能量1维、时间1维),导致精确的数值模拟非常困难,现阶段常用的中子输运特征线方法(MOC)方法兼具计算精度高、几何适应性好、能够精确处理各向异性散射、可并行维度多等优点,是非常重要的“一步法”三维全堆中子输运计算方法,但是,MOC方法计算量较大、内存消耗较高,必须基于大规模并行计算技术,空间区域分解并行是实现大规模并行计算的重要途径,然而,空间区域分解的子区域耦合本质上是分块雅可比迭代过程,随着MOC方法区域分解子区域数目的增长,耦合的内界面角通量数目迅速增长,收敛速率变慢,迭代次数快速增长,导致计算效率降低
[0040] The beneficial effects of the method and system of this invention are as follows: Based on the parallelism of the MOC method in multiple dimensions such as space, angle, ray, and energy, this invention designs a multi-level parallel method to further calculate the outgoing angle flux at the intersection of the feature line and the fine mesh. Based on communication between spatial regions, the inner boundary angle flux information is exchanged, and the average standard flux of the fine mesh is further calculated. The parallelism of all dimensions of the MOC method is mapped onto the hardware architecture. Then, the parallel generalized minimum residual algorithm is used to replace the block Jacobi iterative algorithm, which accelerates the convergence of the inner interface angle flux of the spatial region decomposition, improves the convergence rate, and thus improves the computational efficiency of the parallel MOC method for spatial region decomposition.
Smart Images

Figure CN115935598B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of nuclear reactor core design and reactor physics numerical calculation, and in particular to a parallel acceleration method and system based on spatial region decomposition of characteristic lines. Background Technology
[0002] As the foundation of nuclear reactor system analysis and calculation, reactor physics analysis and calculation obtains core reactivity and fine power distribution across the entire reactor by solving neutron transport equations. To rapidly develop advanced nuclear power reactor cores, advanced, high-precision reactor physics design software is needed. To simulate complex reactor core structures, research is widely underway both domestically and internationally on "one-step" reactor physics calculation methods based on accurate physical models and fine geometric modeling. The neutron angular flux in the three-dimensional neutron transport equations contains seven dependent variables (3-dimensional space, 2-dimensional angle, 1-dimensional energy, and 1-dimensional time), making accurate numerical simulation extremely difficult. Currently, the commonly used neutron transport characteristic line method (MO) is... Method C) combines the advantages of high computational accuracy, good geometric adaptability, accurate handling of anisotropic scattering, and multiple parallel dimensions, making it a very important "one-step" three-dimensional whole-pile neutron transport calculation method. However, the MOC method has a large computational load and high memory consumption, and must be based on large-scale parallel computing technology. Spatial domain decomposition parallelism is an important way to achieve large-scale parallel computing. However, the sub-region coupling of spatial domain decomposition is essentially a block Jacobian iterative process. As the number of sub-regions in the MOC method increases, the number of fluxes at the coupling inner interface corners increases rapidly, the convergence rate slows down, and the number of iterations increases rapidly, resulting in a decrease in computational efficiency. Summary of the Invention
[0003] To address the aforementioned technical problems, the present invention aims to provide a parallel acceleration method and system for spatial region decomposition based on feature lines. By using a parallel generalized minimum residual algorithm, the convergence of the interface angle flux within the spatial region decomposition is accelerated, thereby improving the convergence rate and ultimately enhancing the computational efficiency of the parallel MOC method for spatial region decomposition.
[0004] The first technical solution adopted in this invention is: a parallel acceleration method for spatial region decomposition based on feature lines, comprising the following steps:
[0005] The reactor core is calculated using the characteristic line method to obtain a fine mesh and characteristic line segments;
[0006] Obtain the outgoing angular flux at the intersection of the feature line and the fine mesh and calculate it to obtain the average standard flux of the fine mesh;
[0007] The average standard flux of the fine grid is solved by internal and external iteration strategies, and the neutron standard flux distribution and core growth factor are obtained.
[0008] Furthermore, the step of calculating the reactor core using the characteristic line method to obtain a fine mesh and characteristic line segments specifically includes:
[0009] The reactor core is calculated using the characteristic line method to obtain the spatial region and characteristic lines;
[0010] By dividing the spatial region using feature lines, fine meshes and feature line segments are obtained.
[0011] Furthermore, the characteristic line is a multi-group neutron transport equation in characteristic line form, the specific expression of which is shown below:
[0012]
[0013] In the above formula, denoted by neutron angular flux, g by energy group designation, f by MOC fine grid number, t by characteristic line number, m by azimuth number, n by polar number, and s by characteristic line coordinates. Let q represent the total cross section of the g-group in the fine MOC mesh f. g,i Let g represent the distribution of source terms in grid f.
[0014] Furthermore, the step of obtaining and calculating the outgoing angular flux at the intersection of the feature line and the fine mesh to obtain the average standard flux of the fine mesh specifically includes:
[0015] Based on the principle of flat source approximation, the outgoing angular flux at the intersection of the feature line and the fine mesh is obtained;
[0016] Find the integral equation on the characteristic line segment and average it to obtain the average angular flux of the characteristic line segment.
[0017] Based on the azimuth and polar angle of the feature line segments, the average angular flux of the feature line segments is processed by directional quadrature grouping to obtain the average standard flux of the fine mesh.
[0018] Furthermore, the expression for the average standard flux of the fine mesh is as follows:
[0019]
[0020] In the above formula, φ g,i Let ω represent the group average standard flux of a fine grid f. m The weight of azimuth angle m, ω n The weights representing the polar angles, Let g represent the group average angular flux of the fine mesh f in directions m and n.
[0021] Furthermore, the step of solving for the average standard flux of the fine grid through an internal and external iteration strategy to obtain the neutron standard flux distribution and the core growth factor specifically includes:
[0022] Based on the continuity condition of neutron angular flux, the propagation equation of neutron angular flux is obtained;
[0023] Considering the neutron angular flux in the direction of the fine mesh, and combining the reflection boundary conditions, a cyclic ray is constructed;
[0024] Based on the propagation equation of neutron angular flux, the emission angular flux is processed by characteristic line scanning, and the emission angular flux is expressed as a linear function of the incident angular flux and the fine-grid source term;
[0025] Equivalent linear transformations are performed on the linear functions of the incident angle flux and the fine-grid source term to construct a system of linear equations;
[0026] The linear equation system is solved using a parallel generalized minimum residual algorithm, and the solution results are obtained.
[0027] The solution results are subjected to characteristic line scanning to obtain the neutron standard flux distribution and core growth factor.
[0028] Furthermore, the step of solving the linear equation system based on the parallel generalized minimum residual algorithm to obtain the solution results specifically includes:
[0029] The input vector is obtained and input to any spatial region, wherein the input vector is the outgoing angle flux and the incoming angle flux;
[0030] Based on the continuity condition of angular flux, communication is carried out between adjacent spatial regions to exchange information on the incident angular flux of the inner boundary;
[0031] Based on the parallel generalized minimum residual algorithm interface, the solution is obtained by combining the flux information of the inner boundary incident angle with the input vector.
[0032] Furthermore, the expression for the system of linear equations is as follows:
[0033]
[0034] In the above formula, Subregion D i The vector formed by the outward angular flux of the g-group in the adjacent subregions, D i,Neighbors Subregion D i The set consisting of all adjacent subregions, where f1 and f2 are represented as linear functions. Subregion D i The vector formed by the source terms of the g-group across all fine meshes. Subregion D i The vector formed by the g-group outgoing angular flux of the inner interface. Subregion D i The vector formed by the incident angular flux of the g-group reflecting the outer boundary.
[0035] Furthermore, it also includes determining whether the neutron standard flux distribution and the core growth factor have converged based on the convergence conditions.
[0036] The second technical solution adopted in this invention is: a parallel acceleration system for spatial region decomposition based on feature lines, comprising:
[0037] The modeling module is used to calculate the reactor core using the feature line method, resulting in a fine mesh and feature line segments;
[0038] The acquisition module is used to acquire and calculate the outgoing angular flux at the intersection of the feature line and the fine mesh to obtain the average standard flux of the fine mesh.
[0039] The solver module is used to solve for the average standard flux of the fine grid through internal and external iteration strategies, so as to obtain the neutron standard flux distribution and the core growth factor.
[0040] The beneficial effects of the method and system of this invention are as follows: Based on the parallelism of the MOC method in multiple dimensions such as space, angle, ray, and energy, this invention designs a multi-level parallel method to further calculate the outgoing angle flux at the intersection of the feature line and the fine mesh. Based on communication between spatial regions, the inner boundary angle flux information is exchanged, and the average standard flux of the fine mesh is further calculated. The parallelism of all dimensions of the MOC method is mapped onto the hardware architecture. Then, the parallel generalized minimum residual algorithm is used to replace the block Jacobi iterative algorithm, which accelerates the convergence of the inner interface angle flux of the spatial region decomposition, improves the convergence rate, and thus improves the computational efficiency of the parallel MOC method for spatial region decomposition. Attached Figure Description
[0041] Figure 1 This is a flowchart of the steps of a parallel acceleration method for spatial region decomposition based on feature lines according to the present invention.
[0042] Figure 2 This is a structural block diagram of a parallel acceleration system for spatial region decomposition based on feature lines according to the present invention.
[0043] Figure 3 This is a schematic diagram illustrating the basic principle of the feature line method of this invention;
[0044] Figure 4 This is a schematic diagram of spatial region decomposition based on the MOC method of this invention;
[0045] Figure 5 This refers to any sub-region D in a specific embodiment of the present invention. i Schematic diagram of the definition of angular flux;
[0046] Figure 6 This is a flowchart of the parallel acceleration method for spatial region decomposition based on the PGMRES algorithm of this invention. Detailed Implementation
[0047] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.
[0048] The MOC method has the advantages of high computational accuracy, good geometric adaptability, accurate handling of anisotropic scattering, and parallelization of multiple dimensions, making it a very important "one-step" three-dimensional whole-pile neutron transport calculation method.
[0049] Spatial domain decomposition parallelism refers to decomposing the problem domain to be solved into several sub-domains, each of which is mapped to a different process for independent solution. The sub-domains are coupled through inter-process communication. Spatial domain decomposition has a high degree of parallelism and is particularly suitable for large-scale parallel computing. Therefore, the purpose of this invention is to overcome the problem of reduced convergence rate of the MOC method caused by spatial domain decomposition parallelism.
[0050] The Parallel Generalized Minimum Residual Algorithm (GMRES) is a Krylov subspace method that has been included in many mature numerical computing libraries. It features a user-friendly interface, simple calling, and high computational efficiency.
[0051] Reference Figure 1 This invention provides a parallel acceleration method for spatial region decomposition based on feature lines, which includes the following steps:
[0052] S1. Start the program, MOC method geometric preprocessing, generate feature line segment information for transport scanning;
[0053] Specifically, the reactor core is calculated using the characteristic line method to obtain the spatial region and characteristic lines. The spatial region is then divided using the characteristic lines to obtain a fine mesh and characteristic line segments.
[0054] The multi-group neutron transport equations, whose characteristic lines are in characteristic line form, are expressed as follows:
[0055]
[0056] In the above formula, denoted by neutron angular flux, g by energy group designation, i by MOC fine grid number, t by characteristic line number, m by azimuth number, n by polar angle number, and s by characteristic line coordinates. Let q represent the total cross section of group g for fine mesh i in MOC. g,i Describe the distribution of the source terms of the g group in grid i;
[0057] S2. During the generation of characteristic lines, construct a system of linear equations for the angular flux and source terms of the domain decomposition system to obtain the coefficient matrix of the equations.
[0058] S3. Between two source iterations, assume any subregion D i Source term distribution vector of MOC fine mesh Known;
[0059] Specifically, if the flat-source approximation is used, that is, assuming Solving the first-order ordinary differential equation, we obtain the following expression for the flux at the exit angle when the characteristic line t passes through the fine mesh f:
[0060]
[0061] In the above formula, This represents the angular flux of the g-group, where the characteristic line t with directions m and n passes through a fine grid f. This represents the incident angular flux of the feature line t with directions m and n entering the fine grid i in the g group. The length of the feature line segment t, with directions m and n, passing through the fine grid i;
[0062] Integrating along the characteristic line segment and taking the average yields the average angular flux of that segment. Its expression is as follows:
[0063]
[0064] In the above formula, The g-group average angular flux represents the characteristic line segment of the fine grid i through which the characteristic line t with directions m and n passes;
[0065] The g-group average angular flux of the fine grid i in directions m and n is shown in the following equation:
[0066]
[0067] In the above formula, Let i represent the set of all characteristic lines passing through the fine grid i in directions m and n. Let A represent the g-group average angular flux of the fine mesh i in directions m and n. m,n V represents the area represented by the characteristic lines in directions m and n. i This represents the volume of the finer mesh i;
[0068] According to the definition of the directional quadrature group, the g-group average standard flux of fine grid i is expressed as follows:
[0069]
[0070] In the above formula, φ g,iLet ω represent the g-group average standard flux of a fine grid i. m The weight of azimuth angle m, ω n The weights representing the polar angles, Let g represent the group-average angular flux of the directions m and n of the fine mesh f;
[0071] In summary, the basic equations of the MOC method are given. After obtaining the scalar flux of all fine meshes, the neutron scalar flux distribution and k can be calculated using an internal and external iteration strategy. eff Based on the continuity condition of neutron angle flux, by recursively applying the formula, the propagation equation of neutron angle flux can be obtained, which represents the exponential decay relationship between the incident angle flux and the outgoing angle flux of the characteristic line passing through any region.
[0072] S4. For any subregion D i Map it to process P i Define the inner interface and the outer boundary of the reflection (if sub-region D) i The incident angular flux (with an outer boundary) is 0, combined with the known source term distribution vector. A simplified characteristic line scan is performed in parallel, without accumulating the standard flux, to obtain the right-hand side of the equation;
[0073] S5. For the domain decomposition system, based on the parallel matrix-vector multiplication operation provided by the user, the PGMRES algorithm is used to solve the equations in parallel to obtain the convergent inner interface outgoing angle flux and the incident angle flux of the outer boundary of the reflection of all sub-regions.
[0074] S6. For any subregion D i The outgoing angular flux of adjacent sub-regions is obtained through communication. Update subregion D i incident angular flux
[0075] Specifically, to save memory, this invention does not explicitly construct the coefficient matrix, but only implicitly defines the matrix-vector multiplication operation. The specific implementation steps of the parallel matrix-vector multiplication operation provided to the PGMRES algorithm are as follows: for any sub-region D i , For the unknown variables of the spatial domain decomposition system, establish the input vector based on the unknown variables. According to the continuity condition of angular flux, wherein the continuity condition of angular flux is: For any subregion D i The outgoing angular flux of adjacent sub-regions is obtained through communication. As a sub-region D i Inner interface incident angle flux According to subregion D i input vector and the incident angle flux of the inner interface According to the expression on the left side of the equation, each sub-region is calculated in parallel to obtain the output vector y. The matrix-vector multiplication operation y = Ax is passed to the PGMRES algorithm interface to complete the Amoldi orthogonalization process of the algorithm.
[0076] For a system of linear equations in a spatial domain decomposition system, any algorithm for solving linear equation systems in the field of numerical computation can be used. This invention employs the PGMRES algorithm for solution, such as... Figure 6 As shown; the GMRES algorithm is a type of Krylov subspace method, included in many mature numerical computing libraries. It features a user-friendly interface, simple calling, and high computational efficiency. For the linear equation system Ax = b, the user only needs to provide the algorithm interface with the matrix-vector multiplication operation shown in the following formula to complete the Arnoldi orthogonalization process. The expression of the linear equation system is as follows:
[0077] y = Ax
[0078] In the above formula, A represents the coefficient matrix, x represents the input vector, and y represents the output vector.
[0079] S7. For any subregion D i The convergent incident angle flux calculated using the PGMRES algorithm and known source term distribution vector The feature line scans are performed in parallel, the standard flux is accumulated, and k is calculated. eff ;
[0080] Specifically, refer to Figure 4 The parallel spatial region decomposition algorithm is described using a two-dimensional diagram, and the conclusions obtained are directly applicable to the three-dimensional MOC method. In the parallel spatial region decomposition MOC algorithm, the entire problem region is decomposed into multiple sub-regions. Each sub-region is mapped to different processes and solved separately as an independent problem. Sub-region coupling is achieved by exchanging the inner boundary angle flux, which must be obtained through iterative calculation. It is assumed that the outer boundaries of the original problem are all total reflection boundary conditions, and the feature line arrangement meets the modularity condition. Let N be the number of feature lines incident from the x and y boundaries. x N y Then the number of unknowns in the incident angular flux of the entire system is 2 (N). x +N y If the problem region is divided into D along the x and y directions respectively... x D y If there are 2 subregions, then the number of unknowns in the total angular flux of the whole system after decomposition is 2D. x N y +2D y N xTherefore, when the sub-region is divided into finer parts, i.e., D x D y When the number of unknowns in the angular flux that need to be converged through iteration increases significantly, the number of iterations increases rapidly, which greatly affects the computational efficiency. Therefore, this invention uses the PGMRES algorithm to accelerate the convergence of the internal interface angular flux, instead of the block Jacobian iteration.
[0081] Reference Figure 5 Extract any subregion D separately i (by Figure 5 Taking the lower left sub-region as an example, and considering the neutron angular flux in the four directions Ω1 to Ω4, Ω1 to Ω4 satisfy the following relationship: the characteristic lines in these four directions can form a continuous cyclic ray through the reflection boundary conditions, and its expression is as follows:
[0082] Ω1+Ω2=π,Ω2+Ω3=2π,Ω1+Ω4=2π
[0083] Based on the propagation relationship of neutron angle flux, subregion D can be... i The outgoing angle flux is expressed as a linear function of the incident angle flux and the fine-grid source term, as shown below:
[0084]
[0085] In the above formula, inner represents the interface within the sub-region, and ref represents the outer boundary of the reflection within the sub-region. Subregion D i The vector formed by the source terms of the g-group across all fine meshes. Subregion D i The vector formed by the g-group outgoing angular flux of the inner interface. Subregion D i The vector formed by the incident angular flux of the g-group at the outer boundary of the reflection. Subregion D i The vector formed by the incident angle flux of the g-group of the inner interface, f represents the linear function of the outgoing angle flux with respect to the incident angle flux and the source term, and represents the characteristic line scanning process;
[0086] Based on the properties of linear functions, the following equation can be further expressed as: f1 and f2 are linear functions, and their expressions are shown below:
[0087]
[0088] The exponential decay relation satisfied by f1 and the equivalence relation satisfied by f2 are as follows:
[0089]
[0090]
[0091] In the above formula, This indicates that all feature lines pass through subregion D. i The vector formed by the cumulative optical path of the g group, δ means that when the ray origin is at the outer boundary, δ = 1, otherwise δ = 0, 0 means that the incident angle flux vector is 0, f means that the MOC transport scan process is a linear function, and f2 means that the physical meaning of the linear function is equivalent to the MOC transport scan with the incident angle flux being 0 on all boundaries.
[0092] By performing an equivalent transformation, we obtain the equation. The right-hand side of the equation can be obtained through a simplified characteristic line scan process (without accumulating scalar flux), and its expression is shown below:
[0093]
[0094] Based on the boundary condition of continuous angular flux at the interface within a subregion, i.e., the incident angular flux of this subregion is equal to the outgoing angular flux of the adjacent subregion, the equation can be transformed into the following equation:
[0095]
[0096]
[0097] In the above formula, Subregion D i The vector formed by the outward angular flux of the g-group in the adjacent subregions, D i,Neighbors Subregion D i The set consisting of all adjacent subregions, where f1 and f2 are represented as linear functions. Subregion D i The vector formed by the source terms of the g-group across all fine meshes. Subregion D i The vector formed by the g-group outgoing angular flux of the inner interface. Subregion D i The vector formed by the incident angular flux of the g-group reflecting the outer boundary;
[0098] make For the unknown variables in the spatial domain decomposition system, the outward flux of the inner boundary of adjacent sub-regions is exchanged through communication, and the incident flux of the inner boundary is updated. The equations constitute a self-consistent system of linear equations within the system. For the sub-region D, iFor any characteristic line, both the forward and reverse characteristic line scans represent G equations, where G is the number of energy groups in the transport problem. Except for the pivot term being 1.0, the equations contain only one non-zero coefficient: an exponentially decaying term. Furthermore, for a single characteristic line, the non-zero coefficients of the forward and reverse scan equations are completely equal. This coefficient can be generated simultaneously during the generation of the characteristic line. For the linear equation system of the spatial domain decomposition system composed of these equations, any algorithm for solving linear equation systems in the field of numerical computation can be used.
[0099] S8. Determine the standard flux and k eff Has the algorithm converged? If it has converged, the program ends; otherwise, it returns to step S1 for the next source iteration.
[0100] In summary, referring to Figure 3 The basic principle of this invention is that the characteristic line method divides the solution domain into fine meshes, each containing only one material. Assuming the spatial distribution of source terms within the mesh is known, dense characteristic lines in several directions are used to perform ray tracing on the solution domain divided into fine meshes. The intersection points of the characteristic rays and the fine meshes are found, and characteristic line segment information is generated. Through repeated characteristic line scanning and internal / external iterations, the neutron flux distribution and k are obtained. eff Whether a process is considered convergent can be customized according to the user's own needs. If the customized conditions are met, the process is considered convergent.
[0101] Reference Figure 2 A parallel acceleration system for spatial domain decomposition based on feature lines, comprising:
[0102] The modeling module is used to calculate the reactor core using the feature line method, resulting in a fine mesh and feature line segments;
[0103] The acquisition module is used to acquire and calculate the outgoing angular flux at the intersection of the feature line and the fine mesh to obtain the average standard flux of the fine mesh.
[0104] The solver module is used to solve for the average standard flux of the fine grid through internal and external iteration strategies, so as to obtain the neutron standard flux distribution and the core growth factor.
[0105] The content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.
[0106] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.
Claims
1. A parallel acceleration method for spatial region decomposition based on feature lines, characterized in that, Includes the following steps: S1) The reactor core is calculated using the characteristic line method to obtain the spatial region and characteristic lines. The spatial region is then divided using the characteristic lines to obtain a fine grid and characteristic line segments. The characteristic line is a multi-group neutron transport equation in characteristic line form, and its specific expression is as follows: ; In the above formula, Represents neutron angular flux. Indicates the group label, Indicates the fine mesh number of the MOC. Indicates the feature line number. Indicates the azimuth number. Indicates the polar angle number. Represents the coordinates of the characteristic line. Indicates MOC fine mesh of Group total cross section, Represents a grid of Group source term distribution; S2) During the generation of characteristic lines, construct a system of linear equations for the angular flux and source terms of the domain decomposition system, and obtain the coefficient matrix of the system of linear equations. S3) Between two source iterations, assume any subregion Source term distribution vector of MOC fine mesh Known; S4) For any subregion Map it to a process The incident angular flux of the inner interface and the outer boundary of the reflection is set as follows: Combined with the known distribution vector of source terms in group g A simplified feature line scan is performed in parallel without accumulating standard flux, to obtain the right-hand side terms of the linear equation system. S5) For the domain decomposition system, based on the parallel matrix-vector multiplication operation provided by the user, the parallel generalized minimum residual algorithm is used to solve the linear equation system in parallel to obtain the convergent inner interface outgoing angle flux and the incident angle flux of the outer boundary of the reflection of all sub-regions. S6) For any subregion The g-group emission angular flux of adjacent sub-regions is obtained through communication. Update sub-regions g-group incident angular flux ; S7), for any subregion The convergent subregion obtained by the parallel generalized minimum residual algorithm The incident angular flux of the g-group at the outer boundary of the reflection sub-region g-group incident angular flux of the inner interface and the known distribution vector of source terms in group g The characteristic line scans are performed in parallel to accumulate the standard flux and calculate the core gain factor. ; S8) Determine the neutron standard flux distribution and core augmentation factor. Check if convergence has occurred; if convergence has occurred, the program ends; otherwise, return to step S1) to perform the next source iteration. After obtaining the standard flux of all fine grids, the neutron standard flux distribution and core gain factor are calculated using an internal and external iteration strategy. Specifically, it includes: Based on the continuity condition of neutron angular flux, the propagation equation of neutron angular flux is obtained; Considering the neutron angular flux in the direction of the fine mesh, and combining the reflection boundary conditions, a cyclic ray is constructed; Based on the propagation equation of neutron angular flux, the emission angular flux is processed by characteristic line scanning, and the emission angular flux is expressed as a linear function of the incident angular flux and the fine-grid source term; Equivalent linear transformations are performed on the linear functions of the incident angle flux and the fine-grid source term to construct a system of linear equations; The linear equation system is solved using a parallel generalized minimum residual algorithm, and the solution results are obtained. The solution results are subjected to characteristic line scanning to obtain the neutron standard flux distribution and core growth factor.
2. The parallel acceleration method for spatial region decomposition based on feature lines according to claim 1, characterized in that, In step S3), based on the principle of flat source approximation, the outgoing angle flux at the intersection of the feature line and the fine mesh is obtained; Find the integral equation on the characteristic line segment and average it to obtain the average angular flux of the characteristic line segment. Based on the azimuth and polar angle of the feature line segments, the average angular flux of the feature line segments is processed by directional quadrature grouping to obtain the average standard flux of the fine mesh.
3. The parallel acceleration method for spatial region decomposition based on feature lines according to claim 1, characterized in that: The step of solving the linear equation system based on the parallel generalized minimum residual algorithm to obtain the solution results specifically includes: The input vector is obtained and input to any spatial region, wherein the input vector is the outgoing angle flux and the incoming angle flux; Based on the continuity condition of angular flux, communication is carried out between adjacent spatial regions to exchange information on the incident angular flux of the inner boundary. Based on the parallel generalized minimum residual algorithm interface, the solution is obtained by combining the flux information of the inner boundary incident angle with the input vector.
4. A parallel acceleration system for spatial region decomposition based on feature lines, characterized in that, The system described herein utilizes the method described in any one of claims 1-3 for spatial region decomposition and parallel acceleration, and the system comprises the following modules: The modeling module is used to calculate the reactor core using the feature line method, resulting in a fine mesh and feature line segments; The acquisition module is used to acquire and calculate the outgoing angular flux at the intersection of the feature line and the fine mesh to obtain the average standard flux of the fine mesh. The solver module is used to solve for the average standard flux of the fine grid through internal and external iteration strategies, so as to obtain the neutron standard flux distribution and the core growth factor.
Citation Information
Patent Citations
Neutron transport calculation method for three-dimensional pressurized water reactor core
CN111523233A
Characteristic line method multistage parallel method suitable for modern super computer hardware architecture
CN112346873A