A Method for Constructing Neutron Transport Order Reduction Models Based on Component-Level Domain Decomposition and Coupling

Abstract

This invention discloses a method for constructing a neutron transport order reduction model based on component-level domain decomposition coupling. It employs a core architecture of "divide and conquer, numerical flux coupling." In the offline stage, "operational condition vectors" are extracted from fuel components as subdomains, and their dimensionality is reduced through sampling and independent solving. This constructs a dedicated neutron angular flux basis function library categorized by component type, energy group, and orientation angle. In the online stage, the entire reactor core is treated as a component network. Low-dimensional expansion is performed within each subdomain using basis functions. Based on the upwind numerical flux mechanism of discontinuous Galerkin (DG), robust coupling with physical conservation between components is achieved. Finally, a global block sparse linear equation system is assembled and solved to reconstruct the full-core angular flux distribution. This significantly reduces the offline cost to an acceptable range, ensuring high-precision reconstruction and numerical stability of the method for local non-uniformity. While maintaining high fidelity accuracy, it achieves a computational efficiency improvement of more than three orders of magnitude.

Description

Technical Field

[0001] This invention relates to the field of numerical calculation in nuclear reactor physics, and in particular to an efficient method for reducing the order of neutron transport equations under three-dimensional whole-core component domain decomposition conditions using intrinsic orthogonal decomposition (POD) and discontinuous Galerkin (DG) methods. Background Technology

[0002] The refined solution of the neutron transport equation is the foundation for nuclear reactor core design and safety analysis. At the three-dimensional full core scale, due to the need to simultaneously handle high-dimensional variables such as space, angle, and energy, traditional numerical solution methods have extremely high degrees of freedom and are extremely time-consuming to calculate. As a result, they cannot meet the urgent needs of real-time or near-real-time calculations in scenarios such as digital twins, multi-physics coupled iterations, or transient analysis.

[0003] To improve efficiency, reduced-order model (ROM) technology has emerged. Existing reduced-order models typically employ a global projection strategy, which involves performing numerous high-fidelity calculations across the entire reactor core by changing physical state parameters such as control rod positions and burnup to generate snapshots of the reactor flux distribution under different operating conditions, and then constructing the reactor global basis functions accordingly. However, this calculation method suffers from the following fundamental bottlenecks: (1) High offline cost: In order to cover the possible state space of the stack core, a large amount of full stack core high-fidelity calculation is required to generate snapshots, which makes the calculation and storage costs completely unacceptable; (2) Poor local adaptability: The global basis function is difficult to accurately characterize the strong local flux distortion caused by component heterogeneity, control rod insertion, etc., and is prone to large errors in key areas; (3) Poor generalization ability: When the number or arrangement of core components changes, a new ROM model needs to be reconstructed; (4) Difficulty in sampling high-dimensional distributed parameters: The physical field distribution of the reactor core is actually an infinite-dimensional function, making it difficult to effectively sample it to generate a representative snapshot.

[0004] Although order reduction methods based on domain decomposition have been theoretically proposed, how to handle the angular flux transfer of strong convective coupling between 3D components, how to ensure the physical conservation of interface flux, and how to efficiently obtain universal component-level basis functions at a reasonable computational cost remain key unsolved technical challenges in this field.

[0005] Therefore, existing methods for constructing neutron transport order reduction models based on domain decomposition need to be improved. Summary of the Invention

[0006] The present invention aims to overcome the above-mentioned technical defects and provide a high-efficiency and high-precision component-level domain decomposition and order reduction calculation method for three-dimensional whole-core neutron transport. It has lower offline cost, higher local adaptability, stronger generalization ability, and easier sampling of high-dimensional distributed parameters.

[0007] The technical solution of the present invention is as follows: a method for constructing a neutron transport order reduction model based on component-level region decomposition coupling, which consists of two main steps in the offline stage and four main steps in the online stage; Step S110: Construct a set of component-level operating condition snapshots for the offline phase: Perform at least one full-core reference solution calculation to obtain the reference solution for the entire core under complex physical conditions, and divide the entire core into several component subdomains according to the geometric boundaries of the fuel assemblies. Extract each component subdomain Based on the local physical state information, a component condition snapshot set is constructed, including boundary incident conditions and internal physical parameters, where D represents the component subdomain. a Represents the component index. N c Indicates the number of component subdomains; Step S120: Constructing a component-level neutron angular flux basis function library for the offline stage: Addressing the high-dimensional characteristics of component boundary conditions, internal multi-physics feedback parameters, and neutron angular flux coupling in various directions during neutron transport, a two-level dimensionality reduction strategy is employed to construct the basis function library. First, the component operating condition snapshot set undergoes parameter dimensionality reduction and sampling in the operating condition space to extract the dominant modes governing changes in the local transport physics environment, constructing a low-dimensional operating condition parameter space to generate a representative training set. Second, for each training condition, linear discrete ordinate transport equations are independently solved in the corresponding component subdomain to obtain angular flux distribution samples. Simultaneously, by performing intrinsic orthogonal decomposition (POD) on the angular flux distribution samples, a local angular flux basis function library classified by component type, energy group, and orientation angle is constructed. Step S130: Construct a parameterized locally reduced-order model for the online phase: For the full-core problem to be solved, discretize it into a component network, and in each component subdomain... Within, using the local angular flux basis function library, each energy group is processed according to Formula 1. g ,direction m Unknown neutron angular flux Expanding the equations and substituting them into the parameterized weak form of the local transport equations from Equation 2, we obtain the component's local linear equations; where r represents the spatial coordinates. c This represents the low-dimensional coefficients to be determined. These are local angular flux basis functions. Representation Component a type For numerical flux, n (a)For component subdomain boundaries The outward normal vector, k It is the basis function index. Indicates the first g The total cross section of the energy group, The direction cosine of the neutron's flight direction. Q t,g Indicates the first g The total neutron source term of the energy group; ; (Formula 1) ; (Formula 2) Step S140: Perform interface coupling in the online phase based on the discontinuous Galerkin (DG) method: Define the upwind numerical flux at the interface of the component subdomain, use the numerical flux to couple adjacent components at the interface, and calculate the interface flux transfer term between components. Step S150: Assemble the global block sparse linear equation system in the online stage: Assemble the local equations of all components into a global block sparse linear equation system for the entire core. The unknowns of this equation system are the POD basis function coefficients of each component. Step S160, Online Solution and Global Reconstruction: Solve the global block sparse linear equation system. The basis function coefficients of all components in the entire core are obtained. The three-dimensional neutron angular flux distribution of the entire core is reconstructed using basis functions, where A is the coefficient matrix and L is the right-hand vector. Step S170: By directly replacing the most time-consuming transport scanning part of the power iteration or JFNK iteration with the above online calculation of angular flux, the low-dimensional and efficient solution of the neutron transport eigenvalue equation in the online stage can be easily achieved.

[0008] This invention presents a highly efficient and accurate component-level domain decomposition and order reduction computation method for neutron transport in a three-dimensional whole-core reactor. In the offline stage, "component operating conditions" are extracted from the reference solution of a single whole-core reactor, and neutron angular flux basis functions are trained independently at the component level. In the online stage, the numerical flux mechanism of the discontinuous Galerkin (DG) method is used to couple the low-dimensional subspaces of each component at the interface to construct a global sparse linear equation system. The offline method has lower cost, higher local adaptability, stronger generalization ability, and easier sampling of high-dimensional distributed parameters.

[0009] The method for constructing a neutron transport order reduction model based on component-level domain decomposition coupling, wherein step S110 specifically includes: Step S112: Divide the entire core into several component subdomains. , a Represents a component instance, defining the collection of component types in the entire heap. ,N t Represents the total number of component types for any component instance in the full-core reference solution. a Define its component operating condition vector The vector consists of three parts: the incident neutron angular flux distribution on the component boundary. The distribution of physical state parameters within the component that determine the macroscopic cross-sectional distribution. p (a) and the total neutron source term distribution within the component subscript g and m The energy group and direction index are respectively represented by the discrete ordinate method; the total neutron source term distribution It is the sum of the fission source, the scattering source, and the external source; wherein, the distribution of the physical state parameters is... p (a) This includes, but is not limited to, a series of physical quantities that affect the size of the neutron cross section, such as fuel temperature, coolant density, coolant temperature and boron concentration, which determine the macroscopic cross section distribution within the component through cross section mapping relationships; Step S114: Traverse all spatial locations of the entire heap core and extract the component condition vector for each component instance. By leveraging the natural parameter differences that arise at different locations in the stack core due to varying environments, all instance vectors of the same type of component are collected to form a snapshot set of the operating conditions of that type of component. ; where subscript Indicates a certain component type, and .

[0010] The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling, wherein step S120 specifically includes: Step S122: Snapshot set of operating conditions for each type of component Perform the first-level intrinsic orthogonal decomposition (POD) separately, and then apply the cumulative energy threshold of the POD. Before truncation r ( y ( ) principal modes, to obtain the basis function matrix of the operating conditions. and the corresponding low-dimensional operating condition coefficients; Step S124: Sample within the low-dimensional operating condition coefficient space to generate... N train Each sampling point is used, and these sampling points are projected back to the original physical parameter space to generate... N train Each independent component training scenario; Step S126: For each training condition, calculate the incident neutron angular flux it contains. As a fixed boundary condition, the physical state parametersp (a) Mapping to a macroscopic section, the total neutron source term distribution As a fixed external source, the linear transport equations of a single energy group and a single direction are solved in the component subdomain to obtain the angular flux distribution sample of the component; Step S128: Collect the angular flux distribution samples calculated from all training conditions, perform the second-level intrinsic orthogonal decomposition (POD), and extract the previous... K Each mode serves as the angular flux basis function for this component type in the current energy group and direction. ,in k This is the index for the base function.

[0011] The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling, wherein step S140 specifically includes: Step S142: Determine the direction of neutron discrete motion. The dot product sign with the component interface's external normal vector n, and the component boundary Divided into incident boundary With the exit boundary ; Step S144, if dot product >0 indicates the launch direction; the windward flux value on the interface is used for this. The value is equal to the expanded value of the basis function inside the current component's interface; Step S146, if dot product <0 indicates the incident direction; the windward flux displayed on the interface is the numerical value. The value is equal to the expanded value of the basis function outside the interface of the upstream adjacent component; if the interface is the core physical boundary, then the incident value specified by the boundary conditions is taken. Step S148: Utilize numerical flux The boundary integral term in the weak form of the transport equation is split into two parts: "self-emission contribution" and "neighbor-incidence contribution".

[0012] The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling, wherein step S150 specifically includes: Step S152: Construct the global matrix according to Formula 3. The diagonal block structure describes the transport characteristics of the component itself, consisting of component subdomains. Input operators, total cross-section term, and outflow boundary The area integral operator is calculated by the projection weighted integral over the basis function space, where, Indicates the first diagonal piece l line, number k Column elements: ; (Formula 3) Step S154: Construct the global matrix The off-diagonal block structure describes the coupling relationship between adjacent components. A non-zero block exists only when two components are spatially adjacent and the neutron flow is connected. This non-zero block is calculated by a weighted integral of the basis function values ​​of the upstream component at the shared interface and the POD basis function values ​​of the downstream component at the interface. For each component... a With components b Adjacent, and components b In the case of upstream components, the calculation method for off-diagonal blocks is shown in Formula 4, where, Representation Component b With components a The interface Representation Component a With components b The first coupling block between l line, number k Column elements: ; (Formula 4) Step S156: According to the topological connection relationship of the entire core assembly, assemble all diagonal and off-diagonal blocks into a large block sparse matrix, and construct the right-hand term vector containing the total source term according to Formula 5. ;in, Indicates the core incident boundary. Indicates the core incident boundary conditions. This indicates the column vector corresponding to this component on the right. l Row elements: (Formula 5) .

[0013] This invention solves the fundamental problem of traditional global order reduction models in three-dimensional whole-core transport calculations through a systematic architecture of "component-based training and DG numerical flux coupling." Compared with traditional methods, the advantages of this invention are reflected in three aspects: First, a component operating condition extraction strategy based on at least one full-core reference solution is proposed, which greatly reduces the computation and storage costs of offline modeling; Second, by using discontinuous Galerkin windward flux as the interface coupling method, robust splicing of multiple components and multiple types of low-dimensional subspaces was achieved. Third, the high-dimensional nonlinear solution of the entire reactor core is ultimately transformed into a low-dimensional, sparse linear algebra problem, thereby achieving an order-of-magnitude improvement in computational efficiency while ensuring high-fidelity accuracy, providing a feasible core technology path for real-time applications such as reactor digital twins. Attached Figure Description

[0014] The accompanying drawings described herein are for illustrative purposes only and are not intended to limit the scope of the invention in any way; for example... Figure 1 In step S170, the process of solving the neutron flux online instead of the transport scanning process in the power iteration is merely illustrative and intended to aid in understanding the present invention. It is not intended to specifically limit the nonlinear iterative methods that can be used in the present invention. Those skilled in the art, under the guidance of the present invention, can choose various possible nonlinear iterative methods to implement the present invention according to specific circumstances, such as the JFNK method.

[0015] Figure 1 This is a technical flowchart of an embodiment of the neutron transport order reduction model calculation method based on component-level domain decomposition of the present invention. Detailed Implementation

[0016] The specific embodiments and examples of the present invention will be described in detail below with reference to the accompanying drawings. The specific embodiments described are only used to explain the present invention and are not intended to limit the specific embodiments of the present invention.

[0017] like Figure 1 As shown, this neutron transport order reduction model based on component-level domain decomposition consists of an offline stage and an online stage. Its calculation method includes the following steps: Step S110 (corresponding to step S1): In the offline stage, construct a set of component-level operating condition snapshots: perform at least one high-fidelity or multiple low-precision full-core reference solution calculations to obtain the reference solution of the entire core under complex physical conditions, and divide the entire core into several component subdomains according to the geometric boundaries of the fuel assemblies. Extract each component subdomain The local physical state information is used to construct a component condition snapshot set containing boundary incident conditions and internal physical parameters. N c Indicates the number of component subdomains; Step S120 (corresponding to step S2): In the offline stage, a component-level neutron angular flux basis function library is constructed. Addressing the high-dimensional characteristics of component boundary conditions, internal multi-physics feedback parameters, and neutron angular flux coupling in various directions during neutron transport, a two-level dimensionality reduction strategy is employed to construct the basis function library. First, the component operating condition snapshot set undergoes parameter dimensionality reduction and sampling in the operating condition space to extract the dominant modes governing changes in the local transport physics environment, constructing a low-dimensional operating condition parameter space to generate a representative training operating condition set. Second, for each training operating condition, the linear discrete ordinate transport equation is independently solved on the corresponding component subdomain to obtain angular flux distribution samples. Simultaneously, by performing intrinsic orthogonal decomposition (POD) on the angular flux distribution samples, a local angular flux basis function library classified by component type, energy group, and orientation angle is constructed. Step S130 (corresponding to step S3) In the online stage, construct a parameterized local order reduction model: For the whole core problem to be solved, discretize it into a component network, with the component type as... Components a For example, in each component subdomain Within, as shown in Formula 1, the local angular flux basis function library is used for each energy group. g ,direction m Unknown neutron angular flux Expanding the equations and substituting them into the weak form of the parameterized local transport equations shown in Equation 2, we obtain the component's local linear equations; where r represents the spatial coordinates. c This represents the low-dimensional coefficients to be determined. These are local angular flux basis functions. Representation Component a type For numerical flux, n (a) For component subdomain boundaries The outward normal vector, k It is the basis function index. Indicates the first g The total cross section of the energy group, The direction cosine of the neutron's flight direction. Q t,g Indicates the first g Total neutron source terms of the energy group: ; (Formula 1) ; (Formula 2) Step S140 (corresponding to step S3) In the online stage, interface coupling is performed based on the discontinuous Galerkin (DG) method: the windward numerical flux at the interface of the component subdomain is defined, and the adjacent components are coupled at the interface using the numerical flux, and the interface flux transfer term between components is calculated. Step S150 (corresponding to step S4) Online stage: Assemble the global block sparse linear equation system: Assemble the local equations of all components into a global block sparse linear equation system for the entire core. The unknowns of this equation system are the POD basis function coefficients of each component. Step S160 (corresponding to step S4) Online stage, solving and global reconstruction: solving the global block sparse linear equation system. The basis function coefficients of all components in the entire core are obtained. The three-dimensional neutron angular flux distribution of the entire core is reconstructed using basis functions, where A is the coefficient matrix and L is the right-hand vector. In step S170 (corresponding to step S5), during the online stage, the process of calculating the angular flux online is directly replaced by the most time-consuming transport scanning part in the power iteration or JFNK iteration, which can conveniently realize the low-dimensional and efficient solution of the neutron transport eigenvalue equation in the online stage.

[0018] This invention discloses a neutron transport model reduction calculation method based on component-level domain decomposition coupling, belonging to the field of nuclear reactor physics numerical computation and high-performance computing. This calculation method aims to solve the key bottlenecks of existing global reduction models in three-dimensional whole-core applications, such as high offline costs and poor local adaptability. It adopts a core architecture of "divide and conquer, numerical flux coupling" and includes two stages: offline and online. In the offline stage, only one full-core high-fidelity calculation or multiple low-precision calculations are required. By extracting "operating condition vectors" with fuel assemblies as subdomains and performing dimensionality reduction sampling and independent solution, a dedicated neutron angular flux basis function library classified by component type, energy group, and orientation angle is constructed. In the online stage, the whole core is regarded as a component network. Low-dimensional expansion is performed in each subdomain using basis functions. Based on the upwind numerical flux mechanism of discontinuous Galerkin (DG), robust coupling with physical conservation between components is achieved. Finally, a global block sparse linear equation system is assembled and solved to reconstruct the whole-core angular flux distribution.

[0019] Compared with existing technologies, the beneficial effects of the neutron transport model order reduction calculation method based on component-level domain decomposition coupling in this invention are as follows: First, by generating the training set through at least one reference solution, the offline cost is significantly reduced to an acceptable level; Second, the coupling of component-level basis functions with discontinuous Galerkin (DG) ensures the method's high-precision reconstruction and numerical stability of local non-uniformity; Third, the computational complexity was reduced from billions of degrees of freedom in a full-order model to a low-dimensional sparse system. While maintaining high fidelity accuracy, the computational efficiency was improved by more than three orders of magnitude, providing a feasible technical path for real-time applications such as reactor digital twins and online safety analysis.

[0020] The method for calculating the neutron transport order reduction model based on component-level domain decomposition, wherein step S110 specifically includes: Step S112: Divide the entire core into several component subdomains. , a Represents a component instance. N c Represents the total number of components, defining the set of component types in the entire heap core. , N t Represents the total number of component types for any component instance in the full-core reference solution. a Define its component operating condition vector The vector consists of three parts: the incident neutron angular flux distribution on the component boundary. The distribution of physical state parameters within the component that determine the macroscopic cross-sectional distribution. p (a) and the total neutron source term distribution within the component subscript g and m The energy group and direction index are respectively represented by the discrete ordinate method; the total neutron source term distribution It is the sum of the fission source, the scattering source, and the external source; wherein, the distribution of the physical state parameters is... p (a) This includes, but is not limited to, a series of physical quantities that affect the size of the neutron cross section, such as fuel temperature, coolant density, coolant temperature and boron concentration, which determine the macroscopic cross section distribution within the component through cross section mapping relationships; Step S114: Traverse all spatial locations of the entire heap core and extract the component condition vector for each component instance. By leveraging the natural parameter differences that arise at different locations in the stack core due to varying environments, all instance vectors of the same type of component are collected to form a snapshot set of the operating conditions of that type of component. ; where subscript Indicates a certain component type, and .

[0021] Further, step S120 specifically includes: Step S122 (corresponding to step S2.1) Dimensionality reduction of the working space: For each component type (i.e., a set of operating condition snapshots for each type of component) Perform the first-level intrinsic orthogonal decomposition (POD) separately, truncate according to the preset energy threshold, and calculate the cumulative energy threshold of the POD. Before truncation r ( y ( ) principal modes, to obtain the basis function matrix of the operating conditions. and the corresponding low-dimensional operating condition coefficients; Step S124 (corresponding to step S2.2) Training condition generation: Sampling is performed in the low-dimensional condition coefficient space to generate... N train Each sampling point (i.e., sampling coefficient) is used to project these sampling points back into the original physical parameter space to reconstruct and generate... N train Each independent component training scenario; Step S126 (corresponding to step S2.3) Angular flux sample solution: For each training case, calculate the incident neutron angular flux it contains. As fixed boundary conditions, thermal-hydraulic parameters are used for interpolation to obtain macroscopic cross-sections (e.g., physical state parameters). p (a) Mapped to a macroscopic section, the total neutron source term distribution is... As a fixed external source, the linear transport equations of a single energy group and a single direction are solved in the component subdomain to obtain the angular flux distribution sample of the component; Step S128 (corresponding to step S2.4) Basis function library construction: Collect angular flux distribution samples calculated under all training conditions, perform second-level intrinsic orthogonal decomposition (POD) according to component type, energy group, and orientation angle, and extract the previous... K Each mode serves as the final angular flux basis function for this component type in the current energy group and orientation. ,in k This is the index for the base function.

[0022] Furthermore, the upwind numerical flux mechanism based on the discontinuous Galerkin method in step S140 specifically includes: Step S142: For component subdomain boundaries any point on and discrete direction of motion Determine the direction of discrete motion of neutrons With the component interface outward normal vector n (a) dot product symbol and component boundaries Divided into incident boundary With the exit boundary ; Step S144, if dot product >0 indicates the launch direction; the windward flux value on the interface is used for this. The value is equal to the expanded value of the basis function inside the current component's interface; Step S146, if dot product <0 indicates the incident direction; the windward flux displayed on the interface is the numerical value. The value is equal to the basis function expansion value outside the interface of the upstream adjacent component; if the interface is the core physical boundary, the incident value specified by the boundary conditions is taken, that is, determined by the reflection or vacuum boundary conditions. Step S148: Utilize numerical flux The boundary integral term in the weak form of the transport equation is split into two parts: "self-emission contribution" and "neighbor-incidence contribution".

[0023] Further, step S150 specifically includes: Step S152: Construct the global matrix according to Formula 3. The diagonal block structure describes the transport characteristics of the component itself, consisting of component subdomains. Input operators, total cross-section term, and outflow boundary The area integral operator is calculated by the projection weighted integral over the basis function space, where, Indicates the first diagonal piece l line, number k Column elements: ; (Formula 3) Step S154: Construct the global matrix The off-diagonal block structure describes the coupling relationship between adjacent components. A non-zero block exists only when two components are spatially adjacent and the neutron flow is connected. This non-zero block is calculated by a weighted integral of the basis function values ​​of the upstream component at the shared interface and the POD basis function values ​​of the downstream component at the interface. For each component... a With components b Adjacent, and components b In the case of upstream components, the calculation method for off-diagonal blocks is shown in Formula 4, where, Representation Component b With components a The interface Representation Component a With components b The first coupling block between l line, number k Column elements: ; (Formula 4) Step S156: According to the topological connection relationship of the entire core assembly, assemble all diagonal and off-diagonal blocks into a large block sparse matrix, and construct the right-hand term vector containing the total source term according to Formula 5. ;in, Indicates the core incident boundary. Indicates the core incident boundary conditions. This indicates the column vector corresponding to this component on the right. l Row elements: (Formula 5) .

[0024] Furthermore, this method can be extended to the calculation of multi-physics coupling scenarios such as whole-core transport-burnup coupling or transport-thermal-hydraulic coupling. Taking transport-thermal-hydraulic coupling as an example, the angular flux distribution obtained in steps S150 and S160 is iterated to the power of power or JFNK until the flux converges. The calculated neutron flux is then used to calculate the power distribution and passed to the thermal-hydraulic program. After the thermal-hydraulic program calculates the feedback thermal parameters, it updates the physical state parameters of each component and then iteratively updates the coefficients and right-hand side terms of the global block sparse linear equation system until the coupled system converges.

[0025] Furthermore, in the online solution framework, a reduced-order neutron transport solver consisting of steps S130, S140 and S150, S160 is used to replace the transport scanning process in the traditional high-fidelity solver, and is combined with the Jacobi-less Newton-Krylov (JFNK) method or the power iteration method to solve critical eigenvalue problems containing fission source nonlinearity.

[0026] Furthermore, the neutron transport model order reduction calculation method based on component-level domain decomposition coupling of the present invention is applicable to core physics calculations of pressurized water reactors, boiling water reactors, or small modular reactors. The fuel assembly types include, but are not limited to, UO2 fuel assemblies, MOX fuel assemblies, and assemblies containing control rods or combustible poisons. The local angular flux basis function library supports dynamic loading and reuse at the component level. When the core loading scheme changes, only the global coupling relationship needs to be reassembled, without regenerating the basis function library.

[0027] The present invention provides a neutron transport order reduction calculation method based on component-level domain decomposition and discontinuous Galerkin (DG) splicing. Through a systematic design of "extracting component operating conditions from a reference solution at least once, training basis functions independently at the component level, and coupling the DG upwind flux interface", it transforms the traditionally required strong-coupled nonlinear problem of repeated full-core high-fidelity scanning into a one-time low-cost offline training and efficient online low-dimensional sparse solution. This solves the fundamental problems of the existing global order reduction model (ROM) having unbearable offline costs and insufficient local accuracy and generalization ability. In particular, the strategy of extracting component operating condition vectors based on a single full-core solution in step S110 and the mechanism of using DG upwind numerical flux to achieve physical conservation coupling of low-dimensional subspaces of different types of components in step S140 have not been disclosed or reported in the prior art for any related technical means for the three-dimensional full-core neutron transport problem.

[0028] It should be noted that this invention is based on a component-level domain decomposition coupling neutron transport order reduction calculation method. Through simulation and verification of an internationally recognized benchmark problem for a large commercial pressurized water reactor, using an 8-energy-group pin-by-pin refined full-core steady-state transport-thermal-hydraulic coupling example, the calculation process and results have been verified: while maintaining high accuracy of key physical quantities, the online calculation efficiency can be improved by three orders of magnitude compared with traditional high-fidelity methods; this method does not achieve simple functions through complex steps, nor is it a simple combination of existing conventional technologies. Its core concept and technical path are non-obvious and have been verified to have good engineering applicability.

[0029] The contents not described in detail in this specification are all prior art known to those skilled in the art, such as intrinsic orthogonal decomposition (POD), discontinuous Galerkin (DG), reduced order model (ROM), JFNK and other methods.

[0030] It should be understood that the above embodiments are only used to clearly illustrate the core principles and implementation methods of the present invention, and do not constitute a limitation on the scope of protection. For those skilled in the art, various additions, subtractions, substitutions, or improvements can be made within the core architecture and spirit of the present invention: "component operating condition extraction—component basis function training—numerical flux interface coupling". For example, the "single full-core reference calculation" in claim 1 can be a high-fidelity calculation reference solution obtained by multiple deterministic methods or Monte Carlo methods (specific accuracy indicators such as grid size, SN order, etc.), or it can be the result of one or more high-precision non-homogenized or homogenized transport calculations or diffusion calculations or spherical harmonic function calculations or simplified spherical harmonic function calculations. It can also be the result of pin-by-pin or coarse mesh block calculations using cell homogenization or component homogenization, or it can be the result of multiple low-precision solutions. Even the "single core reference solution" does not have to be "high-fidelity". It can be the result obtained by any transport calculation method, including Monte Carlo methods, deterministic Sn methods, characteristic line methods, spherical harmonic function methods, simplified spherical harmonic function methods, diffusion methods, etc. For example, the intrinsic orthogonal decomposition (POD) method can be replaced by other dimensionality reduction methods, including dynamic mode decomposition, principal component analysis, autoencoder methods, etc.; the numerical flux scheme of discontinuous Galerkin (DG) can be replaced by other stable discretization schemes, including Lax-Friedrichs flux, Roe flux, etc.; and the neutron transport order reduction calculation method based on component-level domain decomposition coupling of this invention can be further extended to transient analysis, fuel consumption calculation, or coupling with computational fluid dynamics (CFD) with higher fidelity, etc. All modifications, equivalent substitutions and improvements based on the core concept of this invention should be included within the scope of protection of the appended claims.

Claims

1. A method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling, characterized in that, Includes the following steps: Offline Training phase: Step S1. Construct a set of component-level operating condition snapshots: Based on at least one full-core reference solution calculation, divide the entire core into multiple component subdomains according to the geometric boundaries of the fuel assemblies. Extract the local physical state information of each component subdomain and construct a component operating condition snapshot set, where D represents the component subdomain. a Represents the component index. N c Indicates the number of component subdomains; Step S2. Constructing a component-level neutron angular flux basis function library: Addressing the high-dimensional characteristics of component boundary conditions, internal multi-physics feedback parameters, and neutron angular flux coupling in various directions within the neutron transport problem, a two-level dimensionality reduction strategy is employed to construct the basis function library. First, parameter dimensionality reduction and sampling are performed on the component operating condition snapshot set to extract the dominant modes governing changes in the local transport physics environment, constructing a low-dimensional operating condition parameter space to generate a representative training condition set. Second, for each training condition, the linearized discrete ordinate transport equation is independently solved on the corresponding component subdomain to obtain angular flux distribution samples. Simultaneously, by performing intrinsic orthogonal decomposition (POD) on all samples, a local angular flux basis function library classified by component type, energy group, and directional angle is constructed. Online solution phase: Step S3. Parametric Local Reduced-Order Model Construction and Coupling Steps: For the whole core problem to be solved, in each component subdomain, the unknown neutron angular flux is expanded in a low dimension using the corresponding local angular flux basis function library, and the upwind numerical flux mechanism based on the discontinuous Galerkin method is used to realize the physical conservation coupling between adjacent component subdomains at the interface. Step S4. Global system assembly and solution reconstruction steps: Assemble the local equations of all coupled component subdomains into a global block sparse linear equation system, solve the equation system to obtain the coefficients of the basis functions of each component, and reconstruct the three-dimensional neutron angle flux distribution of the entire core based on this. Step S5. Embed the above process of solving the neutron angular flux online into a power iteration or JFNK iteration framework to perform efficient calculation of the neutron transport eigenvalue equation.

2. The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling according to claim 1, characterized in that, In step S1, the component operating condition snapshot set is constructed according to component type, such as fuel components like UOX or MOX; for component instances a Its local physical state information is derived from the component operating condition vector. Characterization, the component's operating condition vector Includes: incident neutron angular flux at the component boundary Distribution of internal physical parameters of components p (a) and the distribution of total neutron source terms within the component. ; where subscript g and m These represent the energy group and the direction index of the discrete ordinate, respectively, under the discrete ordinate method.

3. The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling according to claim 2, characterized in that, The distribution of internal physical parameters of the component p (a) It includes at least the physical quantities mapped to fuel temperature, coolant density, coolant temperature, and boron concentration; the total neutron source term distribution. It is the sum of fission sources, scattering sources, and external sources.

4. The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling according to claim 2, characterized in that, Step S2 specifically includes the following sub-steps: S2.1, Dimensionality Reduction of Working Space: For each component type Operating condition snapshot set Perform the first level of intrinsic orthogonal decomposition, truncate according to the preset energy threshold, and then apply the cumulative energy threshold of POD. Before truncation r ( y ) principal modes, to obtain the basis function matrix of the operating conditions. and its low-dimensional coefficient space; S2.2, Training Case Generation: Sampling is performed within the low-dimensional coefficient space to generate... N train Each sampling coefficient is used to reconstruct the operating condition basis function matrix, resulting in... N train Each independent component training scenario; S2.3, Angular flux sample solution: For each training case, calculate the incident neutron angular flux it contains. As boundary conditions, thermal-hydraulic parameters are used for interpolation to obtain macroscopic cross-sections, with the total source term treated as a fixed external source. Solve the linear transport equations of a single energy group and a single direction on the component subdomain to obtain the angular flux distribution sample under this training condition; S2.4, Basis Function Library Construction: Collect angular flux samples from all training scenarios, perform second-level eigenorthogonal decomposition according to component type, energy group, and orientation angle, and extract the frontier function. K The principal modes constitute the final angular flux basis function. ,in k This is the index for the base function.

5. The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling according to claim 1, characterized in that, In step S3, when constructing the parameterized local reduced-order model, in each component subdomain Within, as shown in Formula 1, the local angular flux basis function library is used for each energy group. g ,direction m neutron angular flux Expanding the equations and substituting them into the weak form of the parameterized local transport equations shown in Equation 2, we obtain the component's local linear equations; where r represents the spatial coordinates. c This represents the low-dimensional coefficients to be determined. These are local angular flux basis functions. Representation Component a type For numerical flux, n (a) For each component subdomain boundary The outward normal vector, k It is the basis function index. Indicates the first g The total cross section of the energy group, The direction cosine of the neutron's flight direction. Q t,g Indicates the first g Total neutron source terms of the energy group: (Official 1); (Official 2).

6. The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling according to claim 1, characterized in that, In step S3, the windward numerical flux coupling mechanism based on the discontinuous Galerkin method specifically refers to: For component subdomain boundaries any point on and discrete direction of motion According to the dot product The sign of n determines the flux value. (a) It is the outer normal vector; If dot product >0, this boundary point is the outgoing boundary. The numerical flux value is taken from each component subdomain. Internal flux expansion value; If dot product <0, the boundary point is the incident boundary. The numerical flux is taken as the flux expansion value of the upstream adjacent component subdomain at the interface; if the boundary is the core physical boundary, the numerical flux is determined by the reflection or vacuum boundary conditions.

7. The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling according to claim 1, characterized in that, In step S4, the coefficient matrix of the global block sparse linear equation system It has the following structure: For any component a Its corresponding diagonal piece It consists of the projections of the volume integral operator, the total cross-sectional response term operator, and the outgoing boundary integral operator within the component's subdomain onto the local basis function space; For adjacent components a With components b When the component b In the direction of discrete motion The above is a component. a When upstream, there exists a non-zero non-diagonal block. And the off-diagonal block is composed only of components b The basis functions in the shared interface Top component a The projective integrals of the basis functions constitute the basis functions; global matrix The remaining blocks are all zero, ultimately forming a highly sparse blocky linear system that is 3 to 4 orders of magnitude smaller than the full-order model.

8. The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling according to claim 1, characterized in that, This method is extended to calculate multi-physics coupling scenarios such as whole-core transport-burnup coupling or transport-thermal-hydraulic coupling. In step S4, the angular flux distribution obtained is solved and then iterated to flux convergence through power iteration or JFNK iteration. The calculated neutron flux is used to calculate the power distribution and passed to the thermal-hydraulic program. After the thermal-hydraulic program calculates the feedback thermal parameters, it updates the physical state parameters of each component and then iteratively updates the coefficients and right-hand side terms of the global block sparse linear equation system until the coupled system converges.

9. The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling according to claim 1, characterized in that, In the online solution framework, the reduced-order neutron transport solver, consisting of steps S3 and S4, is used to replace the transport scanning process in the traditional high-fidelity solver. It is combined with the Jacobi-less Newton-Krylov (JFNK) method or the power iteration method to solve critical eigenvalue problems containing fission source nonlinearity.

10. The method for constructing a neutron transport order reduction model based on component-level domain decomposition and coupling according to claim 1, characterized in that, This method is used for core physics calculations of pressurized water reactors, boiling water reactors, or small modular reactors, where fuel assembly types include, but are not limited to, UO2 fuel assemblies, MOX fuel assemblies, and assemblies containing control rods or combustible poisons; and the local angle flux basis function library supports dynamic loading and reuse on an assembly-by-assembly basis; when the core loading scheme changes, only the global coupling relationship needs to be reassembled, without the need to regenerate the basis function library.

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