Gpu-based online homogenization pressurized water reactor core physics calculation method

Abstract

The present application belongs to the technical field of reactor core physics calculation, and particularly relates to an online homogenization pressurized water reactor core physics calculation method based on GPU. The method comprises the following steps: performing actual core modeling; performing multi-group two-dimensional full-core transport calculation for each layer according to the current core condition; performing online homogenization calculation, and combining the two-dimensional full-core transport calculation result to generate super homogenization factors; and after the generation of all layered cell homogenization parameters and super homogenization factors is completed, performing subsequent three-dimensional pin-by-pin SP3 calculation. The present application has the beneficial effect that by using the design based on a small multi-GPU computing platform, the advantages of parallel computing can be fully utilized, and faster calculation speed can be achieved.

Description

Technical Field

[0001] This invention belongs to the field of reactor core physics calculation technology, specifically relating to a GPU-based online homogenization pressurized water reactor core physics calculation method. Background Technology

[0002] The essence of reactor core physics calculations is to obtain the neutron flux distribution at various locations in the core by solving the neutron transport equation. The neutron transport equation is a fundamental equation describing the neutron flux that must be satisfied when neutrons migrate in the medium. It is a differential-integral equation that depends on variables such as space, time, energy, and angle.

[0003]

[0004] Where: v is the neutron velocity; Ω is the direction of neutron motion; ∑ is the neutron fluence rate; t (r,E) represents the macroscopic total cross section of a neutron with energy E at position r; Q f (r,E,Ω,t) represents a fission neutron source with energy E and angle Ω at time t and position r; S(r,E,Ω,t) represents an external neutron source with energy E and angle Ω at time t and position r; ∑ s (r,E') represents the scattering cross section at point r with energy E'; f(r,E'→E,Ω'→Ω) is the scattering function at point r, from energy E' to energy E, with the neutron's motion direction from Ω' to Ω; Let be the neutron flux rate at time t with energy E' and angle Ω' at position r.

[0005] Due to limitations in computer performance, directly solving the three-dimensional neutron transport equations to obtain neutron fluence rates at arbitrary positions, energies, and angles restricts its practical application in engineering due to both computational speed and storage overhead. Only approximate solutions to the three-dimensional neutron transport equations are possible. Currently, the core physics calculation methods used in engineering design were established after the 1970s based on advanced component homogenization theory and modern coarse-grid nodal methods. Within the framework of transport theory, this method first homogenizes the non-homogeneous material spatially, typically on a component-by-component basis, such as... Figure 1 As shown:

[0006] Secondly, the angular distribution of neutron flux is approximated using diffusion theory. Energyly, neutrons within a certain range are grouped into a single energy group. Through these approximations, solving the neutron transport equation is transformed into solving a few-group neutron diffusion equation. The resulting solution is no longer the neutron flux distribution at arbitrary positions, energies, and angles within the three-dimensional core, but rather the neutron flux distribution within a few energy groups within a homogenized coarse mesh. Finally, the neutron flux distribution under its internal non-homogeneous state is obtained through neutron flux rate reconstruction within the homogenized nodes of the coarse mesh. In this method, a homogenized cross-section table needs to be pre-made for each fuel assembly according to core parameters such as fuel temperature, moderator temperature, and boron concentration. During the core coarse mesh diffusion calculation, the homogenized cross-section corresponding to the current core state is retrieved from the cross-section table based on the current fuel temperature, moderator temperature, boron concentration, and other core parameters, and then the coarse mesh diffusion calculation is performed.

[0007] In recent years, driven by the explosive growth in computing power demand in the field of artificial intelligence, graphics processing unit (GPU) technology has been continuously updated, and computing performance has improved rapidly. Thanks to the massively parallel design of GPUs, GPU computing performance has a significant advantage over CPUs. The CPU-GPU heterogeneous platform can leverage the advantages of CPUs in terms of high programmability and control flow generation capabilities, while also taking into account the characteristics of GPUs, which have a large number of computing units and can efficiently complete large-scale calculations. It has been widely used in scientific computing, big data analysis, artificial intelligence and other fields.

[0008] The rapid development of computer technology has made it technically possible to perform detailed modeling and calculations of the entire reactor core at the bar grid level. Extensive research has been conducted both domestically and internationally on next-generation reactor core physics calculation methods, and GPU-based programs are constantly emerging. The technical approaches employed include the following:

[0009] i) Direct 3D transport method. This method directly solves the three-dimensional neutron transport equations of the entire reactor using deterministic methods (usually the 3D MOC method) and non-deterministic methods (Monte Carlo method). This approach does not require homogenization of components or cells, but it places extremely high demands on computer computing speed and storage, making it unlikely to be practical for engineering applications for a long time to come.

[0010] ii) Two-dimensional (2D) transport + one-dimensional (1D) transport / diffusion method. The 2D / 1D method here refers to using the method of characteristics (MOC) to solve the two-dimensional transport equations for each axial layer, and using the discrete coordinate method (Sn) and diffusion method to solve the axial one-dimensional problem for each gate cell. This approach has weak coupling between the two-dimensional and one-dimensional transport methods. The approximation used for lateral leakage during implementation can lead to reduced computational accuracy and convergence problems.

[0011] iii) Two-dimensional transport + three-dimensional transport / diffusion method. The method of characteristics (MOC) is used to solve the two-dimensional transport equations for each axial layer, and the discrete coordinate method (Sn) or diffusion methods are used to solve the overall stack transport or diffusion equations on a rod-grid basis. Currently, most algorithms of this type employ parallel acceleration techniques such as MPI+OPENMP, but the computational efficiency cannot meet the requirements of engineering applications. Summary of the Invention

[0012] The purpose of this invention is to provide a GPU-based online homogenization method for pressurized water reactor core physics calculations. This method has high calculation accuracy and ensures calculation speed, enabling more accurate simulation of nuclear power plant operation, thereby providing assurance for nuclear power plant operation and improving its safety.

[0013] The technical solution of this invention is as follows: A GPU-based online homogenization method for pressurized water reactor core physics calculations, comprising the following steps:

[0014] Step 1: Perform actual reactor core modeling;

[0015] Step 2: Based on the current core condition, perform multi-group two-dimensional whole-core transport calculations for each layer as a prerequisite for implementing the online homogenization method;

[0016] Step 3: Perform online homogenization calculation, generate minority group cell homogenization parameters based on transport calculation results, use the generated minority group homogenization parameters to perform two-dimensional whole-stack pin-by-pin SP3 calculation, and generate super homogenization factor by combining the two-dimensional whole-stack transport calculation results.

[0017] Step 4: After all the layered cell homogenization parameters and super homogenization factors have been generated, perform the subsequent three-dimensional pin-by-pin SP3 calculation;

[0018] Step 5: Once the core neutron flux rate converges to the specified accuracy, calculate the three-dimensional core power distribution at this point, update the core state parameters under this power distribution, and check whether the core state parameters no longer change. If yes, the calculation is complete; otherwise, return to step 2 to recalculate.

[0019] In step 1, the core model is divided into axial layers according to the axial material distribution, and the modeling data and calculations of each layer are allocated to different GPUs.

[0020] In step 2, the two-dimensional whole-stack transport method is used to solve the problem by integrating along the trajectory of the neutron, starting from the differential form of the neutron transport equation.

[0021] The integral solution in step 2 is as follows:

[0022] The steady-state multigroup transport equation for neutrons along a certain direction is:

[0023]

[0024] In the formula: θ n The direction of neutron flight Ω mn The polar angle (where m represents azimuth and n represents polar angle); s is the projection of the neutron trajectory onto the xy plane; ψ g (s) represents the neutron angular fluence rate; Q g (s) represents the neutron source term at that location; ∑ g (s) represents the macroscopic total cross section; the subscript g indicates the energy group;

[0025] Under the assumptions of isotropic scattering and flat source approximation, we have:

[0026]

[0027] Where: χ g For the fission spectrum, k eff Effective value-added factor, vΣ f,g' (s) represents the cross-section of fission neutron generation, Σ sg′→g (s) represents the neutron scattering cross section from energy group g′ to g; φ g' (s) represents the neutron flux of energy group g′.

[0028] With the macroscopic cross section and neutron source term constant, neutrons at an angular fluence rate in a given direction The incident angular fluence of the neutron after passing through the grid element can be explicitly obtained by solving the transport equation (3). and the average angular volume ratio on line segment s

[0029] Given the macroscopic cross section and neutron source terms of each region, a two-dimensional non-uniform core scan is performed using feature lines to ensure that feature lines pass through each material region. The energy group average neutron flux rate of each material region is calculated, and then the neutron source terms of each region are updated according to formula (3). The next feature line scan is then performed until the energy group neutron flux rate of all regions meets the convergence criterion.

[0030] In step 3, an online equivalent homogenization method is used. For the layer containing the active region, given the core state parameters such as fuel temperature, moderator temperature, and boron concentration, a two-dimensional whole-core transport calculation is performed to obtain the neutron fluence energy spectrum at each position of the two-dimensional core. Then, the cell homogenization minority group cross-section parameters are generated with the volume fluence rate as the weight. For the reflector layers at the top and bottom of the core, the neutron fluence distribution of the adjacent active region layer is directly used to generate the cell homogenization cross-section.

[0031] In step 3, the cell neutron fluence rate calculated using the two-dimensional full-repository SP3 method is numerically equal to the cell group neutron fluence rate calculated by transport calculation divided by the SPH factor. Multiplying the SPH factor by the cell group neutron fluence rate calculated by SP3 yields the cell group neutron fluence rate that is completely consistent with the two-dimensional transport calculation. To determine the SPH factor of each cell group neutron fluence rate, iterative solution is required. First, assume that the SPH factor of each cell is 1.0, perform the two-dimensional full-repository SP3 method to obtain the group neutron fluence rate of each cell. Use the ratio of the group neutron fluence rate obtained by the two-dimensional transport calculation to the group neutron fluence rate obtained by the two-dimensional SP3 calculation as the SPH factor for the next iteration. This process is repeated until the group neutron fluence rate of each cell converges to a certain accuracy. For the reflector layers at the top and bottom of the core, the SPH factor is set to 1.0.

[0032] In step 4, the equation form of the generalized SP3 method is used, and the neutron fluence rate of the energy group inside the homogenized gate cell satisfies the generalized SP3 equation:

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] In the formula, ∑ 0，g For the removed section, ∑ t，g For the total cross section, Q g For the neutron source term, χ g For the fission spectrum, k eff Effective proliferation factor, v∑ f，g To generate a cross section for fission neutrons, ∑ sg′g The neutron scattering cross section from energy group g′ to g. This represents the zeroth-order neutron fluence rate, which is the neutron fluence rate. denoted as the second-order neutron fluence rate, with the subscript g or g' indicating the energy group.

[0039] In step 4, the single-node method is used to solve the generalized SP3 equations for the three-dimensional reactor core. For a single node, if the neutron source distribution within the node is known and the incident neutron fluence of each face is given, the energy group neutron fluence distribution within the node is determined by solving the generalized SP3 equations. This leads to the surface-average neutron emission fluence of all faces of the cell, and the emission neutron fluence of one cell is the incident neutron fluence of another cell. Therefore, the surface-average neutron emission fluence of all cells can be obtained more accurately. The new generalized SP3 equations within the block are solved by transverse integration, decomposing the three-dimensional equations into three one-dimensional equations. A polynomial approximation is introduced to solve the transverse integral neutron flux rate. The neutron source distribution within the block is calculated based on the transverse integral neutron flux rate of each energy group within the gate element. The determination of the neutron source distribution and the energy group neutron flux rate distribution within the block is solved iteratively using the source iteration method, while continuously updating the eigenvalue keff during the iteration process.

[0040] The solution process of the three-dimensional neutron transport equation in step 5 is as follows: After the three-dimensional core model is established, the three-dimensional core is first layered, and the core state is assumed, including fuel temperature and moderator temperature. Given the core state, two-dimensional whole-core transport calculation is performed. Then, the cells are homogenized online to obtain homogenized cross-sectional parameters, and the SPH factor is generated. Next, three-dimensional whole-core pin-by-pin SP3 calculation is performed to obtain the three-dimensional neutron flux distribution. The power distribution at this time is used to perform thermal-hydraulic calculation or critical boron calculation to update the core state. Then, it is checked whether the neutron flux distribution and each core state parameter have converged. If they have not converged, the updated core state parameters are used to perform two-dimensional whole-core transport calculation again. This process is repeated iteratively until the three-dimensional neutron flux distribution and each core state parameter converge.

[0041] The beneficial effects of this invention are as follows: By adopting a design based on a small multi-GPU computing platform, the advantages of parallel computing can be fully utilized to achieve faster calculation speeds. This means that the physical calculations for nuclear power plants can be completed in a shorter time, improving operational efficiency and responsiveness. This is crucial for the daily operation and emergency handling of nuclear power plants, providing timely and accurate results and decision-making basis. The high-precision three-dimensional core physics calculation method can be used to evaluate and verify various safety-related parameters. For example, it can calculate the distribution and changes of key safety parameters such as coolant temperature, fuel temperature, and neutron flux density. This helps identify potential safety risks and anomalies, and take necessary measures to ensure system safety. Furthermore, this algorithm also provides a high-precision simulation tool for the research and development of new nuclear power technologies. By using this method for simulation and optimization, research teams can better assess the application potential of new technologies in nuclear power plants, explore the margins for nuclear energy development, and improve the economics of nuclear power plants, providing strong support for the innovation and progress of nuclear energy technology. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of component homogenization;

[0043] Figure 2 This is a schematic diagram illustrating the coupling between two-dimensional whole-stack transport and three-dimensional bar-by-bar SP3 calculation;

[0044] Figure 3 This is a schematic diagram of the feature line method;

[0045] Figure 4 This is a schematic diagram of cell homogenization;

[0046] Figure 5 Here is a flowchart for calculating the SPH factor;

[0047] Figure 6 Here is a flowchart of the SP3 calculation process for the reactor core;

[0048] Figure 7 This is a flowchart of the three-dimensional core physics calculation based on the online homogenization method;

[0049] Figure 8 This is a diagram illustrating thread memory access. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] The three-dimensional neutron transport equation solving algorithm provided in this invention is based on GPU hardware and employs a coupled approach of two-dimensional transport calculation and three-dimensional bar-by-bar SP3 calculation to solve the three-dimensional neutron transport equation. This method divides the actual reactor core into layers according to its axial material properties, performs two-dimensional whole-core transport calculation, and generates cell homogenization cross-section parameters and super-homogenization factors online for subsequent three-dimensional bar-by-bar SP3 calculations. The application of cell homogenization parameters and super-homogenization factors generated online in the two-dimensional whole-core transport calculation ensures that the algorithm can capture the shape of the power distribution at the two-dimensional level, guaranteeing high computational accuracy.

[0052] Compared to current engineering applications of three-dimensional reactor core physics calculation methods, which employ component homogenization and generate two sets of homogenization parameters using a single component model, and utilize a diffusion method for three-dimensional calculations, this approach neither considers the influence of the energy spectrum of surrounding components in the actual reactor core arrangement nor takes into account the non-uniformity effects within the components. Furthermore, the diffusion solution method introduces approximations in its algorithm. In contrast, the method provided by this invention offers higher computational accuracy.

[0053] In next-generation core physics calculation methods, the direct three-dimensional transport method places extremely high demands on computer computing speed and storage, making it unlikely to be practically applicable in engineering for a considerable period. While the two-dimensional (2D) transport plus one-dimensional (1D) transport algorithm offers higher computational accuracy, the weak coupling between the two-dimensional and one-dimensional operations leads to reduced accuracy and convergence issues due to approximations used for lateral leakage during implementation. Furthermore, the use of multi-group computation in both two-dimensional and one-dimensional calculations limits the algorithm's computational speed. The algorithm disclosed in this invention only generates gate homogenization parameters and super-homogenization factors in the two-dimensional calculation; the results of the three-dimensional calculation do not directly affect the two-dimensional calculation, thus making the algorithm more stable. The high computational efficiency of this invention is ensured by combining GPU hardware acceleration with energy group compression technology in online homogenization.

[0054] This invention employs a three-dimensional reactor core neutron transport equation solving algorithm that couples two-dimensional whole-core layer-by-layer transport calculations using graphics processing unit (GPU) hardware to generate homogenization parameters online with three-dimensional pin-by-pin (SP3) third-order simplified spherical harmonic functions. This algorithm, designed for a finely modeled three-dimensional reactor core, performs two-dimensional whole-core non-uniform transport calculations on each axial layer of the reactor core based on real-time reactor conditions (such as fuel temperature distribution, moderator temperature distribution, boron concentration, etc.). Based on the two-dimensional calculation results, it generates online cell homogenization cross-sections (including total neutron energy group cross-section, absorption cross-section, fission cross-section, scattering cross-section, etc.) and a super-homogenization correction factor (SPH factor). Using these homogenization parameters, it performs three-dimensional whole-core pin-by-pin SP3 transport calculations to obtain the flux rate distribution and power distribution at the three-dimensional core cell level. The specific calculation process is as follows: Figure 2 As shown.

[0055] A GPU-based online homogenization method for pressurized water reactor core physics calculations includes the following steps:

[0056] Step 1: Perform actual core modeling. Based on the axial material distribution of the core model, divide it into axial layers and allocate the modeling data and calculations for each layer to different GPUs.

[0057] Step 2: Based on the current core condition, perform multi-group two-dimensional whole-core transport calculations for each layer as a prerequisite for implementing the online homogenization method;

[0058] The two-dimensional whole-stack transport method used in this invention is the characteristic line (MOC) method. This method starts from the differential form of the neutron transport equation and performs integral solutions along the trajectory of neutron movement (called the characteristic line).

[0059] The steady-state multigroup transport equation for neutrons along a certain direction is:

[0060]

[0061] In the formula: θ n The direction of neutron flight Ω mn The polar angle (where m represents azimuth and n represents polar angle); s is the projection of the neutron trajectory onto the xy plane; ψ g (s) represents the neutron angular fluence rate; Q g (s) represents the neutron source term at that location; Σ g (s) represents the macroscopic total cross section; the subscript g indicates the energy group;

[0062] Under the assumptions of isotropic scattering and flat source approximation, we have:

[0063]

[0064] Where: χ g For the fission spectrum, k eff Effective value-added factor, vΣ f,g' (s) represents the cross-section of fission neutron generation, Σ sg′→g (s) represents the neutron scattering cross section from energy group g′ to g; φ g' (s) represents the neutron flux of energy group g′.

[0065] With the macroscopic cross section and neutron source term constant, neutrons at an angular fluence rate in a given direction The incident angular fluence of the neutron after passing through the grid element can be explicitly obtained by solving the transport equation (3). and the average angular volume ratio on line segment s like Figure 3 As shown.

[0066] Given the macroscopic cross section and neutron source terms of each region, a two-dimensional non-uniform core scan is performed using feature lines to ensure that feature lines pass through each material region. The energy group average neutron flux rate of each material region is calculated, and then the neutron source terms of each region are updated according to formula (3). The next feature line scan is then performed until the energy group neutron flux rate of all regions meets the convergence criterion.

[0067] Step 3: Perform online homogenization calculation, generate minority group cell homogenization parameters based on transport calculation results, use the generated minority group homogenization parameters to perform two-dimensional whole-stack pin-by-pin SP3 calculation, and generate super homogenization factor by combining the two-dimensional whole-stack transport calculation results.

[0068] Unlike current engineering applications that use core physics analysis and calculation methods based on component homogenization, the three-dimensional core physics calculation method disclosed in this invention does not require a pre-made homogenization parameter cross-section table, but generates cell homogenization parameters online in real time during the calculation process.

[0069] In the online equivalent homogenization method, for the layer containing the active region, given the core state parameters such as fuel temperature, moderator temperature, and boron concentration, a two-dimensional whole-core transport calculation is performed (with total reflection boundary conditions in the axial direction). After obtaining the neutron fluence energy spectrum at each location in the two-dimensional core, the cell homogenization minority group cross-section parameters are generated with the volume fluence rate as the weight. For the reflector layers at the top and bottom of the core, the neutron fluence distribution of the adjacent active region layer is directly used to generate the cell homogenization cross-section.

[0070] If only the cell homogenized cross-sections generated from two-dimensional whole-reactor transport calculations are used for two-dimensional whole-reactor bar-by-bar SP3 calculations, there will be a discrepancy between the cell neutron fluence distribution obtained from the SP3 calculations and the results from the two-dimensional transport calculations. This is because the SP3 calculations solve for the SP3 equations approximated to the neutron transport equations, and the cells are homogenized. However, the two-dimensional whole-reactor transport calculations solve for the neutron transport equations, and the cells are non-homogeneous. To ensure the accuracy of three-dimensional whole-reactor bar-by-bar SP3 calculations, this discrepancy needs to be reduced at the two-dimensional level first. The Super Homogenization Factor (SPH factor) eliminates this discrepancy at the two-dimensional level. It is a correction factor applied to the cell homogenized energy group cross-sections, multiplying all types of cross-sections for each energy group by a correction factor. The basic principle of super-homogenization equivalence is to ensure that the cell reaction rate is conserved before and after equivalence (the energy group cross section multiplied by the energy group neutron fluence rate remains unchanged). Therefore, using the cell homogenized cross section after applying the super-homogenization factor, the cell neutron fluence rate calculated by SP3 for the entire two-dimensional stack should be equal to the cell energy group neutron fluence rate calculated by transport divided by the SPH factor. Multiplying the SPH factor by the cell energy group neutron fluence rate calculated by SP3 will yield the cell energy group neutron fluence rate that is completely consistent with the two-dimensional transport calculation.

[0071] To determine the SPH factor of the neutron fluence rate for each energy group in each cell, an iterative solution is required. First, assume the SPH factor of each cell is 1.0. Perform two-dimensional full-stack, bar-by-bar SP3 calculations to obtain the energy group neutron fluence rate for each cell. The ratio of the energy group neutron fluence rate obtained from the two-dimensional transport calculation to that obtained from the two-dimensional SP3 calculation is used as the SPH factor for the next iteration. This process is repeated until the energy group neutron fluence rate of each cell converges to a certain accuracy. The calculation process is as follows: Figure 6 As shown. For the reflector layers located at the top and bottom of the reactor core, the SPH factor is set to 1.0.

[0072] Step 4: After all the layered cell homogenization parameters and super homogenization factors have been generated, perform the subsequent three-dimensional pin-by-pin SP3 calculation;

[0073] SP3 theory is based on spherical harmonic functions (P N This invention simplifies the theory; the SP3 equations, solved by SP3 theory, are derived by transforming the neutron transport equations after introducing a third-order spherical harmonic function approximation of the neutron angular fluence distribution. Compared to diffusion theory, the SP3 transport calculations of the entire three-dimensional reactor provide a better approximation of transport theory, balancing computational accuracy and efficiency, making it an ideal choice for bar-by-bar calculations of the entire three-dimensional reactor. This invention employs the equation form of the generalized SP3 method, where the neutron fluence rate of the energy group within the homogenized grid cells satisfies the generalized SP3 equations:

[0074]

[0075]

[0076]

[0077]

[0078]

[0079] In the formula, Σ 0，g For the removed section, ∑ t，g For the total cross section, Q g For the neutron source term, χ g For the fission spectrum, k eff Effective proliferation factor, v∑ f，g To generate a cross section for fission neutrons, ∑ sg′g The neutron scattering cross section from energy group g′ to g. This represents the zeroth-order neutron fluence rate, which is the neutron fluence rate. denoted as the second-order neutron fluence rate, with the subscript g or g' indicating the energy group.

[0080] This invention employs a single-node method to solve the three-dimensional generalized SP3 equations for the reactor core, as shown in Figure 7. For a single node (cell), if the neutron source distribution within the node is known and the incident neutron fluence of each face is given, the neutron fluence distribution of the energy groups within the node is determined by solving the generalized SP3 equations within the node. This leads to the surface-average neutron emission fluence of all faces of the cell, and the emission neutron fluence of one cell is equivalent to the incident neutron fluence of another cell. The surface-average incident neutron fluence of all cells can be updated for the next calculation. The solution to the generalized SP3 equations within the node utilizes transverse integration, decomposing the three-dimensional equations into three one-dimensional equations, and employing a polynomial approximation for the transverse integral neutron fluence. The neutron source distribution within the node can be calculated based on the transverse integral neutron fluence of each energy group within the cell. The distribution of neutron sources and the neutron flux distribution within the energy group within the block are determined iteratively using the source iteration method, while the eigenvalues ​​keff are continuously updated during the iteration process.

[0081] Step 5: Once the core neutron flux rate converges to the specified accuracy, calculate the three-dimensional core power distribution at this point, update the core state parameters (fuel temperature distribution, moderator temperature distribution, etc.) under this power distribution, and check whether the core state parameters no longer change. If yes, the calculation is complete; otherwise, return to step 2 to recalculate.

[0082] Solving the three-dimensional neutron transport equations involves balancing numerous core parameters (such as fuel temperature, moderator temperature, boron concentration, etc.) and neutron distribution. The specific calculation process is as follows: Figure 2As shown. After the three-dimensional core model is established, the three-dimensional core is first layered, and assumptions are made about the core state, including fuel temperature, moderator temperature, etc. Given the core state, two-dimensional whole-core transport calculations are performed. Then, the cells are homogenized online to obtain homogenized cross-sectional parameters, and the SPH factor is generated. Next, three-dimensional whole-core pin-by-pin SP3 calculations are performed to obtain the three-dimensional neutron flux distribution. The power distribution at this time is used to update the core state for thermal-hydraulic calculations or critical boron calculations. Then, it is checked whether the neutron flux distribution and each core state parameter have converged. If they have not converged, the updated core state parameters are used to perform two-dimensional whole-core transport calculations again. This process is repeated iteratively until the three-dimensional neutron flux distribution and each core state parameter converge.

[0083] Given the characteristics of massively parallel computing on GPUs, the algorithm logic and data storage structure of the stacked computing method need to be rationally designed to maximize the performance of the GPU.

[0084] For algorithms, GPU computing requires high parallelism; the higher the parallelism, the higher the GPU's computational efficiency. In the two-dimensional non-uniform transport computation module, the characteristics of the feature line algorithm inherently possess high parallelism. The tracing of each feature line can be carried out in parallel, and the concurrency of hundreds of millions can fully utilize the GPU's performance. In the online homogenization module, the generation of uniform gate energy group cross-sections can be computed concurrently, with the concurrency being the number of gates multiplied by the number of energy groups. For commercial pressurized water reactor examples, the concurrency can reach tens of millions. In the three-dimensional bar-by-bar transport computation module, traditional directional scanning methods limit GPU performance. The single-node scanning method allows the GSP3 equations of each gate node to be solved in parallel, maximizing computational concurrency.

[0085] For highly parallel algorithms, the limiting factor for efficient GPU computation is no longer the algorithm itself, but rather the access speed of GPU memory. A reasonable data storage structure determines the GPU's computation speed. While object-oriented storage structures are developer-friendly, they are not ideal for GPU performance. Accessing data deep within a derived type chain requires multiple pointers and is completely segmented, failing to meet the GPU's memory cohesion requirements. GPU computation favors flattened data structures, where a single array stores a type of data. In fact, during GPU computation, concurrent threads execute the same code, and a single data read simultaneously accesses a contiguous block of memory. Storing a type of data within the same array allows adjacent GPU threads to access adjacent memory locations, and a single access can retrieve data needed by multiple threads. Figure 8As shown, the left side represents a non-merged memory access storage structure. Assuming a thread can read four data lengths at a time, when executing the same code (performing the same load), threads T1, T2, T3, and T4 will need to perform four memory accesses to read the data required for computation. When using... Figure 8 (Right) With the merged memory access storage structure, threads T1, T2, T3, and T4 only need to perform one memory access to complete the reading of the required data, which can greatly improve the computing efficiency.

Claims

1. A GPU-based online homogenization method for pressurized water reactor core physics calculations, characterized in that, Includes the following steps: Step 1: Perform actual reactor core modeling; In step 1, the core model is divided into axial layers according to the axial material distribution, and the modeling data and calculations of each layer are allocated to different GPUs. Step 2: Based on the current core condition, perform multi-group two-dimensional whole-core transport calculations for each layer as a prerequisite for implementing the online homogenization method; In step 2, the two-dimensional whole-pile transport method is used to solve the problem by integrating along the trajectory of the neutron, starting from the differential form of the neutron transport equation. The integral solution in step 2 is as follows: The steady-state multigroup transport equation for neutrons along a certain direction is: （2）， In the formula: The direction of neutron flight The polar angle; s is the projection of the neutron trajectory onto the xy plane; Neutron angle fluence rate; This is the neutron source term at that location; The macroscopic cross section is represented by the subscript g, which indicates the energy group. Under the assumptions of isotropic scattering and flat source approximation, we have: （3）， In the formula: For fission spectrum, Effective value-added factors To generate cross-sections for fission neutrons For the group arrive neutron scattering cross section; With the macroscopic cross section and neutron source term constant, neutrons at an angular fluence rate in a given direction The incident angular fluence of the neutron after passing through the grid element can be obtained explicitly by solving the transport equation (3). and the average angular volume ratio on line segment s , Given the macroscopic cross section and neutron source term of each region, perform a two-dimensional non-uniform core scan with feature lines to ensure that feature lines pass through each material region. Calculate the energy group average neutron flux rate of each material region, and then update the neutron source term of each region according to formula (3). Perform the next feature line scan until the energy group neutron flux rate of all regions meets the convergence criterion. Step 3: Perform online homogenization calculation, generate minority group cell homogenization parameters based on transport calculation results, use the generated minority group homogenization parameters to perform two-dimensional whole-stack pin-by-pin SP3 calculation, and generate super homogenization factor by combining the two-dimensional whole-stack transport calculation results. In step 3, an online equivalent homogenization method is used. For the layer containing the active region, given the core state parameters such as fuel temperature, moderator temperature, and boron concentration, a two-dimensional whole-core transport calculation is performed to obtain the neutron fluence energy spectrum at each position of the two-dimensional core. Then, the cell homogenization minority group cross-section parameters are generated with the volume fluence rate as the weight. For the reflector layers at the top and bottom of the core, the neutron fluence distribution of the adjacent active region layer is directly used to generate the cell homogenization cross-section. In step 3, the cell neutron fluence rate calculated using the two-dimensional full-repository SP3 method is numerically equal to the cell group neutron fluence rate calculated by transport calculation divided by the SPH factor. The SPH factor is then multiplied by the cell group neutron fluence rate calculated by SP3 to obtain the cell group neutron fluence rate that is completely consistent with the two-dimensional transport calculation. To determine the SPH factor of each cell group neutron fluence rate, iterative solution is required. First, assume that the SPH factor of each cell is 1.0, perform the two-dimensional full-repository SP3 method to obtain the group neutron fluence rate of each cell. The ratio of the group neutron fluence rate obtained by the two-dimensional transport calculation to the group neutron fluence rate obtained by the two-dimensional SP3 calculation is used as the SPH factor for the next iteration. This process is repeated until the group neutron fluence rate of each cell converges to a certain accuracy. For the reflector layers at the top and bottom of the core, the SPH factor is set to 1.

0. Step 4: After all the layered cell homogenization parameters and super homogenization factors have been generated, perform the subsequent three-dimensional pin-by-pin SP3 calculation; In step 4, the equation form of the generalized SP3 method is used, and the neutron fluence rate of the energy group inside the homogenized gate cell satisfies the generalized SP3 equation: （4）， （5）， （6）， （7）， （8）， In the formula, To remove the cross section, For the total cross section, For neutron source terms, For fission spectrum, Effective growth factors To generate cross-sections for fission neutrons For the group arrive Neutron scattering cross section This represents the zeroth-order neutron fluence rate, which is the neutron fluence rate. The second-order neutron fluence rate; In step 4, the single-node method is used to solve the generalized SP3 equations for the three-dimensional reactor core. For a single node, if the neutron source distribution within the node is known and the incident neutron fluence of each face is given, the energy group neutron fluence distribution within the node is determined by solving the generalized SP3 equations. This leads to the surface-average neutron emission fluence of all faces of the cell, and the emission neutron fluence of one cell is the incident neutron fluence of another cell. Therefore, the surface-average neutron emission fluence of all cells can be obtained more accurately. The new generalized SP3 equation within the block is solved by transverse integration, which decomposes the three-dimensional equation into three one-dimensional equations. A polynomial approximation is introduced to solve the transverse integral neutron flux rate. The neutron source distribution within the block is calculated based on the transverse integral neutron flux rate of each energy group within the gate element. The determination of the neutron source distribution and the energy group neutron flux rate distribution within the block is solved iteratively using the source iteration method, while continuously updating the eigenvalue keff during the iteration process. Step 5: Once the core neutron flux rate converges to the specified accuracy, calculate the three-dimensional core power distribution at this point, update the core state parameters under this power distribution, and check whether the core state parameters no longer change. If yes, the calculation is complete; otherwise, return to step 2 to recalculate. The solution process of the three-dimensional neutron transport equation in step 5 is as follows: After the three-dimensional core model is established, the three-dimensional core is first layered, and the core state is assumed, including fuel temperature and moderator temperature. Given the core state, two-dimensional whole-core transport calculation is performed. Then, the cells are homogenized online to obtain homogenized cross-sectional parameters, and the SPH factor is generated. Next, three-dimensional whole-core pin-by-pin SP3 calculation is performed to obtain the three-dimensional neutron flux distribution. The power distribution at this time is used to perform thermal-hydraulic calculation or critical boron calculation to update the core state. Then, it is checked whether the neutron flux distribution and each core state parameter have converged. If they have not converged, the updated core state parameters are used to perform two-dimensional whole-core transport calculation again. This process is repeated iteratively until the three-dimensional neutron flux distribution and each core state parameter converge.

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