Neutron transport parallel calculation method and computing device for optimizing lateral leakage term processing

Abstract

A parallel neutron transport calculation method and computing device for optimizing lateral leakage term processing belongs to the field of nuclear power. The parallel neutron transport calculation method for optimizing lateral leakage term processing introduces a second-order Legendre polynomial weighted boundary flow in the calculation process of a single node, and updates adjacent nodes in combination with the boundary neutron flow. The updated node neutron flux and eigenvalue k are obtained by traversing all nodes through parallel calculation. eff The updated data is substituted into the calculation model for iteration to obtain the final calculation result. This method obtains the high-order expansion coefficients of the nodal lateral leakage term based on a single nodal model, improving the calculation stability while ensuring the calculation accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of nuclear power, and in particular relates to a neutron transport parallel calculation method and a calculation device for optimizing lateral leakage term processing. Background Art

[0002] In the calculation of reactor reactivity and full-reactor fine power distribution, accurate calculation of neutron transport behavior is the basis for obtaining accurate calculation results. The transverse integration block method is widely used in neutron transport calculations. This method requires accurate consideration of the transverse leakage term of the block to improve the calculation accuracy. In the high-resolution neutron transport calculation of nuclear reactors based on grid element homogenization, the radial grid size is about 1 cm, with high resolution, and the calculation accuracy can be further improved by using discontinuity factors or super equivalent homogenization factors; the axial grid is about 10 cm, with a larger grid size. In the neutron transport calculation program system based on the transverse integration block method, it is necessary to accurately consider the transverse leakage term to improve the calculation accuracy of the axial power distribution, and thus obtain accurate axial power offset (AO), hot spot factor (F Q ) and other key physical parameters.

[0003] Regarding the lateral leakage term in the neutron transport calculation method based on the transverse integral block method, the existing technical solutions adopt the flat leakage approximation or the high-order leakage term approximation based on the three adjacent block models. The flat leakage approximation method only considers the average value of the leakage term, and the calculation accuracy is low. The high-order leakage term processing method based on the three adjacent block models can obtain higher calculation accuracy, but when performing parallel calculations based on the regional decomposition method, the block boundary flow information at the interface of each parallel region is updated lagging, which will reduce the stability of the parallel calculation and even cause calculation divergence. In order to improve the stability of the neutron transport parallel calculation based on the transverse integral block method, a high-order leakage term processing method based on a single block model is needed. Summary of the Invention

[0004] The present invention aims to provide a parallel neutron transport calculation method that optimizes the processing of lateral leakage terms, thereby simplifying the computational complexity of neutron transport behavior and improving computational efficiency and accuracy. The present invention also provides a calculation device.

[0005] According to an embodiment of one aspect of the present invention, a parallel computation method for neutron transport for optimizing lateral leakage term processing is provided, the method comprising the following steps:

[0006] Step a): providing a simulation model of a reactor neutron transport calculation simulation object, and dividing the simulation model into sections;

[0007] Step b): color-marking the nodes and making adjacent nodes have different colors, and treating the nodes with the same color mark as a same-color node group, and performing parallel region decomposition;

[0008] Step c): Allocate the nodes to multiple computing cores according to the parallel domain decomposition result in step b), perform node response matrix calculation, and provide neutron flux, neutron current, neutron source term and eigenvalue k eff The initial value of

[0009] Step d): calculating the boundary neutron flow, the average leakage term of the node and the boundary flow weighted by the second-order Legendre polynomial of the node in the node group respectively by each computing core;

[0010] Step e): updating the boundary flow calculated in step d) to the adjacent nodes;

[0011] Step f): the node whose boundary flow weighted by the boundary neutron flow, the node average leakage term and the second-order Legendre polynomial has been calculated is regarded as a calculated node, and the remaining nodes are regarded as uncalculated nodes;

[0012] In the uncalculated nodes where the boundary flows are updated, the boundary neutron flows, the node average leakage term, and the boundary flows weighted by the second-order Legendre polynomials are calculated for each group of nodes of the same color one by one, and the calculated boundary neutron flows and the boundary flows weighted by the second-order Legendre polynomials are updated to the adjacent nodes;

[0013] Step g): using a second-order polynomial approximation for the lateral leakage term, and taking the average leakage term of each node and the boundary flow weighted by the second-order Legendre polynomial at the node boundary as constraints, calculating the lateral leakage term expansion coefficient;

[0014] Step h): Calculating and updating the nodal neutron flux according to the neutron balance equation with the neutron source term and the nodal boundary neutron flux as input;

[0015] Step i): Calculate the characteristic value k based on the neutron flux of the node calculated in step h). eff , and updated to all computing cores;

[0016] Step j): updating the neutron source term according to the boundary neutron flow term of the calculated node, the boundary flow weighted by the second-order Legendre polynomial, the expansion coefficient of the lateral leakage term calculated in step g), and the node neutron flux calculated in step h);

[0017] Step k): according to the updated boundary neutron flux and the boundary flux weighted by the second-order Legendre polynomial, the nodal neutron flux and the eigenvalue k effRepeat steps d) to j) until the calculation result converges or reaches a given number of iterations, and output the final calculation result.

[0018] When this method performs parallel calculations of neutron transport based on the transverse integration nodal method, the high-order expansion coefficients of the nodal transverse leakage term can be obtained based on a single nodal model, thereby improving the calculation stability while ensuring the calculation accuracy.

[0019] Furthermore, in some embodiments, in step a), the simulation model includes geometric information, material information, and nuclear reaction cross-section information.

[0020] Furthermore, in some embodiments, in the step b), during the region decomposition process, the load variance of each parallel computing core is minimized, and the surface area to volume ratio of the parallel computing region is minimized.

[0021] When the load variance of each parallel computing core is minimized, the load distribution of each parallel computing core can be balanced; when the surface area to volume ratio of the parallel computing area is minimized, the scale of message communication between each parallel computing core can be reduced.

[0022] Furthermore, in some embodiments, in step d), the boundary flow weighted by the second-order Legendre polynomial is The calculation method is:

[0023]

[0024] Among them, φ(x0,y,z) is the flux value at the coordinate (x0,y,z), and is a second-order Legendre polynomial, Δy k is the width of node k in the y direction, Δz k is the width of node k in the z direction, and x0 is the coordinate value in the x direction.

[0025] Furthermore, in some embodiments, in step g), the expansion coefficient of the lateral leakage term is The calculation method is:

[0026]

[0027] in, is the average leakage term of block k, is the boundary flow weighted by the second-order Legendre polynomial at the left boundary of node k, is the boundary flow weighted by the second-order Legendre polynomial at the right boundary of node k, Δx k is the width of node k in the x direction.

[0028] Furthermore, in some embodiments, in step i), the eigenvalue k eff The calculation method is:

[0029] The total number of fission neutrons produced by all the nodes assigned to it is calculated by each parallel computing core. Where g is the neutron energy group number, is the fission neutron production cross section of the g-th energy group of node k, φ k,g is the neutron flux of the g-th energy group in node k, V k is the volume of block k, the eigenvalue

[0030] Furthermore, in some embodiments, in step k), the convergence criterion is the neutron flux, the neutron source term, the boundary neutron flow, the boundary flow weighted by the second-order Legendre polynomial, and the eigenvalue k in two rounds of calculation. eff The difference is less than a given threshold.

[0031] According to an embodiment of another aspect of the present invention, a computing device is provided, comprising a memory and multiple parallel computing cores, wherein the memory stores a neutron transport parallel computing program, and when the neutron transport parallel computing program is executed by the parallel computing cores, the neutron transport parallel computing method for optimizing lateral leakage term processing provided in any of the aforementioned embodiments can be implemented.

[0032] Furthermore, in some embodiments, the calculation program includes a modeling and initialization module, a node response calculation module, a high-order leakage term calculation module based on a single node model, a source term and eigenvalue solution module, and a parallel scheduling module, wherein:

[0033] The modeling and initialization module is used to read the input information of the calculation object, perform block division, block coloring, parallel region decomposition and calculation result initialization;

[0034] The nodal response calculation module is used to define a boundary flow weighted by a second-order Legendre polynomial, and solve the nodal boundary neutron flow, the nodal average leakage term, and the boundary flow weighted by the second-order Legendre polynomial according to the nodal response matrix and taking the neutron source term and neutron flow data in the previous iteration as input;

[0035] The high-order leakage term calculation module based on the single-node model is used to solve the lateral leakage term expansion coefficient by taking the average leakage term of a single node and the boundary flow weighted by the second-order Legendre polynomial at the node boundary as constraints;

[0036] The source term and eigenvalue solving module is used to solve the neutron flux, eigenvalue k according to the neutron balance equation, taking the block boundary neutron flow, the average boundary flow weighted by the second-order Legendre polynomial, and the lateral leakage term expansion coefficient as input. eff and neutron source terms. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A schematic diagram of a computing object structure in one embodiment;

[0038] Figure 2 This is a schematic diagram of section staining in one embodiment;

[0039] Figure 3 A schematic diagram of node block allocation in one embodiment;

[0040] Figure 4 A schematic diagram of a parallel computing process in one embodiment;

[0041] Figure 5 Schematic diagram of a parallel computing program module in one embodiment.

[0042] The purpose of the above-mentioned drawings is to provide a detailed explanation of the present invention so that those skilled in the art can understand the technical concepts of the present invention, and is not intended to limit the present invention. For the sake of simplicity, the above-mentioned drawings only schematically depict structures related to the technical features of the present invention and do not strictly depict the complete structure and all details according to actual scale. DETAILED DESCRIPTION

[0043] The present invention will be further described in detail below through specific embodiments with reference to the accompanying drawings.

[0044] References to "embodiments" herein mean that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment herein. The appearance of such phrases in various places in the specification does not necessarily refer to the same embodiment, nor does it limit mutually exclusive independent or alternative embodiments. Those skilled in the art will appreciate that an embodiment herein may be combined with other embodiments as long as no structural conflicts arise.

[0045] In the description herein, terms such as "first" and "second" are used only to distinguish different objects and should not be understood to indicate relative importance or to limit the quantity, specific order, or primary and secondary relationship of the described technical features. In the description herein, "plurality" means at least two.

[0046] To address the low computational accuracy and poor computational stability of the transverse leakage term in existing neutron transport calculations, embodiments of the present invention provide a parallel neutron transport calculation method that optimizes transverse leakage processing. This method utilizes a high-order second-order parabolic approximation of the transverse leakage term to improve the computational accuracy of key nuclear characteristic parameters such as eigenvalues, power distribution, and power crest factor. Furthermore, by introducing boundary flows weighted by second-order Legendre polynomials, high-order expansion coefficients of the leakage term can be calculated based on a single nodal model, improving the stability of parallel neutron transport calculations for nuclear reactor nodules based on the domain decomposition method.

[0047] like Figure 4 As shown, the steps of the method are as follows:

[0048] Step 1: Provide a computational model for the nuclear reactor neutron transport computation object, such as Figure 1 As shown, the computational model specifically includes geometric information of the computational object (i.e., geometric structure and size characteristics), material information (material type and distribution), nuclear reaction cross-section information, etc., while providing parallel computing information and control parameters of the system for parallel computing; the computational object is divided into nodes (grids) according to the input information.

[0049] Step 2: If Figure 2 As shown, the nodes are color-coded from 1 to M, ensuring that adjacent nodes have different colors. Based on the parallel computing information input, parallel region decomposition is performed to balance the load of each parallel computing core. Specifically, this is achieved by minimizing the load variance of each core. To reduce the amount of message communication between parallel computing cores, the principle of region decomposition is to minimize the surface area to volume ratio of the parallel region. Blocks with the same color are considered a same-color block group.

[0050] Step 3: If Figure 3 As shown, according to the parallel domain decomposition results in step 2, each parallel computing core performs the node response matrix calculation for its assigned node, giving the initialized neutron flux, neutron flow, neutron source term and eigenvalue k eff Specifically, the initial value can be experimental data, historical simulation calculation data or other artificially given initial values.

[0051] Step 4: For each node marked with the first color, each parallel computing core calculates and updates the node boundary neutron flux, node average leakage term, and boundary flow weighted by the second-order Legendre polynomial based on the node response matrix in step 3, with the initial value (in the first iteration) or the neutron source term and neutron flux of the previous iteration (in the second and subsequent iterations) as input.

[0052] Among them, the boundary flow weighted by the second-order Legendre polynomial of node k is The calculation method is:

[0053]

[0054] Among them, φ(x0,y,z) is the flux value at the coordinate (x0,y,z), and is a second-order Legendre polynomial, Δy k is the width of node k in the y direction, Δz k is the width of node k in the z direction, and x0 is the coordinate value in the x direction.

[0055] Step 5: Each parallel computing core carries out message communication between the first color node group and its adjacent nodes at the interface of the parallel region for the node assigned to it, and updates the latest node boundary neutron flow and boundary flow information weighted by the second-order Legendre polynomial to the adjacent nodes.

[0056] Step 6: Each parallel computing core performs boundary neutron flow, block average leakage term, and second-order Legendre polynomial weighted boundary flow calculations for each of its assigned blocks, for groups of blocks from color 2 to color M that have not yet been calculated. It then updates the boundary neutron flow and second-order Legendre polynomial weighted boundary flow calculation results to adjacent blocks. This continues until all groups of blocks have completed boundary neutron flow, block average leakage term, and second-order Legendre polynomial weighted boundary flow calculations.

[0057] Step 7: Each parallel computing core uses the second-order polynomial approximation of the lateral leakage term for its assigned node, and uses the average leakage term of a single node k and the boundary flow weighted by the second-order Legendre polynomial at the node boundary as constraints to solve the expansion coefficient of the lateral leakage term

[0058] in, is the average leakage term of block k, is the boundary flow weighted by the second-order Legendre polynomial at the left boundary of node k, is the boundary flow weighted by the second-order Legendre polynomial at the right boundary of node k, Δx k is the width of node k in the x direction.

[0059] Step 8: Each parallel computing core calculates and updates the neutron flux of the node to which it is assigned, based on the neutron balance equation as a constraint, and with the neutron source term and the node boundary neutron flux as input.

[0060] Step 9: Each parallel computing core calculates the total number of fission neutrons produced for all the nodes assigned to it. Where g is the neutron energy group number, is the fission neutron production cross section of the g-th energy group of node k, φ k,g is the neutron flux of the g-th energy group in node k, V k is the volume of block k, the eigenvalue The eigenvalue k is transmitted through message communication eff Broadcast to all computing cores for updates.

[0061] Step 10: Each parallel computing core updates the neutron source terms for its assigned node, including data such as fission source, scattering source, and total source terms, based on the boundary neutron flux, boundary flux weighted by the second-order Legendre polynomial, neutron flux, and transverse leakage term expansion coefficient calculated in steps 4 to 9.

[0062] Step 11: Update the boundary neutron flux, the boundary flux weighted by the second-order Legendre polynomial, the nodal neutron flux and the eigenvalue k eff As input, repeat steps 4 to 10 for iterative calculation until the iterative calculation results converge or the iterative calculation reaches a given number of times.

[0063] Convergence criteria include ensuring that the calculated deviations of the neutron flux, neutron source term, neutron current, and eigenvalues ​​are less than specified values. If convergence does not occur after the specified number of iterations, the calculated state itself may be divergent.

[0064] Output the final calculation results to complete the neutron transport calculation.

[0065] The methods provided in the above embodiments can be implemented by a parallel computing device. The parallel computing device includes a memory and multiple computing cores. The memory stores a neutron transport calculation program. When the neutron transport calculation program is executed by the computing cores, the neutron transport parallel calculation method for optimizing lateral leakage processing provided in the above embodiments can be implemented.

[0066] Specifically, neutron transport calculation programs such as Figure 5 As shown, it includes a modeling and initialization module, a node response calculation module, a high-order leakage term calculation module based on a single node model, a source term and eigenvalue solution module, and a parallel scheduling module.

[0067] Among them, the modeling and initialization module is used to read the input information of the calculation object, perform node (grid) division, node coloring, parallel region decomposition, and calculation result initialization.

[0068] The nodal response calculation module defines a boundary flow weighted by a second-order Legendre polynomial. Based on the nodal response matrix, this module takes the neutron source and neutron flow data of the previous iteration as input, and solves the nodal boundary neutron flow, the nodal average leakage term, and the boundary flow weighted by the second-order Legendre polynomial.

[0069] Based on the high-order leakage term calculation module of the single-node model, the lateral leakage term expansion coefficient is solved with the average leakage term of a single node and the boundary flow weighted by the second-order Legendre polynomial at the node boundary as constraints.

[0070] The source term and eigenvalue solving module solves the neutron flux, eigenvalue and neutron source term based on constraints such as the neutron balance equation, taking the block boundary neutron flux, the boundary flow weighted by the second-order Legendre polynomial, and the lateral leakage term expansion coefficient as input.

[0071] Parallel scheduling module: carries out parallel scheduling, message communication, result collection and broadcasting of nuclear reactor neutron transport calculations.

[0072] The purpose of the above embodiments is to provide a further detailed description of the present invention in conjunction with the accompanying drawings so that those skilled in the art can understand the technical concept of the present invention. Within the scope of the present invention, optimization or equivalent replacement of the method steps involved, as well as combination of implementation methods in different embodiments without causing structural or principle conflicts, all fall within the scope of protection of the present invention.

Claims

1. A parallel computation method for neutron transport with optimized lateral leakage term processing, characterized in that: The following steps are involved: Step a): providing a simulation model of a reactor neutron transport calculation simulation object, and dividing the simulation model into sections; Step b): color-marking the nodes and making adjacent nodes have different colors, and treating the nodes with the same color mark as a same-color node group, and performing parallel region decomposition; Step c): Allocate the nodes to multiple computing cores according to the parallel domain decomposition result in step b), perform node response matrix calculation, and provide neutron flux, neutron current, neutron source term and eigenvalue k eff The initial value of Step d): calculating the boundary neutron flow, the average leakage term of the node and the boundary flow weighted by the second-order Legendre polynomial of the node in the node group respectively by each computing core; Step e): updating the boundary flow calculated in step d) to the adjacent nodes; Step f): the node whose boundary flow weighted by the boundary neutron flow, the node average leakage term and the second-order Legendre polynomial has been calculated is regarded as a calculated node, and the remaining nodes are regarded as uncalculated nodes; In the uncalculated nodes where the boundary flows are updated, the boundary neutron flows, the node average leakage term, and the boundary flows weighted by the second-order Legendre polynomials are calculated for each group of nodes of the same color one by one, and the calculated boundary neutron flows and the boundary flows weighted by the second-order Legendre polynomials are updated to the adjacent nodes; Step g): using a second-order polynomial approximation for the lateral leakage term, and taking the average leakage term of each node and the boundary flow weighted by the second-order Legendre polynomial at the node boundary as constraints, calculating the lateral leakage term expansion coefficient; Step h): Calculating and updating the nodal neutron flux according to the neutron balance equation with the neutron source term and the nodal boundary neutron flux as input; Step i): Calculate the characteristic value k based on the neutron flux of the node calculated in step h). eff , and updated to all computing cores; Step j): updating the neutron source term according to the boundary neutron flow term of the calculated node, the boundary flow weighted by the second-order Legendre polynomial, the expansion coefficient of the lateral leakage term calculated in step g), and the node neutron flux calculated in step h); Step k): according to the updated boundary neutron flux and the boundary flux weighted by the second-order Legendre polynomial, the nodal neutron flux and the eigenvalue k eff Repeat steps d) to j) until the calculation result converges or reaches a given number of iterations, and output the final calculation result.

2. The neutron transport parallel calculation method for optimizing lateral leakage term processing according to claim 1 is characterized in that: In the step a), the simulation model includes geometric information, material information, and nuclear reaction cross-section information.

3. The neutron transport parallel calculation method for optimizing lateral leakage term processing according to claim 1 is characterized in that: In the step b), during the process of performing the domain decomposition, the load variance of each of the parallel computing cores is minimized, and the surface area to volume ratio of the parallel computing region is minimized.

4. The neutron transport parallel calculation method for optimizing lateral leakage term processing according to claim 1 is characterized in that: In the step d), the boundary flow weighted by the second-order Legendre polynomial The calculation method is: Among them, φ(x0,y,z) is the flux value at the coordinate (x0,y,z), and is a second-order Legendre polynomial, Δy k is the width of node k in the y direction, Δz k is the width of node k in the z direction, and x0 is the coordinate value in the x direction.

5. The neutron transport parallel calculation method for optimizing lateral leakage term processing according to claim 1, characterized in that: In step g), the expansion coefficient of the lateral leakage term The calculation method is: in, is the average leakage term of block k, is the boundary flow weighted by the second-order Legendre polynomial at the left boundary of node k, is the boundary flow weighted by the second-order Legendre polynomial at the right boundary of node k, Δx k is the width of node k in the x direction.

6. The neutron transport parallel calculation method for optimizing lateral leakage term processing according to claim 1, characterized in that: In the step i), the eigenvalue k eff The calculation method is: The total number of fission neutrons produced by all the nodes allocated to it is calculated by each parallel computing core. Where g is the neutron energy group number, is the fission neutron production cross section of the g-th energy group of node k, φ k,g is the neutron flux of the g-th energy group in node k, V k is the volume of block k, the eigenvalue 7. The neutron transport parallel calculation method for optimizing lateral leakage term processing according to claim 1, characterized in that: In step k), the convergence criteria are the neutron flux, the neutron source term, the boundary neutron flow, the boundary flow weighted by the second-order Legendre polynomial and the eigenvalue k in the two rounds of calculation. eff The difference is less than a given threshold.

8. A computing device comprising a memory and a plurality of parallel computing cores, characterized in that: The memory stores a computing program, and when the computing program is executed by the parallel computing core, the neutron transport parallel computing method for optimizing lateral leakage term processing according to any one of claims 1 to 7 can be implemented.

9. The computing device according to claim 8, wherein: The calculation program includes a modeling and initialization module, a node response calculation module, a high-order leakage term calculation module based on a single node model, a source term and eigenvalue solution module, and a parallel scheduling module, wherein: The modeling and initialization module is used to read the input information of the calculation object, perform block division, block coloring, parallel region decomposition and calculation result initialization; The nodal response calculation module is used to define a boundary flow weighted by a second-order Legendre polynomial, and solve the nodal boundary neutron flow, the nodal average leakage term, and the boundary flow weighted by the second-order Legendre polynomial according to the nodal response matrix and taking the neutron source term and neutron flow data in the previous iteration as input; The high-order leakage term calculation module based on the single-node model is used to solve the lateral leakage term expansion coefficient by taking the average leakage term of a single node and the boundary flow weighted by the second-order Legendre polynomial at the node boundary as constraints; The source term and eigenvalue solving module is used to solve the neutron flux, eigenvalue k according to the neutron balance equation, taking the block boundary neutron flow, the average boundary flow weighted by the second-order Legendre polynomial, and the lateral leakage term expansion coefficient as input. eff and neutron source terms; The parallel scheduling module is used for parallel scheduling, message communication, and result collection and broadcasting of neutron transport calculations.

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