Combined discrete longitudinal standard method for eliminating ray effect
By generating basic and dual discrete vertical scale sets and establishing conserved interpolation algorithms, the alternating calculation method eliminates the ray effect, solves the numerical solution distortion problem in the discrete vertical scale method, and achieves high precision and high confidence calculation results.
Patent Information
- Application Number
- CN202510592167.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-08
- Publication Date
- 2025-08-08
AI Technical Summary
The existing discrete vertical standard method has ray effect problems in the calculation, resulting in numerical solution distortion and large errors. The traditional mitigation method has randomness and conservation error accumulation.
The combined discrete vertical standard method is used to generate the basic discrete vertical standard set and the dual discrete vertical standard set, and a conservative interpolation algorithm is established. The ray effect is eliminated through alternating calculation methods. The combined discrete vertical standard set is used to remap the angular flux distribution in the solution program of the transport equation system.
The ray effect is effectively eliminated, the accuracy and confidence of the calculation results are improved, the calculation amount and randomness are reduced, the particle number is maintained, and the calculation results are determined and efficient.
Smart Images
Figure CN120448670A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the technical fields of nuclear reactor calculation and inertial confinement fusion numerical simulation, and in particular to a combined discrete ordinate method for eliminating ray effects. Background Art
[0002] The discrete ordinate method (DOM) was proposed by American physicist Chandrasekhar in the 1950s. It is used to solve systems of partial differential equations related to the neutron transport equation, radiation transport equation, and the Boltzmann equation. It has been widely used in astrophysics, nuclear reactor physics, inertial confinement fusion, and weapons physics. The DOM for numerical calculations was proposed by Carlson. Because it takes into account certain symmetries of the discrete ordinate quadrature system, it is often simply referred to as the Sn method.
[0003] The discrete ordinate calculation method has excellent performance in terms of computational effort and computational confidence, and can provide definite computational results. It is a currently widely used deterministic calculation method. The most important defect that can be recognized by discrete ordinates is called the ray effect. The ray effect is a numerical oscillation phenomenon caused by the angular discretization and spatial discretization of the transport equation. In the case of a local strong source and weak spatial scattering, the numerical solution value with discrete ordinate directions along the strong source is significantly larger, while the numerical solution without discrete ordinate directions is significantly smaller due to the defects in the angular discretization direction. This phenomenon leads to the distortion of the numerical solutions brought about by the calculation of certain problems, and the error is often significantly greater than the discretization error of the spatial format, which seriously affects the final simulation results.
[0004] At present, among the commonly used methods to alleviate the ray effect, the discrete ordinate method based on frame transformation can change the discrete ordinate in different time step calculations, and remap the angular flux in the original direction to the new discrete ordinate direction. However, this algorithm has some defects: 1) It introduces a certain degree of randomness. Since the angle of the transformation has a certain degree of freedom and randomness. The rotation transformation is ergodic to each direction of the discrete ordinate group, it will bring more calculations and randomness, resulting in uncertainty during implementation. 2) The angular flux on the new discrete ordinate group needs to adopt remapping technology. The remapping method for arbitrary transformations generally brings conservation errors, and long-term calculations are prone to accumulation of conservation errors. 3) The existing numerical calculation technology still has obvious residual ray effects, and the results are related to the number of directions of the discrete ordinate. More directions have better results, while fewer directions have poor results. Summary of the Invention
[0005] The purpose of this application is to provide a combined discrete ordinate method for eliminating ray effects. The discrete ordinates used are fixed combined discrete ordinate groups, and the ray effects can be eliminated by alternately using two discrete ordinate groups.
[0006] To achieve the above objectives, this application provides the following solutions:
[0007] In a first aspect, the present application provides a combined discrete ordinate method for eliminating ray effects, comprising:
[0008] Generate a combined discrete ordinate group; the combined discrete ordinate group includes a basic discrete ordinate group and a dual discrete ordinate group, which are dual grids of each other; the basic discrete ordinate group has the direction of the algebraic average of the coordinate vectors of the four vertices of the spherical quadrilateral of the spherical subdivision grid as the direction of the discrete ordinate group, and the integral weight is the area of the spherical quadrilateral; the dual discrete ordinate group is generated from the dual grid of the spherical subdivision grid;
[0009] Establishing a conservative interpolation algorithm between the basic discrete ordinate group and the dual discrete ordinate group;
[0010] Based on the conservative interpolation algorithm and the alternating calculation method, the combined discrete ordinate group is input into the solver of the gas kinetic transport equations to obtain the angular flux distribution of the gas kinetic transport equations after eliminating the ray effect.
[0011] Optionally, generating a combined discrete vertical scale group specifically includes:
[0012] Generate a spherical mesh based on the projection of the unit cube surface mesh onto the unit sphere;
[0013] generating a basic discrete vertical scale group according to the spherical grid;
[0014] The node coordinate directions of the spherical quadrilateral corresponding to the basic discrete ordinate group are used as discrete directions to construct a dual discrete ordinate group; the weights of the basic discrete ordinate group and the dual discrete ordinate group are the areas of the corresponding spherical grids, and the sum of the weights is equal to 4π.
[0015] Optionally, the direction of the basic discrete ordinate group is the algebraic mean direction of the vertex coordinate vectors of the spherical quadrilateral; and the direction of the dual discrete ordinate group is the node coordinate direction of the spherical quadrilateral.
[0016] Optionally, the conservation interpolation algorithm is based on the dual grid relationship between the basic discrete ordinate group and the dual discrete ordinate group, and establishes a bidirectional interpolation mapping between the basic discrete ordinate group and the dual discrete ordinate group; the bidirectional interpolation mapping satisfies the particle number conservation in the discrete ordinate calculation or forces conservation through a conservation correction algorithm.
[0017] Optionally, based on a conservative interpolation algorithm and an alternating calculation method, the combined discrete ordinate group is applied to a solver of the transport equations to obtain the angular flux distribution of the gas kinetic transport equations after eliminating the ray effect, specifically including:
[0018] At the first time step, the angular flux distribution of the gas kinetic transport equations is generated based on the basic discrete ordinate group;
[0019] At even time steps, the discrete ordinate group is switched to the dual discrete ordinate group, and the angular flux distribution is remapped to the dual discrete ordinate group using a conservative interpolation algorithm, and the angular flux distribution under the dual discrete ordinate group is determined.
[0020] At odd time steps other than the first time step, the dual discrete ordinate is switched to the basic discrete ordinate group, and the angular flux distribution is remapped to the basic discrete ordinate group by a conservative interpolation algorithm, and the angular flux distribution under the basic discrete ordinate group is determined;
[0021] The calculation is repeated until the calculation is terminated, and the angular flux distribution of the gas kinetic transport equations after eliminating the ray effect is obtained.
[0022] Optionally, when switching the discrete vertical scale group, the remapping algorithm uses a piecewise polynomial interpolation or least squares projection method to complete the reconstruction of the angular flux distribution in the angle space.
[0023] According to the specific embodiments provided in this application, this application discloses the following technical effects:
[0024] The present application provides a combined discrete ordinate method for eliminating ray effects. First, a combined discrete ordinate group is generated. The combined discrete ordinate group consists of a basic discrete ordinate group and a dual discrete ordinate group, and the two are dual grids of each other. The direction of the basic discrete ordinate group is determined by the algebraic average direction of the four vertex vectors of each spherical grid unit in the discrete ordinate group, and its weight is the area of the spherical quadrilateral. Subsequently, a conservative interpolation algorithm is established between the basic discrete ordinate group and the dual discrete ordinate group. The combined discrete ordinate group is applied to the solution program of the transport equations, and the conservative interpolation algorithm and the alternating calculation method are used to obtain the angular flux distribution of the gas kinetic transport equations after eliminating the ray effect. The present application effectively solves the ray effect problem that is prevalent in traditional discrete ordinate methods. BRIEF DESCRIPTION OF THE DRAWINGS
[0025] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.
[0026] Figure 1 A schematic flow chart of a combined discrete vertical scale method for eliminating ray effects provided in one embodiment of the present application;
[0027] Figure 2 Schematic diagram of calculation results of discrete ordinates (S4) and combined discrete ordinates (C2) for a point source problem provided in one embodiment of the present application:
[0028] Figure 3 A schematic diagram of a spherical subdivision of a C5 discrete vertical scale group provided in one embodiment of the present application;
[0029] Figure 4 This is a schematic diagram of the calculation results of the discrete ordinates (S8 in 80 directions) and combined discrete ordinates (C3 in 54 / 56 directions) for the point source problem provided in one embodiment of the present application. DETAILED DESCRIPTION
[0030] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.
[0031] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.
[0032] Example 1
[0033] like Figure 1 As shown, this embodiment provides a combined discrete vertical scale method for eliminating ray effects, including:
[0034] Step 101: Generate a combined discrete ordinate group; the combined discrete ordinate group includes a basic discrete ordinate group and a dual discrete ordinate group, which are dual grids of each other; the basic discrete ordinate group has the direction of the algebraic mean of the coordinate vectors of the four vertices of the spherical quadrilateral of the spherical subdivision grid as the direction of the discrete ordinate group, and the integral weight is the area of the spherical quadrilateral; the dual discrete ordinate group is generated from the dual grid of the spherical subdivision grid;
[0035] Step 102: establishing a conservative interpolation algorithm between the basic discrete ordinate group and the dual discrete ordinate group;
[0036] Step 103: Based on the conservative interpolation algorithm and the alternating calculation method, the combined discrete ordinate group is input into the solution program of the gas kinetic transport equations to obtain the angular flux distribution of the gas kinetic transport equations after eliminating the ray effect.
[0037] In some embodiments, generating a combined discrete vertical index group specifically includes:
[0038] Generate a spherical mesh based on the projection of the unit cube surface mesh onto the unit sphere;
[0039] generating a basic discrete vertical scale group according to the spherical grid;
[0040] The node coordinate directions of the spherical quadrilateral corresponding to the basic discrete ordinate group are used as discrete directions to construct a dual discrete ordinate group; the weights of the basic discrete ordinate group and the dual discrete ordinate group are the areas of the corresponding spherical grids, and the sum of the weights is equal to 4π.
[0041] Specifically, the steps for generating a combined discrete vertical scale group are as follows:
[0042] The combined discrete ordinate method differs significantly from the traditional discrete ordinate method. Traditional discrete ordinates use a fixed set of discrete ordinate groups that remain unchanged during the calculation process. The combined discrete ordinate method is based on two sets of discrete ordinate groups.
[0043] 1) Determine a set of basic discrete vertical scale groups:
[0044] A typical primitive discrete vertical scale group can use a common discrete vertical scale group, such as an LQN discrete vertical scale group or a PN-TN discrete vertical scale group. Figure 2 Displays the discrete ordinate group (C5). This discrete ordinate group projects the surface mesh of the unit cube from the center of the sphere onto the unit sphere, resulting in a spherical mesh. This method generates a mesh that is evenly distributed across the sphere and exhibits good symmetry.
[0045] 2) Establish basic discrete vertical scale groups:
[0046] Based on Figure 3 In the spherical subdivision shown, the direction of the algebraic average of the four vertex vectors of each spherical quadrilateral is taken as the direction of the discrete ordinate group, and the corresponding integral weight is the area of the spherical quadrilateral, forming a basic discrete ordinate group.
[0047] 3) Establish dual discrete vertical scale groups:
[0048] In constructing discrete ordinate groups, the orientation of the discrete ordinates is based on the orientation of the spherical quadrilateral nodes corresponding to the base discrete ordinate group. For these discrete orientations, a dual mesh is constructed around each node. This dual mesh consists of polygons formed by connecting the centers of the spherical quadrilaterals surrounding the node and the midpoints of the edges surrounding the node. These polygons form a mesh subdivision on the unit sphere.
[0049] The weights of the basic and dual discrete ordinate groups are equal to the spherical area of the grid. It can be shown that the sum of the integral weights of each discrete ordinate group is 4π.
[0050] In some embodiments, when executing step 102, the specific steps may be as follows:
[0051] The grid divisions corresponding to the two discrete ordinate groups between the combined discrete ordinate groups are dual grids, that is, the nodes of the basic grid unit are exactly the centers of the dual grid units, and vice versa, the centers of the basic grid units are the nodes of the dual grid units.
[0052] The dual relationship between grids allows for a conservative interpolation algorithm to be established. That is, the values in the directions of the primary discrete ordinate group are interpolated to the values in the directions of the dual discrete ordinate group; conversely, the values in the directions of the dual discrete ordinate group are interpolated to the values in the directions of the primary discrete ordinate group.
[0053] In order to maintain conservation in discrete ordinate calculations, the interpolation algorithm is required to maintain conservation; if the interpolation algorithm cannot maintain conservation, it can be made to maintain conservation through conservation correction.
[0054] Therefore, the conservative interpolation algorithm is based on the dual grid relationship between the basic discrete ordinate group and the dual discrete ordinate group, and establishes a bidirectional interpolation mapping between the basic discrete ordinate group and the dual discrete ordinate group; the bidirectional interpolation mapping satisfies the particle number conservation in the discrete ordinate calculation or forces the conservation to be maintained through a conservation correction algorithm.
[0055] In some embodiments, when executing step 103, the specific steps may be as follows:
[0056] At the first time step, the angular flux distribution of the gas kinetic transport equations is generated based on the basic discrete ordinate group;
[0057] At even time steps, the discrete ordinate group is switched to the dual discrete ordinate group, and the angular flux distribution is remapped to the dual discrete ordinate group using a conservative interpolation algorithm, and the angular flux distribution under the dual discrete ordinate group is determined.
[0058] At odd time steps other than the first time step, the dual discrete ordinate is switched to the basic discrete ordinate group, and the angular flux distribution is remapped to the basic discrete ordinate group through a conservative interpolation algorithm to determine the angular flux distribution under the basic discrete ordinate group; when switching the discrete ordinate group, the remapping algorithm uses a piecewise polynomial interpolation or a least squares projection method to complete the spatial reconstruction of the angular flux distribution.
[0059] The calculation is repeated until the calculation is terminated, and the angular flux distribution of the gas kinetic transport equations after eliminating the ray effect is obtained.
[0060] Specifically, when the basic discrete ordinate group and the dual discrete ordinate group are alternately used to solve the transport equations, the basic discrete ordinate group and the dual discrete ordinate group are written into the program at the initial time. At the initial time, the angular flux distribution of the transport equation is generated based on the basic discrete ordinate group.
[0061] In the first time step, the basic discrete ordinate group is used to solve the transport equation, and the calculation steps are the same as the traditional discrete ordinate method.
[0062] In the second step of calculation, the discrete ordinate group is switched to the dual discrete ordinate group, and the remapping algorithm in step 2 is used to remap the angular flux distribution of the basic discrete ordinate group to the angular flux distribution of the dual discrete ordinate group, and then the calculation is performed based on this distribution using the dual discrete ordinate group.
[0063] In the third time step, we return to the basic discrete ordinate group. At this time, we use the remapping algorithm to remap the angular flux distribution of the dual discrete ordinate group to the angular flux distribution of the basic discrete ordinate group, and use the basic discrete ordinate group for calculation.
[0064] The calculation results of the combined discrete ordinate group method are as follows: Figure 4 As shown in the figure, the results show that the new discrete vertical scale group can effectively eliminate the ray effect. Figure 4 Results of computing the local point source problem for the traditional discrete ordinate group S8 (left) and the combined discrete ordinate group C3 (right).
[0065] This application also provides an application scenario that utilizes the aforementioned combined discrete ordinate method for eliminating radiation effects. Specifically, in the calculation of neutron transport equations in nuclear reactors and radiation transport calculations for inertial confinement fusion, strict requirements are placed on the distribution of neutron and radiation fields, particularly to suppress non-physical phenomena such as radiation effects. If existing discrete ordinate calculation methods fail to meet these requirements, the combined discrete ordinate method provided in this application can be used to effectively eliminate phenomena such as radiation effects.
[0066] The implementation steps of the calculation method of this application are as follows:
[0067] 1. Use the combined discrete vertical scale group data provided by this application, which is a set of product groups, stored in a file, read by the calculation program, and stored in the memory.
[0068] 2. When calculating in the program, the combined discrete vertical scale group is used to replace the original discrete vertical scale data; and the transport calculation is performed according to the method introduced above.
[0069] 3. At each calculation step, switch between the basic discrete ordinate group and the dual discrete ordinate group using the conservation remapping tool provided in this special topic to reconstruct a new neutron field or radiation field.
[0070] 4. Complete the calculation and obtain the result after eliminating the ray effect.
[0071] In summary, this application has the following technical effects:
[0072] The discrete vertical scale used in the algorithm provided in this application is fixed, the algorithm is deterministic, and the calculation results are also deterministic, without introducing random factors.
[0073] The remapping algorithm provided in this application is pre-determined, computationally efficient, and highly reliable. It maintains a constant total particle count, resulting in a higher confidence level. Combined with high-precision spatial discretization, this algorithm can produce highly accurate and reliable results.
[0074] In the present application, the elimination of the ray effect is weakly correlated with the number of discrete ordinate directions. Even if a small number of discrete ordinate directions are used, the algorithm provided in the present application can effectively eliminate the ray effect.
[0075] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0076] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.
Claims
1. A combined discrete ordinate method for eliminating ray effects, characterized in that: include: Generate a combination of discrete vertical scale groups; The combined discrete ordinate group includes a basic discrete ordinate group and a dual discrete ordinate group which are dual grids of each other; The basic discrete ordinate group is the direction of the algebraic average of the coordinate vectors of the four vertices of the spherical quadrilateral of the spherical subdivision grid, and the integral weight is the area of the spherical quadrilateral; the dual discrete ordinate group is generated by the dual grid of the spherical subdivision grid; Establishing a conservative interpolation algorithm between the basic discrete ordinate group and the dual discrete ordinate group; Based on the conservative interpolation algorithm and the alternating calculation method, the combined discrete ordinate group is input into the solver of the gas kinetic transport equations to obtain the angular flux distribution of the gas kinetic transport equations after eliminating the ray effect.
2. A combined discrete vertical scale method for eliminating ray effects according to claim 1, characterized in that: Generate a combination of discrete vertical scale groups, including: Generate a spherical mesh based on the projection of the unit cube surface mesh onto the unit sphere; generating a basic discrete vertical scale group according to the spherical grid; The node coordinate directions of the spherical quadrilateral corresponding to the basic discrete ordinate group are used as discrete directions to construct a dual discrete ordinate group; the weights of the basic discrete ordinate group and the dual discrete ordinate group are the areas of the corresponding spherical grids, and the sum of the weights is equal to 4π.
3. The combined discrete vertical scale method for eliminating ray effects according to claim 2, characterized in that: The direction of the basic discrete ordinate group is the algebraic mean direction of the vertex coordinate vectors of the spherical quadrilateral; the direction of the dual discrete ordinate group is the node coordinate direction of the spherical quadrilateral.
4. The combined discrete vertical scale method for eliminating ray effects according to claim 1, characterized in that: The conservative interpolation algorithm is based on the dual grid relationship between the basic discrete ordinate group and the dual discrete ordinate group, and establishes a bidirectional interpolation mapping between the basic discrete ordinate group and the dual discrete ordinate group; the bidirectional interpolation mapping satisfies the particle number conservation in the discrete ordinate calculation or forces conservation through a conservation correction algorithm.
5. The combined discrete vertical scale method for eliminating ray effects according to claim 4, characterized in that: Based on the conservative interpolation algorithm and the alternating calculation method, the combined discrete ordinate group is applied to the solution program of the transport equations to obtain the angular flux distribution of the gas kinetic transport equations after eliminating the ray effect, specifically including: At the first time step, the angular flux distribution of the gas kinetic transport equations is generated based on the basic discrete ordinate group; At even time steps, the discrete ordinate group is switched to the dual discrete ordinate group, and the angular flux distribution is remapped to the dual discrete ordinate group using a conservative interpolation algorithm, and the angular flux distribution under the dual discrete ordinate group is determined. At odd time steps other than the first time step, the dual discrete ordinate is switched to the basic discrete ordinate group, and the angular flux distribution is remapped to the basic discrete ordinate group by a conservative interpolation algorithm, and the angular flux distribution under the basic discrete ordinate group is determined; The calculation is repeated until the calculation is terminated, and the angular flux distribution of the gas kinetic transport equations after eliminating the ray effect is obtained.
6. The combined discrete vertical scale method for eliminating ray effects according to claim 5, characterized in that: The remapping algorithm uses piecewise polynomial interpolation or least squares projection method to complete the reconstruction of angular flux distribution in angle space when switching discrete vertical scale groups.