Method for accelerating iterative convergence speed of highly nonlinear surface-to-surface radiation problem

Abstract

The invention discloses a method for accelerating the iterative convergence speed of a highly nonlinear surface-to-surface radiation problem, and the method comprises the steps: S1, building a geometric model of a to-be-analyzed structure, and carrying out the mesh generation, and obtaining a temperature field finite element model; s2, setting properties, grid control parameters, boundary conditions, initial conditions and solving information of the temperature field finite element model; s3, information of the temperature field finite element model is obtained, and initialization is carried out; s4, establishing a heat transfer overall matrix; S5, selecting a radiation facet, and calculating to obtain a radiation angle coefficient matrix; s6, establishing a cavity radiation energy equation; s7, obtaining a final temperature iterative calculation equation based on the cavity radiation energy equation and the heat transfer overall matrix, and solving the final temperature iterative calculation equation; and S8, iteratively solving until the set calculation ending time, and obtaining the temperature field. According to the method, the cavity radiation energy equation and the heat transfer overall matrix are processed through the semi-implicit separation Newton method, so that the final temperature field iteration equation is obtained, iteration calculation is carried out, and the convergence efficiency can be remarkably improved.

Description

Technical Field

[0001] The invention relates to the technical field of heat transfer surface-to-surface radiation calculation, and in particular to a method for accelerating the iterative convergence speed of a highly nonlinear surface-to-surface radiation problem. Background Art

[0002] Surface-to-surface radiation has always been a challenging problem to solve in heat transfer analysis. In ordinary heat transfer analysis, the problem is often linear, and the accuracy and efficiency of the solution can be effectively guaranteed. However, in the surface-to-surface radiation problem, heat exchange will occur between any two unit surfaces involved in the calculation, and the heat flux of the heat radiation is related to the temperature of the current unit surface, the radiation angle coefficient matrix between surfaces, the radiation coefficient, and the ambient temperature. The radiation is proportional to the fourth power of the temperature, so the problem is a highly nonlinear problem.

[0003] The convergence algorithms used to solve surface radiation problems require coupling analysis of the heat transfer equation and the cavity radiation energy equation. The current mainstream algorithms include the full coupling method and the sequential coupling method: 1) Full coupling method: By expanding the degree of freedom of the radiation heat flow in the temperature field, the heat transfer equation and the cavity radiation energy equation are solved simultaneously to achieve the purpose of thermal field coupling iterative calculation and solution. The degrees of freedom solved in this method are the temperature field and the radiation heat flow. The theory of this method is relatively direct and the degree of coupling is high. Therefore, it works well in smaller model cases. However, this method requires the temperature degree of freedom to be combined with the radiation heat flow degree of freedom. Since the degrees are calculated simultaneously, the overall solution matrix needs to be expanded on the basis of the solution matrix of the heat transfer equation, which leads to an overly large matrix, high computational consumption, and excessive memory demand. This is particularly evident in large-scale calculations, so it has not been widely used. 2) The sequential coupling method is a method that adopts sequential coupling. It first calculates the radiation heat flux through the temperature field results of the current time step, and then uses some method to act on the heat transfer equation to construct the temperature iteration equation. The biggest difference between it and the full coupling method is that the degree of freedom of the radiation heat flux is not expanded, so the calculation matrix scale is relatively small. The memory requirement is also low; the sequential coupling method includes the explicit separated Picard method and the semi-implicit separated Picard method, in which: the explicit separated Picard method first calculates the radiation heat flux for the next step through the current temperature field results, and then directly loads the radiation heat flux as the node heat flux load on the right side of the heat transfer equation to construct the temperature field iteration equation for solution. However, this method is an explicit calculation method. Although it does not expand the degrees of freedom of the radiation heat flux and has a small memory requirement, the method directly loads the radiation heat flux as a load, resulting in a low solution accuracy. Therefore, this method is not very effective in solving stable The effect of the semi-implicit separated Picard method on transient problems is poor, and its accuracy is often difficult to meet the requirements in transient analysis. Compared with the explicit separated Picard method, the semi-implicit separated Picard method increases the implicit degree. This method linearizes the radiation energy in the radiation heat flux formula, expresses the radiation heat flux in an implicit form, and then brings the radiation heat flux into the heat transfer equation, so that the method has the characteristics of semi-implicit. Although the accuracy is significantly improved compared with the explicit separated Picard method, it is difficult to converge in many large cases, and its accuracy is also poor. This phenomenon is particularly obvious in cases where radiation dominates the heat transfer analysis. Summary of the invention

[0004] The present invention provides a method for accelerating the iterative convergence speed of a highly nonlinear surface-to-surface radiation problem, so as to overcome the technical problems of poor calculation accuracy, slow iterative convergence and low calculation efficiency existing in the convergence algorithm used to solve the surface-to-surface radiation problem.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A method for accelerating the iterative convergence speed of a highly nonlinear surface-to-surface radiation problem, the specific steps comprising:

[0007] S1: Establishing a geometric model of the structure to be analyzed, and meshing the geometric model to obtain a temperature field finite element model;

[0008] S2: Set the properties of the temperature field finite element model; set the mesh control parameters of the temperature field finite element model; set the boundary conditions and initial conditions of the temperature field finite element model; set the solution information of the temperature field finite element model;

[0009] S3: obtaining mesh degree of freedom information, node information, unit information, boundary information, material information and solution information of the temperature field finite element model, and initializing the temperature field finite element model;

[0010] S4: Establish the overall heat transfer matrix:

[0011] S5: Select a radiation facet from the temperature field finite element model according to actual needs, and calculate the radiation angle coefficient matrix according to the node coordinates and normal direction of the selected radiation facet;

[0012] S6: Establish the cavity radiation energy equation according to the radiation angle coefficient matrix and the current temperature of each radiation surface;

[0013] S7: Based on the cavity radiation energy equation and the overall heat transfer matrix, the final temperature iteration calculation equation is obtained and solved. When the set convergence conditions are met, the temperature result of the current time step is output, the temperature field is updated, and the calculation of the next time step is entered;

[0014] S8: Iterate the solution until the set calculation end time, and obtain the temperature field of each successful iterative time step.

[0015] Furthermore, in S5, the process of calculating the radiation angle coefficient matrix according to the node coordinates and normal direction of the selected radiation facet is:

[0016] Use the Z-buffer buffer to save the distance between all target faces j and the current calculation face i, and initialize the distance value in the Z-buffer buffer to the set maximum value; traverse the current calculation face i and the target face j, and perform the following operations during each traversal:

[0017] 1) Calculate the vector between the calculation surface i and the target surface j, denoted as V ij ; Determine V by Hemicube algorithm ij Whether it belongs to the infinitesimal element within the vector bounding box, if so, the radiation angle coefficient value between the calculation surface i and the target surface j is calculated and recorded by the Hemicube algorithm;

[0018] 2) Calculate V ijlength and compares it with the distance value in the Z-buffer buffer. ij If the length of V is smaller, the distance value between the calculated surface i and the target surface j in the Z-buffer buffer is updated to the current V ij Length;

[0019] 3) Calculate V in the Z-buffer buffer ij The length of the target surface j and the normal vector n j If the dot product is greater than or equal to 0, it means that the calculation surface i and the target surface j are not relative, and the radiation angle coefficient of the current microelement is set to 0; if the dot product is less than 0, it means that the calculation surface i and the target surface j are relative, and the radiation angle coefficient of the current microelement and the serial number of the target surface j are updated based on the radiation angle coefficient value recorded in 1);

[0020] 4) After traversing all the radiating faces, the radiation angle coefficient matrix is ​​obtained.

[0021] Furthermore, in S6, according to the radiation angle coefficient matrix and the current temperature of each radiation surface, the cavity radiation energy equation is established as follows:

[0022]

[0023] Among them, F kj is the radiation angle coefficient from the k radiating facet to the j radiating facet, σ is the Stefan-Boltzmann constant, ε j is the radiation coefficient, Q j is the radiation heat of the j radiation surface, T k and T j The temperature of the k-radiation surface and the j-radiation surface respectively; δ kj is the unit matrix; A j is the area of ​​the j radiating facet; F k,amb is the radiation angle coefficient from the k radiating facet to the environment, T amb is the ambient temperature.

[0024] Furthermore, in S7, the semi-implicit separated Newton method is used to process the cavity radiation energy equation and the overall heat transfer matrix to obtain the final temperature iteration calculation equation. The specific process is:

[0025] S71: According to the cavity radiation energy equation, the radiation heat flux on each radiation facet is solved, including expressing the cavity radiation energy equation in matrix form, which is expressed as:

[0026]

[0027] Where I is the identity matrix; F is the radiation angle coefficient matrix; ∈ is the radiance vector; σ is the Stefan-Boltzmann constant; ρ is the reflectance vector; is the temperature vector composed of the temperatures on each small surface of the surface radiation, is the radiation heat flux vector composed of each small surface of the surface radiation;

[0028] Simplify the above formula and let A=(I-Fρ), get:

[0029]

[0030] S72: Add the radiation heat flux vector to the overall heat transfer matrix K(T)T=F(T), and obtain:

[0031]

[0032] Set its iteration form to:

[0033]

[0034] Among them, K(T n ) is the heat transfer matrix constructed according to the temperature field of the nth iteration step, F(T n ) is the load vector constructed according to the temperature field of the nth iteration step, is the radiation heat flux vector of the n+1th iteration step, To discretize the radiation heat flux vector, subtract The temperature iteration calculation equation before improvement is expressed as:

[0035]

[0036] S73: Increase in radiation heat flux Taylor expansion is performed, which is expressed as:

[0037]

[0038] in, is the difference between the radiation heat flux vector of the n+1th iteration step and the radiation heat flux vector of the previous step;

[0039] S74: The radiation heat flux vector is obtained based on the radiation energy and the incident energy, expressed as:

[0040]

[0041] Where E is the radiation heat flux; G is the incident heat flux;

[0042] S75: Substituting formula S74 into formula S73, while ignoring the derivative of the temperature with respect to the far-field incident, we obtain:

[0043]

[0044] S76: The temperature iteration calculation equation before improvement is adjusted by the approximate Jacobian method and the time integral formula to obtain the final temperature iteration calculation equation, which is expressed as:

[0045]

[0046] Where B is the discrete matrix; γ is the time integration coefficient; Δt is the time step; is the temperature increment; is the equivalent heat transfer coefficient; is the incident absorbed energy density.

[0047] Furthermore, in S4, the process of establishing the overall heat transfer matrix is:

[0048] According to the total degree of freedom information n of the grid, an n×n order heat transfer matrix is ​​established. Through the unit traversal loop, the heat conduction matrix and specific heat matrix of each unit are calculated in turn. According to the mapping relationship between the unit degree of freedom and the overall degree of freedom, the heat conduction matrix and specific heat matrix of each unit are assembled into the heat transfer matrix accordingly, and finally the overall heat transfer matrix is ​​formed.

[0049] Beneficial effect: The present invention establishes a heat transfer overall matrix, selects radiation faces from the temperature field finite element model according to actual needs, calculates the radiation angle coefficient matrix according to the node coordinates and normal directions of the selected radiation faces, and establishes the cavity radiation energy equation according to the radiation angle coefficient matrix and the current temperatures of each radiation facet; the cavity radiation energy equation and the heat transfer overall matrix are processed by the semi-implicit separated Newton method to obtain the final temperature field iterative equation, and iterative calculation is performed, which can significantly improve the convergence efficiency, thereby improving the problems of poor calculation accuracy, slow iterative convergence and low calculation efficiency in traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0051] Figure 1 A flow chart of a method for accelerating the iterative convergence speed of a highly nonlinear surface-to-surface radiation problem in the present invention;

[0052] Figure 2 It is a temperature-time curve comparison diagram of the semi-implicit separation Newton method, the explicit separation Picard method, and the semi-implicit separation Picard method in the embodiment of the present invention;

[0053] Figure 3 This is a comparison chart of the number of iteration steps for convergence calculation at each time step using the semi-implicit separated Newton method, the explicit separated Picard method, and the semi-implicit separated Picard method in an embodiment of the present invention. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] This embodiment provides a method for accelerating the iterative convergence speed of highly nonlinear surface radiation problems, such as Figure 1 As shown, the specific steps include:

[0056] S1: Establishing a geometric model of the structure to be analyzed, and meshing the geometric model to obtain a temperature field finite element model;

[0057] Specifically, in this embodiment, the geometric model may be divided into thermal shell units or solid units according to actual application conditions.

[0058] S2: Set the properties of the temperature field finite element model, including unit properties and material properties; set the mesh control parameters of the temperature field finite element model; set the boundary conditions and initial conditions of the temperature field finite element model, including temperature boundary conditions, heat flow load, initial temperature boundary, environmental radiation load, convection load, surface radiation load and heat generation load parameters; set the solution information of the temperature field finite element model, including transient or steady-state analysis settings, total calculation time, time step settings and convergence conditions;

[0059] S3: obtaining mesh freedom information, node information, unit information, boundary information, material information and solution information of the temperature field finite element model, wherein the mesh freedom information includes node numbers and coordinates, unit topology, total freedom of the finite element mesh, and a mapping relationship between unit freedom and overall freedom, and initializing the temperature field finite element model;

[0060] S4: Establish the overall heat transfer matrix:

[0061] In a specific embodiment, in S4, the process of establishing the overall heat transfer matrix is:

[0062] According to the total degree of freedom information n of the grid, an n×n order heat transfer matrix is ​​established. Through the unit traversal loop, the heat conduction matrix and specific heat matrix of each unit are calculated in turn. According to the mapping relationship between the unit degree of freedom and the overall degree of freedom, the heat conduction matrix and specific heat matrix of each unit are assembled into the heat transfer matrix accordingly, and finally the overall heat transfer matrix is ​​formed.

[0063] S5: Select a radiation facet from the temperature field finite element model according to actual needs, and calculate the radiation angle coefficient matrix according to the node coordinates and normal direction of the selected radiation facet;

[0064] Specifically, the radiation facet is the loading site of the facet-to-face radiation. For example, if a hexahedral unit is loaded with facet-to-face radiation on one of its faces, then this face of the unit is the radiation facet.

[0065] In a specific embodiment, in S5, the process of calculating the radiation angle coefficient matrix according to the node coordinates and normal direction of the selected radiation facet is:

[0066] The Z-buffer buffer is used to save the distance between all target surfaces j and the current calculation surface i, and the distance value in the Z-buffer buffer is initialized to the set maximum value. All target surfaces j and the current calculation surface i are the selected radiation small surfaces; the current calculation surface i and the target surface j are traversed, and the following operations are performed during each traversal:

[0067] 1) Calculate the vector between the calculation surface i and the target surface j, denoted as V ij ; Determine V by Hemicube algorithm ij Whether it belongs to the infinitesimal element within the vector bounding box, if so, the radiation angle coefficient value between the calculation surface i and the target surface j is calculated and recorded by the Hemicube algorithm;

[0068] 2) Calculate V ij length and compares it with the distance value in the Z-buffer buffer. ij If the length of V is smaller, the distance value between the calculated surface i and the target surface j in the Z-buffer buffer is updated to the current V ij Length;

[0069] 3) Calculate V in the Z-buffer buffer ij The length of the target surface j and the normal vector n j If the dot product is greater than or equal to 0, it means that the calculation surface i and the target surface j are not relative, and the radiation angle coefficient of the current microelement is set to 0; if the dot product is less than 0, it means that the calculation surface i and the target surface j are relative, and the radiation angle coefficient of the current microelement and the serial number of the target surface j are updated based on the radiation angle coefficient value recorded in 1);

[0070] Specifically, in the calculation process, the occlusion relationship between the solid or thermal shell planes needs to be considered. Therefore, for the planes with occlusion relationships, the Z-buffer algorithm is used to determine the plane closest to the current radiation facet, and store its plane number and radiation angle coefficient; specifically, Z-buffer, also known as depth buffer (Depth Buffer), is a buffer used to store the depth of each pixel, mainly used to realize hidden surface removal (Hidden Surface Removal) and depth testing (Depth Testing) in three-dimensional scenes. Through depth testing, Z-buffer can automatically handle occlusion relationships in three-dimensional scenes, ensuring that only the surface closest to the viewpoint is rendered to the screen, thereby realizing the function of hidden surface elimination in planes with occlusion relationships.

[0071] 4) After completing the traversal of all radiating facets, the radiation angle coefficient matrix reflecting the geometric relationship of each radiating facet is obtained.

[0072] S6: Establish the cavity radiation energy equation according to the radiation angle coefficient matrix and the current temperature of each radiation surface;

[0073] In a specific embodiment, in S6, according to the radiation angle coefficient matrix and the current temperature of each radiation facet, the cavity radiation energy equation established is:

[0074]

[0075] Among them, F kj is the radiation angle coefficient from the k radiating facet to the j radiating facet, σ is the Stefan-Boltzmann constant, ε j is the radiation coefficient, Q j is the radiation heat of the j radiation surface, T k and T j The temperature of the k-radiation surface and the j-radiation surface respectively; δ kj is the unit matrix; A j is the area of ​​the j radiating facet; F k,amb is the radiation angle coefficient from the k radiating facet to the environment, T amb is the ambient temperature.

[0076] S7: Based on the cavity radiation energy equation and the overall heat transfer matrix, the final temperature iteration calculation equation is obtained and solved. When the set convergence conditions are met, the temperature result of the current time step is output, the temperature field is updated, and the calculation of the next time step is entered;

[0077] In a specific embodiment, in S7, the semi-implicit separated Newton method is used to process the cavity radiation energy equation and the heat transfer overall matrix to obtain the final temperature iteration calculation equation. The specific process is:

[0078] S71: According to the cavity radiation energy equation, the radiation heat flux on each radiation facet is solved, including expressing the cavity radiation energy equation in matrix form, which is expressed as:

[0079]

[0080] Where I is the identity matrix; F is the radiation angle coefficient matrix; ∈ is the radiance vector; σ is the Stefan-Boltzmann constant; ρ is the reflectance vector; is the temperature vector composed of the temperatures on each small surface of the surface radiation, is the radiation heat flux vector composed of each small surface of the surface radiation;

[0081] Simplify the above formula and let A=(I-Fρ), get:

[0082]

[0083] S72: Add the radiation heat flux vector to the overall heat transfer matrix K(T)T=F(T), and obtain:

[0084]

[0085] Set its iteration form to:

[0086]

[0087] Among them, K(T n ) is the heat transfer matrix constructed according to the temperature field of the nth iteration step, F(T n ) is the load vector constructed according to the temperature field of the nth iteration step, is the radiation heat flux vector of the n+1th iteration step, To discretize the radiation heat flux vector, subtract The temperature iteration calculation equation before improvement is expressed as:

[0088]

[0089] S73: Increase in radiation heat flux Taylor expansion is performed, which is expressed as:

[0090]

[0091] in, is the difference between the radiation heat flux vector of the n+1th iteration step and the radiation heat flux vector of the previous step;

[0092] S74: The radiation heat flux vector is obtained based on the radiation energy and the incident energy, expressed as:

[0093]

[0094] Where E is the radiation heat flux; G is the incident heat flux;

[0095] S75: Substituting formula S74 into formula S73, while ignoring the derivative of the temperature with respect to the far-field incident, we obtain:

[0096]

[0097] S76: The temperature iteration calculation equation before improvement is adjusted by the approximate Jacobian method and the time integral formula to obtain the final temperature iteration calculation equation, which is expressed as:

[0098]

[0099] Where B is the discrete matrix; γ is the time integration coefficient; Δt is the time step; is the temperature increment; is the equivalent heat transfer coefficient; is the incident absorbed energy density.

[0100] Specifically, the nonlinear effect of the radiation surface temperature on the radiation energy is considered by adopting the approximate Jacobian method.

[0101] Specifically, during the process of solving the equation, the user can set the relaxation process according to the actual situation, that is, add a part of the current calculation increment to the temperature field, thereby enhancing the calculation stability, but at the same time the convergence efficiency will decrease. In this embodiment, the convergence condition can generally adopt the relative tolerance, that is, when the ratio of the current residual term to the residual term of the previous step is less than the set relative tolerance, convergence is determined.

[0102] S8: Iterate the solution until the set calculation end time, and obtain the temperature field of each successful iterative time step.

[0103] In order to verify the effectiveness of the method proposed in this embodiment, a geometric model of the structure to be analyzed is set, and the geometric parameters and material parameters are set as shown in Table 1 and Table 2. The geometric body consists of four parts, including two inner and outer layers and two front and rear ends. The upper edge length l1 of the inner and outer layers is 0.8950m, the lower edge length l2 is 0.5127m, and the distance d between the inner and outer layers is 0.1m; the front end height h1 is 1.8419m, the front end width w1 is 0.7305m, the rear end height h2 is 2.0277m, and the rear end width w2 is 0.7204m. The normal directions of the front and rear ends are inclined relative to the positive direction of the x-axis, and the inclination angle θ is 20°; the inner and outer layers and the front and rear ends are all thermal shell units, and the thickness of the thin shell is 0.001m. All unit faces of the entire model consider the surface radiation effect, and a forced temperature boundary is applied to the inner layer nodes, and the temperature value is 500℃; a convection boundary is applied to the outer layer, and the convection coefficient is 1W / m 2 ·℃, the ambient temperature is 20℃, the analysis type is set to transient heat conduction, the total calculation time is 50s, the fixed time step is 1s, the convergence tolerance is 1.0e-5, and the maximum number of steps allowed for convergence is 15.

[0104] Table 1:

[0105] Geometric parameters value <![CDATA[Front-end height h1]]> 1.8419m <![CDATA[Front-end width w1]]> 0.7305m Distance between inner and outer layers d 0.1m <![CDATA[Upper edge length l1]]> 0.8950m <![CDATA[Lower edge length l2]]> 0.5127m <![CDATA[Rear height h2]]> 2.0277m <![CDATA[Rear width w2]]> 0.7204m Tilt angle θ 20° Shell thickness t 0.001m

[0106] Table 2:

[0107] Model parameters value density <![CDATA[2770kg / m 3 ]]> Thermal conductivity 273.5W / m·℃ Specific Heat 951J / kg·℃ Stefan-Boltzmann constant <![CDATA[5.6704e-08W / m 2 ·℃ 4 ]]> Default temperature -273.15℃

[0108] like Figure 2 As shown in the figure, the temperature-time curve comparison of a node of the model is shown when the semi-implicit separation Newton method, the explicit separation Picard method, and the semi-implicit separation Picard method are used. It can be seen from the figure that as the calculation proceeds, the temperature of the node shows an upward trend. The semi-implicit separation Picard method has a large error at 3s, and its calculation is terminated at 7s. Although the explicit separation Picard method has good stability, the accumulated errors caused by its algorithm will gradually amplify, and its final result has a large error compared with the empirical value. The temperature-time curve calculated by the semi-implicit separation Newton method has a smaller error than the empirical value.

[0109] like Figure 3 As shown in the figure, it is a comparison chart of the number of iteration steps for convergence calculation in each time step when using the semi-implicit separated Newton method, the explicit separated Picard method and the semi-implicit separated Picard method respectively. It can be seen from the figure that the number of convergence steps required for the semi-implicit separated Picard method in the initial stage of calculation is greater than 10, and in the subsequent calculation to the 7th second, the convergence condition can no longer be met within 15 steps, and the calculation is terminated; the explicit separated Picard method has an explicit algorithm, so its convergence step number is always 1; and as the calculation proceeds, the number of convergence steps of each step of the semi-implicit separated Newton method gradually decreases, reflecting its calculation stability and accelerated convergence characteristics.

[0110] The present invention can be widely used in a wide range of fields such as aviation, aerospace, ships, automobiles, electronic appliances, etc., and is of great significance for the accurate and rapid solution of heat transfer analysis that requires the calculation of highly nonlinear surface radiation.

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for accelerating the iterative convergence speed of highly nonlinear surface-to-surface radiation problems, characterized in that: The specific steps include: S1: Establishing a geometric model of the structure to be analyzed, and meshing the geometric model to obtain a temperature field finite element model; S2: Set the properties of the temperature field finite element model; set the mesh control parameters of the temperature field finite element model; set the boundary conditions and initial conditions of the temperature field finite element model; set the solution information of the temperature field finite element model; S3: obtaining mesh degree of freedom information, node information, unit information, boundary information, material information and solution information of the temperature field finite element model, and initializing the temperature field finite element model; S4: Establish the overall heat transfer matrix: S5: Select a radiation facet from the temperature field finite element model according to actual needs, and calculate the radiation angle coefficient matrix according to the node coordinates and normal direction of the selected radiation facet; S6: Establish the cavity radiation energy equation according to the radiation angle coefficient matrix and the current temperature of each radiation surface; S7: Based on the cavity radiation energy equation and the overall heat transfer matrix, the final temperature iteration calculation equation is obtained and solved. When the set convergence conditions are met, the temperature result of the current time step is output, the temperature field is updated, and the calculation of the next time step is entered; S8: Iterate the solution until the set calculation end time, and obtain the temperature field of each successful iterative time step.

2. The method for accelerating the iterative convergence speed of highly nonlinear surface-to-surface radiation problems according to claim 1, characterized in that: In S5, the process of calculating the radiation angle coefficient matrix according to the node coordinates and normal direction of the selected radiation facet is: Use the Z-buffer buffer to save the distance between all target faces j and the current calculation face i, and initialize the distance value in the Z-buffer buffer to the set maximum value; traverse the current calculation face i and the target face j, and perform the following operations during each traversal: 1) Calculate the vector between the calculation surface i and the target surface j, denoted as V ij ; Determine V by Hemicube algorithm ij Whether it belongs to the infinitesimal element within the vector bounding box, if so, the radiation angle coefficient value between the calculation surface i and the target surface j is calculated and recorded by the Hemicube algorithm; 2) Calculate V ij length and compares it with the distance value in the Z-buffer buffer. ij If the length of V is smaller, the distance value between the calculated surface i and the target surface j in the Z-buffer buffer is updated to the current V ij Length; 3) Calculate V in the Z-buffer buffer ij The length of the target surface j and the normal vector n j If the dot product is greater than or equal to 0, it means that the calculation surface i and the target surface j are not relative, and the radiation angle coefficient of the current microelement is set to 0; if the dot product is less than 0, it means that the calculation surface i and the target surface j are relative, and the radiation angle coefficient of the current microelement and the serial number of the target surface j are updated based on the radiation angle coefficient value recorded in 1); 4) After traversing all the radiating faces, the radiation angle coefficient matrix is ​​obtained.

3. The method for accelerating the iterative convergence speed of highly nonlinear surface-to-surface radiation problems according to claim 1, characterized in that: In S6, according to the radiation angle coefficient matrix and the current temperature of each radiation surface, the cavity radiation energy equation is established as follows: Among them, F kj is the radiation angle coefficient from the k radiating facet to the j radiating facet, σ is the Stefan-Boltzmann constant, ε j is the radiation coefficient, Q j is the radiation heat of the j radiation surface, T k and T j The temperature of the k-radiation surface and the j-radiation surface respectively; δ kj is the unit matrix; A j is the area of ​​the j radiating facet; F k,amb is the radiation angle coefficient from the k radiating facet to the environment, T amb is the ambient temperature.

4. The method for accelerating the iterative convergence speed of highly nonlinear surface-to-surface radiation problems according to claim 3, characterized in that: In S7, the semi-implicit separated Newton method is used to process the cavity radiation energy equation and the overall heat transfer matrix to obtain the final temperature iteration calculation equation. The specific process is as follows: S71: According to the cavity radiation energy equation, the radiation heat flux on each radiation facet is solved, including expressing the cavity radiation energy equation in matrix form, which is expressed as: Where I is the identity matrix; F is the radiation angle coefficient matrix; ∈ is the radiance vector; σ is the Stefan-Boltzmann constant; ρ is the reflectance vector; is the temperature vector composed of the temperatures on each small surface of the surface radiation, is the radiation heat flux vector composed of each small surface of the surface radiation; Simplify the above formula and let A=(I-Fρ), get: S72: Add the radiation heat flux vector to the overall heat transfer matrix K(T)T=F(T), and obtain: Set its iteration form to: Among them, K(T n ) is the heat transfer matrix constructed according to the temperature field of the nth iteration step, F(T n ) is the load vector constructed according to the temperature field of the nth iteration step, is the radiation heat flux vector of the n+1th iteration step, To discretize the radiation heat flux vector, subtract The temperature iteration calculation equation before improvement is expressed as: S73: Increase in radiation heat flux Taylor expansion is performed, which is expressed as: in, is the difference between the radiation heat flux vector of the n+1th iteration step and the radiation heat flux vector of the previous step; S74: The radiation heat flux vector is obtained based on the radiation energy and the incident energy, expressed as: Where E is the radiation heat flux; G is the incident heat flux; S75: Substituting formula S74 into formula S73, while ignoring the derivative of the temperature with respect to the far-field incident, we obtain: S76: The temperature iteration calculation equation before improvement is adjusted by the approximate Jacobian method and the time integral formula to obtain the final temperature iteration calculation equation, which is expressed as: Where B is the discrete matrix; γ is the time integration coefficient; Δt is the time step; is the temperature increment; is the equivalent heat transfer coefficient; is the incident absorbed energy density.

5. The method for accelerating the iterative convergence speed of highly nonlinear surface-to-surface radiation problems according to claim 1, characterized in that: In S4, the process of establishing the overall heat transfer matrix is: According to the total degree of freedom information n of the grid, an n×n order heat transfer matrix is ​​established. Through the unit traversal loop, the heat conduction matrix and specific heat matrix of each unit are calculated in turn. According to the mapping relationship between the unit degree of freedom and the overall degree of freedom, the heat conduction matrix and specific heat matrix of each unit are assembled into the heat transfer matrix accordingly, and finally the overall heat transfer matrix is ​​formed.

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