A numerical iterative method based on chemical nonequilibrium source term limiter

Abstract

The present invention discloses a numerical iteration method based on a chemical non-equilibrium source term limiter, which relates to the field of aerodynamics technology, including: constructing and adding a source term limiter in a time advancement format, and using different time layer source term calculation values ​​to replace the current time calculation source term through flow field characteristics and flow instantaneous state identification, thereby simplifying the source term calculation process, saving calculation time and improving calculation efficiency. The present invention can significantly reduce the repeated calculation process of chemical source terms and reduce the overall time consumption of chemical non-equilibrium flow simulation, which is of great help to improve the performance of high-speed CFD simulation software in terms of calculation efficiency.

Description

Technical Field

[0001] The invention relates to the technical field of aerodynamics, and in particular to a numerical iteration method based on a chemical non-equilibrium source term limiter. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.

[0003] When an aircraft is flying at high speed, the high-temperature shock wave layer flow in its surrounding flow will experience complex chemical reactions and flow physics coupling effects such as dissociation, ionization, recombination, and exchange, which are referred to as chemical non-equilibrium effects in the literature. In computational fluid dynamics (CFD), chemical non-equilibrium NS equations (Navier Stokes equations) are usually used to simulate chemical non-equilibrium flows.

[0004] The chemical non-equilibrium NS equation is a tightly coupled computational equation system based on the classical NS equation and the continuity equations of multiple components. It has a large number of computational equations, and the transport system of mass, momentum and energy and the calculation of chemical source terms are complex. In engineering simulation applications, it has prominent problems such as large memory resource consumption, time-consuming calculation and long cycle. On the other hand, due to the wide range and large span of the time distribution of chemical elementary reactions, there is an order of magnitude difference between the characteristic time of flow and the characteristic time of chemical reaction. Therefore, the equation system of chemical reaction and flow tightly coupled has strong numerical rigidity, which seriously affects the convergence of numerical iteration and further restricts the computational efficiency of flow simulation. Therefore, the computational efficiency of chemical non-equilibrium flow simulation has always been one of the most concerned "hot spots" and key issues that urgently need to be solved in engineering simulation applications.

[0005] A large number of numerical simulation tests have found that compared with the conventional simulation method based on the perfect gas assumption, the chemical non-equilibrium simulation method based on the single temperature model will increase the computational time by more than 2 times. Similarly, the complete chemical non-equilibrium equation will increase the computational time by 10% to 40% compared to the calculation equation that ignores the source term. At the same time, the larger the calculation domain, the more components, and the more complex the chemical reaction system, the computational time saved when ignoring the source term can even reach more than 50%. From this analysis, it can be seen that the source term is the most complex and time-consuming calculation term in solving the chemical non-equilibrium NS equation.

[0006] At the same time, the analysis of the spatiotemporal dynamic evolution of the flow field shows that there are actually many unnecessary and invalid repeated calculations in the chemical non-equilibrium flow field. Taking the simulation of the chemical non-equilibrium flow of the cylindrical model (using the incoming flow parameters to give the initial value of the flow field) as an example, as the iterative process progresses over time, the flow parameters and the calculated values ​​of the chemical source items in the outer area of ​​the shock layer remain unchanged. At this time, the flow situation is similar to the frozen flow, and it is meaningless to repeatedly calculate the source items; inside the shock layer and in the downstream area of ​​the flow, when the local flow is not affected by the disturbance or is close to a stable flow state, the change amplitude of the flow parameters and the calculated values ​​of the source items in the corresponding area is close to zero. At this time, the flow situation is also similar to the frozen flow, and the source items no longer need to be repeatedly calculated.

[0007] In summary, reducing the source term calculation process has a positive and significant effect on improving the efficiency of chemical non-equilibrium flow simulation. Efficient solution methods related to chemical non-equilibrium flow simulation can be developed by simplifying the source term calculation process. Summary of the invention

[0008] The purpose of the present invention is to provide a numerical iteration method based on a chemical non-equilibrium source term limiter to address the problems existing in the prior art, construct and add a source term limiter in a time-marching format, and use different time layer source term calculation values ​​to replace the current time calculation source term through flow field characteristics and instantaneous state identification of the flow, thereby simplifying the source term calculation process and achieving the purpose of saving calculation time and improving calculation efficiency.

[0009] The technical solution of the present invention is as follows:

[0010] A numerical iterative method based on chemical non-equilibrium source term limiter constructs and adds source term limiter in time marching format, and replaces the current time calculated source term with the calculated value of source term at different time layers through flow field characteristics and instantaneous flow state identification, thereby simplifying the source term calculation process.

[0011] Furthermore, the method specifically includes the following steps:

[0012] Step S1: calculation pre-processing and flow field initialization;

[0013] Step S2: Use the calculated values ​​of source terms at different time layers to construct a chemical source term limiter, and perform numerical iteration based on the LU-SGS (Lower-Upper Symmetry Guass-Seidel) time-marching format of the chemical source term limiter;

[0014] Step S3: using the instantaneous flow velocity and the rate of change of the average temperature to determine the source term restriction coefficient, and realizing the calculation and update of the flow field and the source term restriction coefficient;

[0015] Step S4: Calculate post-processing and output flow field parameters; determine whether the flow field iteration tends to be stable based on the calculation convergence condition. If it tends to be stable, stop the numerical iteration process and output relevant flow field parameters according to the calculation needs; otherwise, return to step S2 and repeat the numerical iteration.

[0016] Furthermore, in step S1, during the flow field initialization process, an additional three-dimensional array is established to store global parameters representing the calculation state of the grid unit. , Represents the source term limitation coefficient.

[0017] Furthermore, the global parameter There are only two possible values, namely or ;when When , the chemical source term and its approximate diagonal matrix of the calculation unit do not need to be calculated, and the previous moment is used, that is, n -1 The calculated value of the time layer is updated and replaced; when , indicating that the chemical source term and its approximate diagonal matrix of the computational unit need to be recalculated, using the current moment, that is, n The calculated values ​​of the time layer are updated and replaced; during the flow field initialization process, the calculated states of all grid cells are taken .

[0018] Furthermore, the LU-SGS time advancement format based on the chemical source term limiter is as follows:

[0019]

[0020] Where:

[0021] It indicates the temporary conservation quantity increment;

[0022] represents a diagonal matrix;

[0023] Indicates calculation of the right-hand side;

[0024] represents a lower triangular matrix;

[0025] represents the increase in the conserved quantity at the current moment, Indicates the current moment;

[0026] represents an upper triangular matrix.

[0027] Furthermore, the diagonal matrix , lower triangular matrix , upper triangular matrix and the right-hand side The specific form is:

[0028]

[0029] Where:

[0030] is the volume of the current calculation unit;

[0031] is the time step at the current moment;

[0032] represents the direction of the grid coordinate system, ;

[0033] , are the Jacobian matrices of the convection flux of the current computational unit in the direction of the corresponding grid coordinate system. and the viscous flux Jacobian matrix The spectral radius of

[0034] represents the identity matrix;

[0035] is the Jacobian approximation diagonal matrix of chemical source terms; Represents the Jacobian approximation diagonal matrix of the chemical source term at the current moment, Represents the Jacobian approximation diagonal matrix of the chemical source term at the previous moment;

[0036] i , j , k Indicates the serial number of the computing unit in the corresponding direction of the grid coordinate system, and its combination represents the serial coordinate of the current computing unit in the grid;

[0037] , , , , , They are i , j , k The Jacobian matrix of the convection flux of adjacent computational units in the direction; correspondingly, , , , , , are the spectral radius of the Jacobian matrix of the convective flux respectively;

[0038] , , , , , They are i , j , k The Jacobian matrix of the viscosity flux of the adjacent computational units in the direction, correspondingly, , , , , , are the spectral radius of the Jacobian matrix of the viscosity flux, respectively;

[0039] represents the total convective flux in and out of the computational cell boundary surface, Represents the total convective flux in and out of the boundary surface of the computational unit at the current moment;

[0040] represents the total viscous flux in and out of the computational cell boundary surface, Represents the total viscous flux entering and leaving the boundary surface of the computational unit at the current moment;

[0041] is the chemical source term, is the chemical source term at the current moment, is the chemical source term at the previous moment;

[0042] For adjacent computational units ( i -1, j , k )The conserved quantity increases at the current moment;

[0043] For adjacent computational units ( i , j -1, k )The conserved quantity increases at the current moment;

[0044] For adjacent computational units ( i , j , k -1) The conserved quantity increases at the current moment;

[0045] For adjacent computational units ( i +1, j , k )The conserved quantity increases at the current moment;

[0046] For adjacent computational units ( i , j +1, k)The conserved quantity increases at the current moment;

[0047] For adjacent computational units ( i , j , k +1) The conserved quantity at the current moment increases.

[0048] Furthermore, the chemical source term Jacobian approximation diagonal matrix Defined as:

[0049]

[0050] Where:

[0051] is the symbol of the partial derivative operator;

[0052] is the chemical source term, represents transpose, For the The chemical source term corresponding to each gas component is: For the The chemical source term corresponding to each gas component;

[0053] is the conserved quantity; For the The conserved quantity corresponding to each gas component is: For the The conserved quantity corresponding to each gas component;

[0054] is the total number of gas components;

[0055] is the Kronecker symbol;

[0056] is the first diagonal matrix of the Jacobian approximation of the chemical source term The main diagonal elements corresponding to the gas components;

[0057] is the first diagonal matrix of the Jacobian approximation of the chemical source term The main diagonal elements corresponding to the gas components;

[0058] represents a diagonal matrix.

[0059] Furthermore, the source term limitation coefficient is determined by the change rate of the instantaneous flow velocity and the average temperature, and the specific expression is:

[0060]

[0061] Where:

[0062] is the flow rate;

[0063] The flow rate calculated for the current moment;

[0064] is the average temperature;

[0065] The average temperature calculated for the current moment;

[0066] is the threshold value.

[0067] Furthermore, the average temperature is defined as follows:

[0068]

[0069] Where:

[0070] and are the translation temperature and vibration temperature respectively;

[0071] Threshold The method of determining is as follows:

[0072]

[0073] Where:

[0074] Calculate the control coefficient for the entire domain, are two control coefficients related to speed and temperature respectively, is the incoming flow velocity, Total temperature of incoming flow.

[0075] Furthermore, in step S4, the judgment condition of whether the flow field iteration tends to be stable is:

[0076]

[0077] Where:

[0078] Set the maximum number of iterations for the calculation;

[0079] Represents a computational unit The conservation quantity increases at the current moment, Represents a computational unit The conserved quantity at the initial moment increases.

[0080] Compared with the prior art, the present invention has the following beneficial effects:

[0081] 1. A numerical iterative method based on chemical non-equilibrium source term limiter has a rigorous theoretical basis, is equivalent to the integral form of chemical non-equilibrium flow NS solution equation, is compatible with the implicit time iteration format in conventional LU-SGS, and has reliable calculation accuracy and iterative convergence.

[0082] 2. A numerical iterative method based on a chemical non-equilibrium source term limiter simplifies and saves the complex calculation process of the chemical source term, can avoid the invalid repeated calculation of the chemical source term in a large range of flow areas before the shock wave, and significantly improves the computational efficiency of chemical reaction flow simulation.

[0083] 3. A numerical iteration method based on chemical non-equilibrium source term limiter is applicable to high-speed complex flows such as chemical non-equilibrium and thermochemical non-equilibrium. The algorithm is easy to transplant and simple to implement, which has a significant impact on improving the performance of high-speed CFD software in terms of computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a flow chart of a numerical iterative method based on chemical non-equilibrium source term limiter;

[0085] Figure 2 This is the curve of CPU time changing with the number of iterations in Example 2;

[0086] Figure 3 This is the wall pressure distribution curve of Example 2;

[0087] Figure 4 This is the wall heat flux distribution curve of Example 2. DETAILED DESCRIPTION

[0088] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0089] The features and performance of the present invention are further described in detail below in conjunction with the embodiments.

[0090] Embodiment 1

[0091] See also Figure 1 A numerical iterative method based on chemical non-equilibrium source term limiter is proposed. The source term limiter is constructed and added in the time marching format. The source term calculation value of different time layers is used to replace the current time calculation source term through flow field characteristics and instantaneous state identification, thereby simplifying the source term calculation process and achieving the purpose of saving calculation time and improving calculation efficiency.

[0092] In this embodiment, specifically, based on the chemical nonequilibrium flow NS equation and the LU-SGS implicit time marching method, the calculation steps include:

[0093] Step S1: calculation pre-processing and flow field initialization;

[0094] It should be noted that the calculation pre-processing includes the main steps of reading the grid and boundary conditions, setting the calculation and control conditions, etc. On this basis, the flow field initialization process establishes a series of access data structures based on the grid topology and assigns initial values. These access data include original variables or conserved quantities, time steps, convective flux spectrum radius, viscous flux spectrum radius, residuals, main diagonal elements of diagonal matrices, etc.

[0095] Therefore, in order to carry out numerical iteration based on chemical non-equilibrium source term limiter, an additional three-dimensional array is established in this process to store global parameters representing the calculation state of the grid cell. , Represents the source term limitation coefficient.

[0096] In this embodiment, specifically, the global parameter There are only two possible values, namely or ;when When , the chemical source term and its approximate diagonal matrix of the calculation unit do not need to be calculated, and the previous moment is used, that is, n -1 The calculated value of the time layer is updated and replaced; when , indicating that the chemical source term and its approximate diagonal matrix of the computational unit need to be recalculated, using the current moment, that is, n The calculated values ​​of the time layer are updated and replaced; during the flow field initialization process, the calculated states of all grid cells are taken .

[0097] Step S2: construct a chemical source term limiter using calculated values ​​of source terms at different time layers, and perform numerical iteration based on the LU-SGS time-marching format of the chemical source term limiter;

[0098] The traditional LU-SGS time marching format is defined as:

[0099]

[0100] The diagonal matrix , lower triangular matrix , upper triangular matrix and the right-hand side The specific form is:

[0101]

[0102] Where:

[0103] i , j , k Indicates the serial number of the computing unit in the corresponding direction of the grid coordinate system, and its combination represents the serial coordinate of the current computing unit in the grid;

[0104] is the volume of the current calculation unit;

[0105] Indicates the current moment;

[0106] is the time step at the current moment;

[0107] represents the direction of the grid coordinate system, ;

[0108] , are the Jacobian matrices of the convection flux of the current computational unit in the direction of the corresponding grid coordinate system. and the viscous flux Jacobian matrix The spectral radius of

[0109] represents the identity matrix;

[0110] is the Jacobian approximation diagonal matrix of chemical source terms; Represents the Jacobian approximation diagonal matrix of the chemical source term at the current moment, Represents the Jacobian approximation diagonal matrix of the chemical source term at the previous moment;

[0111] is the chemical source term;

[0112] is the chemical source term at the current moment, is the chemical source term at the previous moment;

[0113] Represents the total convective flux in and out of the boundary surface of the computational unit; Represents the total convective flux in and out of the boundary surface of the computational unit at the current moment;

[0114] represents the total viscous flux in and out of the boundary surface of the computational unit; Represents the total viscous flux entering and leaving the boundary surface of the computational unit at the current moment;

[0115] It indicates the temporary conservation quantity increment;

[0116] It indicates the increase of the conserved quantity at the current moment;

[0117] For adjacent computational units ( i -1, j , k )The conserved quantity increases at the current moment;

[0118] For adjacent computational units ( i , j -1, k )The conserved quantity increases at the current moment;

[0119] For adjacent computational units ( i , j , k -1) The conserved quantity increases at the current moment;

[0120] For adjacent computational units ( i +1, j , k )The conserved quantity increases at the current moment;

[0121] For adjacent computational units ( i , j +1, k )The conserved quantity increases at the current moment;

[0122] For adjacent computational units ( i , j , k +1) The conserved quantity increases at the current moment;

[0123] , , , , , They are i , j , k The Jacobian matrix of the convection flux of adjacent computational units in the direction; correspondingly, , , , , , are the spectral radius of the Jacobian matrix of the convective flux respectively;

[0124] , , , , , They are i , j , k The Jacobian matrix of the viscosity flux of the adjacent computational units in the direction, correspondingly, , , , , , are the spectral radius of the Jacobian matrix of the viscosity flux respectively; it should be noted that for the sake of simplicity, the subscript symbols of the relevant variables are omitted Variables without special subscripts are represented by calculation units. calculate;

[0125] Use current time n and the previous moment n -1 chemical source term and its Jacobian approximation diagonal matrix to construct the chemical source term limiter, and add the traditional LU-SGS time advancement format to obtain the new LU-SGS time advancement format based on the chemical source term limiter. The new iterative format is the same as the traditional LU-SGS format in mathematical form, the difference is that the diagonal matrix and right end , their specific definitions are as follows:

[0126]

[0127] The Jacobian approximation of the chemical source term is a diagonal matrix Defined as:

[0128]

[0129] Where:

[0130] is the symbol of the partial derivative operator;

[0131] is the chemical source term, represents transpose, For the The chemical source term corresponding to each gas component is: For the The chemical source term corresponding to each gas component;

[0132] is the conserved quantity; For the The conserved quantity corresponding to each gas component is: For the The conserved quantity corresponding to each gas component;

[0133] is the total number of gas components;

[0134] is the Kronecker symbol;

[0135] is the first diagonal matrix of the Jacobian approximation of the chemical source term The main diagonal elements corresponding to the gas components;

[0136] is the first diagonal matrix of the Jacobian approximation of the chemical source term The main diagonal elements corresponding to the gas components;

[0137] represents a diagonal matrix;

[0138] In summary, the connotation of the LU-SGS time-marching format based on the chemical source term limiter is:

[0139] When the source term limits the coefficient When the source term of the right-hand side and the Jacobian approximation matrix of the chemical source term in the diagonal matrix adopt the previous moment (i.e. n -1 time layer) is updated and replaced; when = 0, the source term on the right side and the Jacobian approximation matrix of the chemical source term in the diagonal matrix adopt the current moment (i.e. n The conservation of the time layer) is recalculated. n When the calculated value of the -1 time layer is updated and replaced, the repeated calculation of the chemical source term is avoided, thereby reducing the time consumption of the source term calculation process. When , the time-marching format degenerates into the source-term explicit format; when = 0, the time-marching format degenerates into a completely implicit format. Therefore, the LU-SGS time-marching format based on the chemical source term limiter has a rigorous mathematical theoretical basis, is compatible with the traditional LUSGS format, and is equivalent to the differential form of the chemical non-equilibrium NS equations.

[0140] Step S3: using the instantaneous flow velocity and the rate of change of the average temperature to determine the source term restriction coefficient, and realizing the calculation and update of the flow field and the source term restriction coefficient;

[0141] Specifically, the source term limitation coefficient is determined by the change rate of the instantaneous flow velocity and the average temperature, and the specific expression is:

[0142]

[0143] Where:

[0144] is the flow rate;

[0145] The flow rate calculated for the current moment;

[0146] is the average temperature;

[0147] The average temperature calculated for the current moment;

[0148] is the threshold value;

[0149] The mean temperature is defined as follows:

[0150]

[0151] Where:

[0152] and are the translation temperature and vibration temperature respectively;

[0153] Threshold The method of determining is as follows:

[0154]

[0155] Where:

[0156] Calculate the control coefficient for the entire domain, are two control coefficients related to speed and temperature respectively, is the incoming flow velocity, Total temperature of incoming flow.

[0157] Step S4: Calculate post-processing and output flow field parameters; determine whether the flow field iteration tends to be stable according to the calculation convergence condition. If it tends to be stable, stop the numerical iteration process and output relevant flow field parameters according to the calculation needs; otherwise, return to step S2 and repeat the numerical iteration;

[0158] In step S4, the judgment condition of whether the flow field iteration tends to be stable is:

[0159]

[0160] Where:

[0161] Set the maximum number of iterations for the calculation;

[0162] Represents a computational unit The conservation value at the current moment (i.e. the residual value) is increased. Represents a computational unit The conserved quantity at the initial moment increases in value (i.e., the residual value).

[0163] Embodiment 2

[0164] Based on high-speed CFD software, a cylindrical model of the HEG shock tunnel test was selected, and the method of the present invention was applied to carry out high-speed sonic chemical non-equilibrium flow simulation. The computational model and experimental conditions refer to the literature "Hannemann K., High EnthalpyFlows in the HEG Shock Tunnel: Experiment and Numerical Rebuilding, AIAA2003-0978, 41st Aerospace Sciences Meeting and Exhibit 6-9 January 2003, Reno, Nevada, 2003:1-18". The incoming flow velocity is 4776m / s, the temperature is 690K, and the pressure is 687Pa. The numerical simulation adopts the thermodynamic single-temperature 5-component Dunn-Kang chemical model, the convective flux selects the mixed format of Steger and AUSMpw+, the CFL number is 200, the wall conditions are isothermal fully catalytic wall and non-catalytic wall conditions (wall temperature is 300K), and the 48-core parallel iteration steps are 20,000 steps.

[0165] Figure 2 The time variation curves calculated by the method of the present invention and the conventional method in Example 2 are given. It can be seen that the calculation time of the method of the present invention is reduced by 15.56% to 17.52% when the number of iterations is the same, indicating that the method of the present invention is significantly helpful in improving the calculation efficiency.

[0166] Figure 3 and 4 The wall pressure distribution and wall heat flux distribution obtained by the method of the present invention and the conventional method under the condition of 20,000 iterations in Example 2 are respectively given. It can be seen that the pressure and heat flux curves calculated by the method of the present invention are basically consistent with the calculation results of the conventional method, which shows that the method of the present invention is accurate and reliable in predicting the aerodynamic and thermal characteristics related to thermochemical non-equilibrium flow.

[0167] In summary, the method of the present invention has a significant effect of improving computational efficiency when dealing with typical chemical non-equilibrium flow simulations, and the aerodynamic / thermal characteristics prediction accuracy is reliable, so it has good engineering application prospects.

[0168] The above-mentioned embodiments only express the specific implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the protection scope of the present application. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the technical solution concept of the present application, and these all belong to the protection scope of the present application.

[0169] This background section is provided to generally present the context of the invention, and the work of the presently named inventors, the work to the extent described in this background section, and aspects of this section that did not constitute prior art at the time of application are neither explicitly nor implicitly admitted to be prior art to the present invention.

Claims

1. A numerical iterative method based on chemical non-equilibrium source term limiter, characterized in that: The source term limiter is constructed and added in the time advancement format, and the source term calculation value of different time layers is used to replace the current time calculation source term through the flow field characteristics and the instantaneous state identification of the flow, so as to simplify the source term calculation process; The specific steps include: Step S1: calculation pre-processing and flow field initialization; Step S2: construct a chemical source term limiter using calculated values ​​of source terms at different time layers, and perform numerical iteration based on the LU-SGS time-marching format of the chemical source term limiter; Step S3: using the instantaneous flow velocity and the rate of change of the average temperature to determine the source term restriction coefficient, and realizing the calculation and update of the flow field and the source term restriction coefficient; Step S4: Calculate post-processing and flow field parameter output; determine whether the flow field iteration tends to be stable according to the calculation convergence condition. If it tends to be stable, stop the numerical iteration process and output relevant flow field parameters according to the calculation needs; otherwise, return to step S2 and repeat the numerical iteration.

2. A numerical iteration method based on chemical non-equilibrium source term limiter according to claim 1, characterized in that: In step S1, during the flow field initialization process, an additional three-dimensional array is established to store global parameters representing the calculation state of the grid unit. , Represents the source term limitation coefficient.

3. A numerical iteration method based on chemical non-equilibrium source term limiter according to claim 2, characterized in that: The global parameters There are only two possible values, namely or ;when When , the chemical source term and its approximate diagonal matrix of the calculation unit do not need to be calculated, and the previous moment is used, that is, n -1 The calculated value of the time layer is updated and replaced; when , indicating that the chemical source term and its approximate diagonal matrix of the computational unit need to be recalculated, using the current moment, that is, n The calculated values ​​of the time layer are updated and replaced; during the flow field initialization process, the calculated states of all grid cells are taken .

4. A numerical iteration method based on chemical non-equilibrium source term limiter according to claim 1, characterized in that: The LU-SGS time advancement format based on the chemical source term limiter is as follows: Where: It indicates the temporary conservation quantity increment; represents a diagonal matrix; Indicates calculation of the right-hand side; represents a lower triangular matrix; represents the increase in the conserved quantity at the current moment, Indicates the current moment; represents an upper triangular matrix.

5. A numerical iteration method based on chemical non-equilibrium source term limiter according to claim 4, characterized in that: The diagonal matrix , lower triangular matrix , upper triangular matrix and the right-hand side The specific form is: Where: is the volume of the current calculation unit; is the time step at the current moment; represents the direction of the grid coordinate system, ; , are the Jacobian matrices of the convection flux of the current computational unit in the direction of the corresponding grid coordinate system. and the viscous flux Jacobian matrix The spectral radius of represents the identity matrix; is the Jacobian approximation diagonal matrix of chemical source terms; Represents the Jacobian approximation diagonal matrix of the chemical source term at the current moment, Represents the Jacobian approximation diagonal matrix of the chemical source term at the previous moment; i , j , k Indicates the serial number of the computing unit in the corresponding direction of the grid coordinate system, and its combination represents the serial coordinate of the current computing unit in the grid; , , , , , They are i , j , k The Jacobian matrix of the convection flux of adjacent computational units in the direction; correspondingly, , , , , , are the spectral radius of the Jacobian matrix of the convective flux respectively; , , , , , They are i , j , k The Jacobian matrix of the viscosity flux of the adjacent computational units in the direction, correspondingly, , , , , , are the spectral radius of the Jacobian matrix of the viscosity flux, respectively; represents the total convective flux in and out of the computational cell boundary surface, Represents the total convective flux in and out of the boundary surface of the computational unit at the current moment; represents the total viscous flux in and out of the computational cell boundary surface, Represents the total viscous flux entering and leaving the boundary surface of the computational unit at the current moment; is the chemical source term, is the chemical source term at the current moment, is the chemical source term at the previous moment; For adjacent computational units ( i -1, j , k )The conserved quantity increases at the current moment; For adjacent computational units ( i , j -1, k )The conserved quantity increases at the current moment; For adjacent computational units ( i , j , k -1) The conserved quantity increases at the current moment; For adjacent computational units ( i +1, j , k )The conserved quantity increases at the current moment; For adjacent computational units ( i , j +1, k )The conserved quantity increases at the current moment; For adjacent computational units ( i , j , k +1) The conserved quantity at the current moment increases.

6. A numerical iteration method based on chemical non-equilibrium source term limiter according to claim 5, characterized in that: The Jacobian approximation of the chemical source term is a diagonal matrix Defined as: Where: is the symbol of the partial derivative operator; is the chemical source term, represents transpose, For the The chemical source term corresponding to each gas component is: For the The chemical source term corresponding to each gas component; is the conserved quantity; For the The conserved quantity corresponding to each gas component is: For the The conserved quantity corresponding to each gas component; is the total number of gas components; is the Kronecker symbol; is the first diagonal matrix of the Jacobian approximation of the chemical source term The main diagonal elements corresponding to the gas components; is the first diagonal matrix of the Jacobian approximation of the chemical source term The main diagonal elements corresponding to the gas components; represents a diagonal matrix.

7. A numerical iteration method based on chemical non-equilibrium source term limiter according to claim 1, characterized in that: The source term limitation coefficient is determined by the change rate of the instantaneous flow velocity and the average temperature, and the specific expression is: Where: is the flow rate; The flow rate calculated for the current moment; is the average temperature; The average temperature calculated for the current moment; is the threshold value.

8. A numerical iteration method based on chemical non-equilibrium source term limiter according to claim 7, characterized in that: The mean temperature is defined as follows: Where: and are the translation temperature and vibration temperature respectively; Threshold The method of determining is as follows: Where: Calculate the control coefficient for the entire domain, are two control coefficients related to speed and temperature respectively, is the incoming flow velocity, Total temperature of incoming flow.

9. The numerical iteration method based on chemical non-equilibrium source term limiter according to claim 1, characterized in that: In step S4, the judgment condition of whether the flow field iteration tends to be stable is: Where: Set the maximum number of iterations for the calculation; Represents a computational unit The conservation quantity increases at the current moment, Represents a computational unit The conserved quantity at the initial moment increases.

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