Aircraft numerical simulation method based on improved GMR-WENO algorithm and medium

Abstract

The invention discloses an aircraft numerical simulation method based on an improved GMR-WENO algorithm and a medium, and relates to the field of aircraft performance tests.The method comprises the steps that a three-dimensional calculation area is determined, and tetrahedral mesh generation is carried out; setting fluid physical parameters of each grid at an initial moment; an improved GMR-WENO algorithm is adopted to carry out high-order reconstruction on fluid physical parameters; in the improved GMR-WENO algorithm, a real quadratic algebraic polynomial is constructed by applying an orthogonal basis function, and a virtual first-order polynomial and a virtual zero-order polynomial are constructed by applying an L2 projection technology; determining fluid physical parameters at the final moment based on the third-order reconstruction polynomial; and determining the aerodynamic performance of the aircraft according to the fluid physical parameters at the final moment. According to the method, the orthogonal basis function and the L2 projection technology are combined into the GMR-WENO method to simulate the distribution condition of the aerodynamic characteristics of the aircraft, and the efficiency and accuracy of performance testing of the aircraft are improved.

Description

Technical Field

[0001] The present application relates to the field of aircraft performance testing, and in particular to an aircraft numerical simulation method and medium based on an improved GMR-WENO algorithm. Background Art

[0002] In real life, the testing of aircraft performance is full of uncertainties, which may have a significant impact on the accuracy and reliability of the test results. As an effective pre-processing method, numerical simulation methods can perform good numerical simulations of aircraft before actual testing, thereby overcoming many uncertainties. Therefore, how to design a powerful numerical simulation method is particularly important. The numerical simulation methods for this type of problem often have relatively high requirements, because algorithms are often required to capture some detailed features of aerodynamic performance, such as the formation of shock waves or the flow characteristics of boundary layers. However, at present, especially when constructing high-order and high-dimensional algorithms on three-dimensional unstructured tetrahedral grids, the efficiency and accuracy of numerical simulations cannot be guaranteed. Summary of the Invention

[0003] The purpose of this application is to provide an aircraft numerical simulation method and medium based on an improved GMR-WENO algorithm, which can improve the efficiency and accuracy of aircraft numerical simulation.

[0004] To achieve the above objectives, this application provides the following solutions:

[0005] In a first aspect, the present application provides an aircraft numerical simulation method based on an improved GMR-WENO algorithm, comprising:

[0006] Determining a three-dimensional calculation region and performing tetrahedral meshing on the three-dimensional calculation region;

[0007] Set the fluid physical parameters at the initial moment corresponding to each grid according to the set Mach number and angle of attack;

[0008] The improved GMR-WENO algorithm is used to reconstruct the fluid physical parameters at the initial moment in high order, and the third-order reconstruction polynomial of the fluid object parameters at the final moment is obtained; in the improved GMR-WENO algorithm, the orthogonal basis function is used to construct the true quadratic algebraic polynomial of the fluid physical parameters, and the L 2 Projection technology constructs virtual first-order polynomials and zero-order polynomials of fluid physical parameters;

[0009] Determine the fluid physical parameters of the three-dimensional calculation area at the final moment based on the third-order reconstruction polynomial of the fluid object parameters at the final moment;

[0010] The aerodynamic performance of the aircraft at the current Mach number and angle of attack is determined based on the fluid physical parameters of the three-dimensional calculation area at the final moment.

[0011] In a second aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-mentioned aircraft numerical simulation method based on the improved GMR-WENO algorithm.

[0012] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0013] The present application provides an aircraft numerical simulation method and medium based on an improved GMR-WENO algorithm, which is aimed at the numerical simulation of the distribution of aerodynamic characteristics of an aircraft at different Mach numbers and angles of attack (i.e., the GMR-WENO algorithm). When reconstructing high-order polynomials of fluid physical parameters, orthogonal basis functions are used to construct true quadratic algebraic polynomials of fluid physical parameters, and L is used to 2 Projection technology constructs virtual first-order polynomials and zero-order polynomials of fluid physical parameters, which greatly reduces the complexity of reconstructing polynomials in the GMR-WENO algorithm, improves computational efficiency, and has strong robustness, thereby enabling better numerical simulation of the aerodynamic characteristics of the aircraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] 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.

[0015] Figure 1 A flowchart of an aircraft numerical simulation method based on an improved GMR-WENO algorithm provided in one embodiment of the present application;

[0016] Figure 2 A schematic diagram of a reconstruction template of a third-order format provided in an embodiment of the present application;

[0017] Figure 3 A comparison diagram of Mach number contour lines for a third-order format provided in one embodiment of the present application;

[0018] Figure 4 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0019] 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.

[0020] When numerically simulating aircraft performance, especially when constructing high-order and high-dimensional algorithms on three-dimensional unstructured tetrahedral meshes, many challenges arise: First, the construction of the final high-order reconstruction polynomial requires the calculation of linear weights, and the calculation of existing linear weights needs to be obtained manually, which not only takes a lot of time, but the calculation results may be negative or even non-existent, which may have a certain degree of impact on the simulation results, and may even cause program interruption. Second, the algorithm construction process is extremely difficult. For example, in terms of template selection, multiple templates need to be selected, which is not only difficult to write programs, but also has low computational efficiency and is not easy to expand to high dimensions and high orders. Third, it is not robust. Therefore, it is particularly critical to design a numerical simulation method that is robust, simple in structure, and computationally efficient.

[0021] The purpose of this application is to provide an aircraft numerical simulation method and medium based on an improved GMR-WENO algorithm, which can improve the efficiency and accuracy of aircraft numerical simulation and has strong robustness.

[0022] 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.

[0023] In an exemplary embodiment, Figure 1 As shown, a method for numerical simulation of an aircraft based on an improved GMR-WENO algorithm is provided. The method is executed by a computer device and includes the following steps.

[0024] S1: Determine a three-dimensional calculation area, and perform tetrahedral meshing on the three-dimensional calculation area.

[0025] Determine a spherical calculation area based on the actual problem to be simulated Where x, y, and z are the coordinates of the centroid of the element. A spatial rectangular coordinate system is established, and the spherical calculation area is meshed to obtain a tetrahedral mesh. The target mesh is denoted as Δ0.

[0026] In addition, according to the actual numerical simulation results, the corresponding density residual range [δ min ,δ max ] and the number of iteration steps N to end the calculation.

[0027] S2: Set the fluid physical parameters for each grid at the initial moment based on the set Mach number and angle of attack. The fluid physical parameters include the average density, average momentum in the x-direction, average momentum in the y-direction, average momentum in the z-direction, and average total energy.

[0028] According to the actual problem to be simulated, the Mach number and angle of attack of the aircraft to be simulated as well as the density, pressure, energy, specific heat ratio and other parameters of the fluid are given.

[0029] Set the corresponding fluid physical parameters at the initial moment in the grid. According to the set Mach number M ∞ , angle of attack α, specific heat ratio γ of the fluid, average density of the fluid and average pressure Defines the average velocity in the x direction of the target grid Average velocity in the y direction Average speed in the z direction So we can get the average momentum in the x direction Average momentum in the y direction Average momentum in the z direction The average total energy is

[0030] S3: The improved GMR-WENO algorithm is used to perform high-order reconstruction of the fluid physical parameters at the initial moment, and the third-order reconstruction polynomial of the fluid object parameters at the final moment is obtained; in the improved GMR-WENO algorithm, the orthogonal basis function is used to construct the true quadratic algebraic polynomial of the fluid physical parameters, and the L 2 Projection technology constructs virtual first-order polynomials and zero-order polynomials of fluid physical parameters.

[0031] S4: Determine the fluid physical parameters of the three-dimensional calculation area at the final moment based on the third-order reconstruction polynomial of the fluid object parameters at the final moment.

[0032] S5: Determine the aerodynamic performance of the aircraft at the current Mach number and angle of attack based on the fluid physical parameters of the three-dimensional calculation area at the final moment.

[0033] Implement the above steps S1 to S5, through the orthogonal basis function and L 2 Projection technology is combined with the existing GMR-WENO algorithm to simulate the distribution of aircraft aerodynamic characteristics at different Mach numbers and angles of attack. This can optimize the design of the aircraft and improve the efficiency, effectiveness and accuracy of its performance testing.

[0034] In another exemplary embodiment of the present application, in step S3, the GMR-WENO method is used to perform high-order spatial reconstruction of the physical quantities based on the fluid physical parameters at the initial moment obtained in step S2 to obtain the final third-order reconstruction polynomial: U(x,y,z)=[ρ0(x,y,z),ρu0(x,y,z),ρv0(x,y,z),ρw0(x,y,z),ρE0(x,y,z)], where the five components represent the density polynomial of the fluid, the momentum polynomial in the x-direction, the momentum polynomial in the y-direction, the momentum polynomial in the z-direction, and the total energy polynomial, respectively.

[0035] The improved GMR-WENO algorithm is used to perform high-order reconstruction of the fluid physical parameters, and the third-order reconstruction polynomial of the fluid physical parameters is obtained, including:

[0036] (3-1) Determine a reconstruction template for each target grid; the reconstruction template includes the target grid and its coplanar neighbor grids, such as Figure 2 As shown in the figure; the total number of grids in the reconstruction template is not less than 10; the target grid is any grid in the three-dimensional calculation area. Figure 2 In the figure, the orange line represents the target grid, the green line represents the four coplanar neighbors of the first layer of the target grid, and the blue line represents the second layer of neighbors of the target grid, that is, the coplanar neighbors found by the unit marked by the green line when continuing to move outward.

[0037] (3-2) Using the geometric information and fluid information of the target grid in the flow field of the three-dimensional calculation area, the orthogonal basis functions are used on the reconstruction template to construct the true quadratic algebraic polynomial of the fluid physical parameters corresponding to the target grid.

[0038] (3-3) According to the real quadratic algebraic polynomial of fluid physical parameters, L 2 The projection technology constructs virtual first-order polynomials and zero-order polynomials of the fluid physical parameters corresponding to the target grid.

[0039] according to Figure 2 The real large template (reconstruction template) with at least ten grids including the target unit is shown. The geometric information of the units contained therein and the internal fluid information are used to reconstruct the real quadratic algebraic polynomial on the reconstruction template using orthogonal basis functions.

[0040] For ease of description, mark

[0041] First, the expression of the orthogonal basis function is given:

[0042]

[0043] According to the orthogonality of basis functions:

[0044]

[0045] The coefficients A in the basis function can be obtained by solving the above linear equations κ,υ .

[0046] Therefore, the expression for the true quadratic algebraic polynomial is:

[0047]

[0048] Where q1(x, y, z) refers to a real quadratic algebraic polynomial; x, y, z represent the horizontal, vertical, and vertical coordinates of the Gaussian point on the boundary surface of the target grid, respectively; x0, y0, z0 represent the horizontal, vertical, and vertical coordinates of the center of gravity of the target grid, respectively; |Δ0| represents the volume of the target grid in the flow field; A 2,1 To A 9,9 Represents the coefficients of the internal variables of the basis function; span() represents the space consisting of the data in the brackets.

[0049] The unknown coefficients of the quadratic polynomial q1(x,y,z) are obtained by the least squares technique as shown below:

[0050]

[0051] A={1,2,3,4,11,12,13,21,22,23,31,32,33,41,42,43}

[0052] Use L for real quadratic algebraic polynomials 2 Projection technology can obtain a virtual first-degree polynomial q2(x,y,z) and a virtual zero-degree polynomial q3(x,y,z). Both satisfy the following conditions:

[0053]

[0054] Therefore, the expression of the imaginary first-degree polynomial is:

[0055]

[0056] The expression of the virtual zero-degree polynomial is:

[0057]

[0058] Where q2(x,y,z) refers to a fictitious first-degree polynomial; q3(x,y,z) refers to a fictitious zero-degree polynomial; Represents the density of the fluid at the initial moment of the target grid, the momentum in the x, y, and z directions, and the average of the total energy.

[0059] (3-4) Construct a third-order reconstruction polynomial of the fluid object parameters corresponding to the target grid based on the real quadratic algebraic polynomial, virtual first-order polynomial and zero-order polynomial of the fluid physical parameters corresponding to the target grid.

[0060] In another exemplary embodiment of the present application, in step (3-4), a third-order reconstruction polynomial of the fluid object parameters corresponding to the target grid is constructed based on the real quadratic algebraic polynomial, the virtual linear polynomial, and the zero-order polynomial of the fluid physical parameters corresponding to the target grid, specifically including:

[0061] (1) A specific form of a third-order reconstruction polynomial is defined; the linear weight parameter in the specific form of the third-order reconstruction polynomial is any positive number whose sum is one.

[0062]

[0063] As an example, take the unnormalized linear weight parameter So the normalized linear weight parameter is obtained The linear weight parameter can also take any other value.

[0064] (2) Calculate the smoothing factors of real quadratic algebraic polynomials, imaginary linear polynomials and zero-degree polynomials.

[0065] Calculate the smoothness factor on the target grid to measure the smoothness of the polynomials q1(x,y,z) and q2(x,y,z):

[0066]

[0067] Here,

[0068] In the formula, in the formula, β jj Indicates q jj The smoothing factor corresponding to (x, y, z). When jj is 1, it indicates the smoothing factor corresponding to q1(x, y, z). When jj is 2, it indicates the smoothing factor corresponding to q2(x, y, z). Indicates q jj (x,y,z) order partial derivatives; Indicates q jj (x,y,z) for x order partial derivatives; Indicates q jj (x,y,z) find y order partial derivatives; Indicates q jj (x,y,z) calculates z order partial derivatives; Indicates the order of partial derivative; Take values ​​greater than or equal to 0 and not exceeding the highest degree of the polynomial.

[0069] Since q3(x,y,z) is a zero-degree polynomial, the smoothing factor is directly solved to be zero. Therefore, in order to avoid ambiguous shock wave transitions when calculating strong shock waves or contact discontinuities, the following method is used for calculation:

[0070] Construct four first-degree algebraic polynomials using the target mesh and its four coplanar neighbor meshes:

[0071] x s ,y s ,z s Respectively represent the horizontal, vertical and vertical coordinates of the focus of the coplanar neighbor grid of the target grid; |Δ s | represents the volume of the coplanar neighboring meshes of the target mesh and satisfies:

[0072]

[0073] Where, Represents the average value of the physical quantity of the sth coplanar neighbor grid of the target grid; Represents the average value of the physical quantity of the jth coplanar neighbor grid of the first coplanar neighbor grid of the target grid, j = 1, 2, 3; Represents the average value of the physical quantity of the jth coplanar neighbor grid of the second coplanar neighbor grid of the target grid; Represents the average value of the physical quantity of the jth coplanar neighbor grid of the third coplanar neighbor grid of the target grid; represents the average value of the physical quantity of the jth coplanar neighbor grid of the fourth coplanar neighbor grid of the target grid; (x 1j ,y 1j ,z 1j ) represents the centroid of the jth coplanar neighbor grid of the first coplanar neighbor grid of the target grid; (x 2j ,y 2j ,z 2j ) represents the centroid of the jth coplanar neighbor grid of the second coplanar neighbor grid of the target grid; (x 3j ,y 3j ,z 3j ) represents the centroid of the jth coplanar neighbor grid of the third coplanar neighbor grid of the target grid; (x 4j ,y 4j ,z 4j ) represents the centroid of the jth coplanar neighbor grid of the 4th coplanar neighbor grid of the target grid.

[0074] Using the aforementioned β jj The expression of p is used to solve the above1,s (x,y,z) corresponding to the smoothing factor β 1,s ,s=1,2,3,4。

[0075] Assumptions:

[0076]

[0077] B=|β 1,1 -β 1,2 |+|β 1,1 -β 1,3 |+|β 1,1 -β 1,4 |+|β 1,2 -β 1,3 |+|β 1,2 -β 1,4 |+|β 1,3 -β 1,4 |.

[0078]

[0079] Therefore, the expression of the smooth factor of the virtual zero-degree polynomial can be obtained as follows:

[0080]

[0081] Where β3 represents the smoothing factor corresponding to q3(x,y,z); Indicates that p 1,s (x,y,z) finds the c-order partial derivative; Indicates p 1,s (x,y,z) calculates the c1-order partial derivative with respect to x; Indicates p 1,s (x,y,z) calculates the c2-order partial derivative with respect to y; Indicates p 1,s (x,y,z) calculates the c3-order partial derivative with respect to z; s=1,2,3 ,4 ;x s ,y s ,z s Respectively represent the values ​​of the horizontal, vertical, and vertical coordinates of the centroid of the coplanar neighboring grid of the target grid; |Δ s | represents the volume of the coplanar neighboring grid of the target grid; c = c1 + c2 + c3; c1, c2, c3 represent the order of partial derivatives; c1, c2, c3 are values ​​greater than or equal to 0 and not exceeding the highest degree of the polynomial.

[0082] (3) Calculate the nonlinear weight parameters in the third-order reconstruction polynomial based on the smoothing factor.

[0083] Based on the obtained smoothing factor, calculate a factor that is important for maintaining accuracy:

[0084]

[0085] The nonlinear weight parameters are calculated according to the following formula:

[0086]

[0087] in,

[0088] Where, ω hh is the nonlinear weight parameter, which refers to ω1, ω2, ω3; d hh is the linear weight parameter; β hh Refers to smoothing factors β1, β2 and β3.

[0089] (4) Substitute the real quadratic algebraic polynomial, the virtual first-order polynomial, the virtual zero-order polynomial, the linear weight parameter and the nonlinear weight parameter into the specific form of the third-order reconstruction polynomial to obtain the third-order reconstruction polynomial of the fluid object parameters corresponding to the target grid.

[0090] Among them, the expression of the third-order reconstruction polynomial of the fluid object parameters corresponding to the target grid is:

[0091]

[0092] Here, Q(x,y,z) represents a third-order reconstruction polynomial of a fluid physical parameter, such as the fluid density, momentum in the x-direction, momentum in the y-direction, momentum in the z-direction, and total energy.

[0093] After obtaining the third-order reconstruction polynomial of the fluid physical parameters, the third-order reconstruction polynomial of the fluid object parameters is advanced in time and iterated continuously. After reaching the maximum number of iterations, the fluid physical parameters of the three-dimensional calculation area at the final moment are obtained.

[0094] Among them, the numerical simulation of the GMR-WENO method performs high-order spatial discretization and calculates the corresponding numerical flux as follows:

[0095] Consider the three-dimensional hyperbolic conservation law equation:

[0096]

[0097] The above three-dimensional hyperbolic conservation law equation is volume-integrated on the target grid Δ0 to obtain the spatial semi-discrete finite volume format:

[0098]

[0099] in, is the cell mean of the target grid; F = (f(U), g(U), r(U)); U = [ρ, ρu, ρv, ρw, ρE] T The conserved quantities are the density of the fluid, momentum in the x, y, and z directions, and total energy, respectively. f(U)=[ρu,ρu 2 +p,ρvu,ρwu,u(E+p)] T ,g(U)=[ρv,ρvu,ρv 2 +p,ρwv,v(E+p)] T ,r(U)=[ρw,ρuw,ρwv,ρw 2 +p,w(E+p)] T is the corresponding flux. ρ, u, v, w, p, E represent the density of the fluid, the velocity in the x, y, z directions, the pressure, and the total energy, respectively. t represents time, Δ0 is the target grid, represents the boundary surface of the target grid in the flow field, |Δ0| represents the volume of the target grid, U0(x,y,z) represents the density of the fluid at the initial moment, the momentum and total energy in the x,y,z directions, and U t represents the partial derivative of U with respect to time t, f(U) x ,g(U) y ,r(U) z They represent the partial derivatives of f(U), g(U), and r(U) with respect to x, y, and z in space, respectively. L(U) represents -f(U). x -g(U) y -r(U) z The semi-discrete form of L is the spatial discretization factor, m represents the four faces of the target grid, and h represents the six Gaussian integration points on each face. Represents the area of ​​the triangular face of the target unit, σ h represents the integral coefficient corresponding to the Gaussian integral point, represents the Gaussian integration point, Represents the unit external normal vector of the face. is the numerical flux.

[0100] Based on the above content, this application uses the third-order TVD Runge-Kutta time discretization formula to discretize the above-mentioned spatial semi-discrete finite volume format into a space-time fully discrete finite volume format. The specific process includes:

[0101] The third-order TVD Runge-Kutta time discretization formula is used:

[0102]

[0103] A fully discrete finite volume format in space and time is obtained.

[0104] Among them, Δt is the time step, n represents the nth time layer, U(1) ,U (2) is the intermediate transition value, L(U n ),L(U (1) ),L(U (2) ) is an approximation of the higher-order spatial discretization form of the right-hand side of the aforementioned L(U) equation. The superscripts (1) and (2) refer to the intermediate process from the nth time layer to the n+1th time layer.

[0105] The above-mentioned third-order TVD Runge-Kutta time discretization formula can be used to obtain the value of the conservation quantity U in the n+1 time layer. The residual value η0 of the density in the target grid Δ0 of the n-th time layer and the n+1-th time layer is compared. The residuals of all grids in the calculation area are summed to obtain the total residual η in the calculation area. If η exceeds the maximum residual η max , stop the calculation. If η is in [η min ,η max ] and the number of iterations does not exceed the maximum number of iterations N, the calculation continues until η exceeds η max , at this time, by observing the numerical results in the flow field, we can obtain the aerodynamic characteristics distribution of the aircraft, such as the Mach number contour map. min represents the minimum residual.

[0106] For the classical method of the same order, sixteen four-grid templates are needed, while in this application, no matter how many-order format, only a large central template (i.e., a reconstruction template containing at least ten grids) is needed. At the same time, the linear weight can take any positive number that sums to one. Therefore, the present application greatly reduces the complexity of the three-dimensional GMR-WENO algorithm, improves computational efficiency, has strong robustness, and is easier to extend to solving higher-dimensional and higher-order problems. The present application solves the problem that the linear weights need to be manually calculated when constructing the final high-order reconstruction polynomial in the existing numerical simulation method, resulting in insufficient numerical simulation accuracy and low computational efficiency, and also solves the problem of low computational efficiency caused by template selection during the construction of high-order reconstruction polynomials.

[0107] like Figure 3 As shown, a comparison diagram of the Mach number contour lines of the third-order format is shown; the Mach number is 0.8; and the angle of attack is 1.0. Figure 3 The Mach number contour map on the left is generated based on the GMR-WENO algorithm improved in this application, and the calculation time is 50586.13 seconds. Figure 3 The Mach number contour plot on the right is generated based on the original GMR-WENO algorithm, with a calculation time of 53384.53 seconds. Experiments show that this application can also achieve almost the same results as traditional numerical simulation methods in a shorter time.

[0108] The present application also provides an application scenario, which applies the above-mentioned aircraft numerical simulation method based on the improved GMR-WENO algorithm. Specifically: The aircraft numerical simulation method based on the improved GMR-WENO algorithm provided in this embodiment can be applied in an aircraft performance evaluation scenario. The scenario includes a performance numerical simulation link and a performance evaluation link; the performance numerical simulation link is used to apply the improved GMR-WENO algorithm to perform aircraft numerical simulation; the performance evaluation link is used to evaluate the aircraft performance based on the numerical simulation results to optimize the aircraft's own structure. The aircraft numerical simulation method based on the improved GMR-WENO algorithm provided in this embodiment belongs to the performance numerical simulation link.

[0109] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 4 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, memory and input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device is used to store aircraft numerical simulation data based on the improved GMR-WENO algorithm. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. In an exemplary embodiment, a computer device is provided, including a memory and a processor, the memory stores a computer program, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0110] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0111] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0112] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0113] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0114] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0115] 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.

[0116] 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 numerical simulation method for aircraft based on an improved GMR-WENO algorithm, characterized in that: include: Determining a three-dimensional calculation region and performing tetrahedral meshing on the three-dimensional calculation region; Set the fluid physical parameters at the initial moment corresponding to each grid according to the set Mach number and angle of attack; The improved GMR-WENO algorithm is used to reconstruct the fluid physical parameters at the initial moment in high order, and the third-order reconstruction polynomial of the fluid object parameters at the final moment is obtained; in the improved GMR-WENO algorithm, the orthogonal basis function is used to construct the true quadratic algebraic polynomial of the fluid physical parameters, and the L 2 Projection technology constructs virtual first-order polynomials and zero-order polynomials of fluid physical parameters; Determine the fluid physical parameters of the three-dimensional calculation area at the final moment based on the third-order reconstruction polynomial of the fluid object parameters at the final moment; The aerodynamic performance of the aircraft at the current Mach number and angle of attack is determined based on the fluid physical parameters of the three-dimensional calculation area at the final moment.

2. The aircraft numerical simulation method based on the improved GMR-WENO algorithm according to claim 1, characterized in that: The improved GMR-WENO algorithm is used to perform high-order reconstruction of the fluid physical parameters at the initial moment, and the third-order reconstruction polynomial of the fluid object parameters at the final moment is obtained, specifically including: Determine a reconstruction template for each target grid; the reconstruction template includes the target grid and its coplanar neighbor grids; the total number of grids in the reconstruction template is not less than 10; the target grid is any grid in the three-dimensional calculation area; By using the geometric information and fluid information of the target grid in the flow field of the three-dimensional calculation area, the orthogonal basis functions are used on the reconstruction template to construct the true quadratic algebraic polynomial of the fluid physical parameters corresponding to the target grid; According to the real quadratic algebraic polynomial of fluid physical parameters, L 2 The projection technology constructs virtual first-order polynomials and zero-order polynomials of the fluid physical parameters corresponding to the target grid; A third-order reconstruction polynomial of the fluid object parameters corresponding to the target grid is constructed according to the real quadratic algebraic polynomial, virtual first-order polynomial and zero-order polynomial of the fluid physical parameters corresponding to the target grid.

3. The aircraft numerical simulation method based on the improved GMR-WENO algorithm according to claim 2, characterized in that: According to the real quadratic algebraic polynomial, virtual linear polynomial and zero-order polynomial of the fluid physical parameters corresponding to the target grid, a third-order reconstruction polynomial of the fluid object parameters corresponding to the target grid is constructed, specifically including: Defining a specific form of a third-order reconstruction polynomial; wherein the linear weight parameter in the specific form of the third-order reconstruction polynomial is any positive number whose sum is one; Compute smooth factors of real quadratic algebraic polynomials, imaginary linear polynomials, and zero-degree polynomials; Calculate the nonlinear weight parameter in the third-order reconstruction polynomial according to the smoothing factor; The real quadratic algebraic polynomial, the virtual first-order polynomial, the virtual zero-order polynomial, the linear weight parameter and the nonlinear weight parameter are substituted into the specific form of the third-order reconstruction polynomial to obtain the third-order reconstruction polynomial of the fluid object parameters corresponding to the target grid.

4. The aircraft numerical simulation method based on the improved GMR-WENO algorithm according to claim 3, characterized in that: The expression for a true quadratic algebraic polynomial is: in, Where q1(x, y, z) refers to a real quadratic algebraic polynomial; x, y, z represent the horizontal, vertical, and vertical coordinates of the Gaussian point on the boundary surface of the target grid, respectively; x0, y0, z0 represent the horizontal, vertical, and vertical coordinates of the center of gravity of the target grid, respectively; |Δ0| represents the volume of the target grid in the flow field; A 2,1 To A 9,9 Represents the coefficients of the internal variables of the basis function; span() represents the space consisting of the data in the brackets.

5. The aircraft numerical simulation method based on the improved GMR-WENO algorithm according to claim 4, characterized in that: The expression of the virtual first-order polynomial is: The expression of the virtual zero-degree polynomial is: Where q2(x,y,z) refers to a fictitious first-degree polynomial; q3(x,y,z) refers to a fictitious zero-degree polynomial; Represents the density of the fluid at the initial moment of the target grid, the momentum in the x, y, and z directions, and the average of the total energy.

6. The aircraft numerical simulation method based on the improved GMR-WENO algorithm according to claim 5, characterized in that: The expressions for the smooth factors of real quadratic algebraic polynomials and imaginary linear polynomials are: Where, β jj Indicates q jj The smoothing factor corresponding to (x, y, z). When jj is 1, it indicates the smoothing factor corresponding to q1(x, y, z). When jj is 2, it indicates the smoothing factor corresponding to q2(x, y, z). Indicates q jj (x,y,z) order partial derivatives; Indicates q jj (x,y,z) for x order partial derivatives; Indicates q jj (x,y,z) find y order partial derivatives; Indicates q jj (x,y,z) calculates z Order partial derivatives. Indicates the order of partial derivatives.

7. The aircraft numerical simulation method based on the improved GMR-WENO algorithm according to claim 6, characterized in that: The expression of the smooth factor of the virtual zero-degree polynomial is: Where β3 represents the smoothing factor corresponding to q3(x,y,z); Indicates that p 1,s (x,y,z) finds the c-order partial derivative; Indicates p 1,s (x,y,z) calculates the c1-order partial derivative with respect to x; Indicates p 1,s (x,y,z) calculates the c2-order partial derivative with respect to y; Indicates p 1,s (x,y,z) calculates the c3-order partial derivative with respect to z; x s ,y s ,z s Respectively represent the horizontal, vertical and vertical coordinates of the focus of the coplanar neighbor grid of the target grid; |Δ s | represents the volume of the coplanar neighboring grid of the target grid; c = c1 + c2 + c3; c1, c2, c3 represent the order of partial derivatives.

8. The aircraft numerical simulation method based on the improved GMR-WENO algorithm according to claim 7, characterized in that: The expression of the nonlinear weight parameter is: in, Where, ω hh is the nonlinear weight parameter; d hh is the linear weight parameter; β hh Refers to smoothing factors β1, β2 and β3.

9. The aircraft numerical simulation method based on the improved GMR-WENO algorithm according to claim 8, characterized in that: The expression of the third-order reconstruction polynomial of the fluid object parameters corresponding to the target grid is: Where ω1, ω2, and ω3 are nonlinear weight parameters; d1, d2, and d3 are linear weight parameters.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the aircraft numerical simulation method based on the improved GMR-WENO algorithm described in any one of claims 1 to 9 is implemented.

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