Wing performance testing method based on the ALW-MR-WENO algorithm

Abstract

The present invention discloses a wing performance testing method based on the ALW-MR-WENO algorithm, which relates to the technical field of aircraft performance testing. The method includes: determining a calculation region and performing grid division on the calculation region; setting corresponding initial fluid physical parameters in the grid according to the set Mach number and angle of attack; using the ALW-MR-WENO method to perform high-order reconstruction on the initial fluid physical parameters to obtain a final reconstruction polynomial; determining the fluid physical parameters in the calculation region based on the final reconstruction polynomial; and determining the wing performance of the aircraft at different Mach numbers and angles of attack according to the fluid physical parameters in the calculation region. By means of the adaptive linear weight technology and in combination with the existing numerical methods to simulate the distribution of the aerodynamic characteristics on the wing surface when the Mach number and the angle of attack are different, the efficiency and accuracy of the wing performance testing of the aircraft can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft performance testing, and particularly relates to a wing performance testing method based on the ALW-MR-WENO algorithm. Background Art

[0002] In real life, the testing of aircraft performance is full of various uncertainties. Therefore, it is particularly important to design a numerical method to simulate such problems. For the numerical simulation methods of such problems, it is often necessary to capture some detailed characteristics in terms of aerodynamic performance, which puts higher requirements on the performance of the algorithm. However, for existing high-dimensional high-order algorithms, especially on unstructured grids, such as triangular or tetrahedral grids, there have always been the following problems: First, it is necessary to artificially solve the linear weights during the process of reconstructing high-degree polynomials, which requires a lot of time; Second, the linear weights may be negative or even non-existent after solution, which will have a great impact on the simulation of such problems and even lead to the interruption of the simulation process; Third, the algorithm structure is complex and the computational efficiency is low; Fourth, it is not easy to solve high-dimensional high-order problems. Therefore, it is crucial to design an algorithm with a simple structure, high computational efficiency and strong robustness. Summary of the Invention

[0003] Based on this, the purpose of the present invention is to provide a wing performance testing method based on the ALW-MR-WENO algorithm, which simulates the distribution of aerodynamic characteristics on the wing surface when the Mach number and angle of attack are different through the adaptive linear weight technology and in combination with existing numerical methods.

[0004] To achieve the above purpose, the present invention provides the following solutions:

[0005] A wing performance testing method based on the ALW-MR-WENO algorithm, comprising:

[0006] Determine the computational domain and perform grid division on the computational domain;

[0007] Set the corresponding initial fluid physical parameters in the grid according to the set Mach number and angle of attack; the fluid physical parameters include the average fluid density, the average fluid velocity in the x direction, the average fluid velocity in the y direction, and the average total energy of the fluid;

[0008] Use the ALW-MR-WENO method to perform high-order reconstruction on the initial fluid physical parameters to obtain the final reconstructed polynomial; the final reconstructed polynomial includes the final reconstructed polynomial of the third-order format and the final reconstructed polynomial of the fourth-order format;

[0009] Determine the fluid physical parameters in the computational domain based on the final reconstructed polynomial;

[0010] Determine the performance of the aircraft wing at different Mach numbers and angles of attack according to the fluid physical parameters within the calculation domain.

[0011] To achieve the above object, the present invention also provides the following solutions:

[0012] A wing performance test system based on the ALW-MR-WENO algorithm, comprising:

[0013] A calculation domain determination and division module, configured to determine a calculation domain and perform grid division on the calculation domain;

[0014] An initial fluid physical parameter setting module, configured to set corresponding initial fluid physical parameters within the grid according to the set Mach number and angle of attack; the fluid physical parameters include the average fluid density, the average fluid velocity in the x direction, the average fluid velocity in the y direction, and the average total energy of the fluid;

[0015] A high-order reconstruction module, configured to perform high-order reconstruction on the initial fluid physical parameters by using the ALW-MR-WENO method to obtain a final reconstruction polynomial; the final reconstruction polynomial includes a third-order format final reconstruction polynomial and a fourth-order format final reconstruction polynomial;

[0016] A fluid physical parameter determination module, configured to determine the fluid physical parameters within the calculation domain based on the final reconstruction polynomial;

[0017] A performance determination module, configured to determine the performance of the aircraft wing at different Mach numbers and angles of attack according to the fluid physical parameters within the calculation domain.

[0018] According to the specific embodiments provided by the present invention, the following technical effects are disclosed by the present invention:

[0019] The numerical method (i.e., the ALW-MR-WENO method) designed by the present invention for the distribution of the aerodynamic characteristics on the wing surface at different Mach numbers and angles of attack, combined with the novel adaptive linear weight technology of the present invention, greatly simplifies the algorithm structure, improves the calculation efficiency, and has strong robustness, so as to better test the performance of the aircraft wing. Description of the Drawings

[0020] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0021] Figure 1 It is a flowchart of the wing performance test method based on the ALW-MR-WENO algorithm provided by the present invention;

[0022] Figure 2 These are schematic diagrams of each template. Specific implementation manners

[0023] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0024] The object of the present invention is to provide a wing performance test method based on the ALW-MR-WENO algorithm, which simulates the distribution of aerodynamic characteristics on the wing surface when the Mach number and angle of attack are different by using the adaptive linear weight technology and combining with the existing numerical methods.

[0025] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0026] Embodiment 1

[0027] As shown in FIG. 1, the wing performance test method based on the ALW-MR-WENO algorithm provided in this embodiment includes the following steps:

[0028] S1: Determine the calculation area and perform grid division on the calculation area.

[0029] S2: Set the corresponding initial fluid physical parameters in the grid according to the set Mach number and angle of attack; the fluid physical parameters include the average fluid density, the average fluid velocity in the x direction, the average fluid velocity in the y direction, and the average total energy of the fluid.

[0030] S3: Use the ALW-MR-WENO method to perform high-order reconstruction on the initial fluid physical parameters to obtain the final reconstruction polynomial; the final reconstruction polynomial includes the final reconstruction polynomial in the third-order format and the final reconstruction polynomial in the fourth-order format.

[0031] S4: Determine the fluid physical parameters in the calculation area based on the final reconstruction polynomial.

[0032] S5: Determine the wing performance of the aircraft at different Mach numbers and angles of attack according to the fluid physical parameters in the calculation area.

[0033] Further, step S1 specifically includes:

[0034] Determine a rectangular calculation region [XMIN, XMAX] * [YMIN, YMAX] according to the simulated problem. Among them, XMIN is the left position of the calculation region, XMAX is the right position of the calculation region, YMIN is the lower position of the calculation region, and YMAX is the upper position of the calculation region. Establish a spatial rectangular coordinate system, divide the calculation region into grids to obtain the required unstructured triangular grids, and each triangular grid unit is denoted as i.

[0035] According to the required effect of the actual simulation, give the corresponding density residual range [δ min , δ max and the number of iteration steps N to end the calculation.

[0036] Furthermore, step S2 specifically includes:

[0037] According to the problem of the actual simulation, give the Mach number and angle of attack of the aircraft to be simulated; the density, pressure, energy, and medium parameters of the fluid.

[0038] Set the corresponding initial fluid physical parameters in the grid. According to the set Mach number M ∞ , angle of attack θ, medium parameter γ of the fluid, average density of the fluid and average pressure to define the average velocity in the x - direction in the unit average velocity in the y - direction Therefore, the average momentum in the x - direction can be obtained average momentum in the y - direction average total energy

[0039] Furthermore, step S3 specifically includes: Using the geometric information of the target unit in the flow field and the internal fluid information, reconstruct the first - order algebraic polynomial, second - order algebraic polynomial, and third - order algebraic polynomial on the small template, the first large template, and the second large template respectively; the small template only contains the target unit, the first large template includes the target unit and its co - edge neighbor target units, and the number of units is not less than six, the second large template includes the target unit and its co - edge neighbor target units, and the number of units is not less than ten; for the third - order format, determine the final reconstructed polynomial based on the first - order algebraic polynomial and the second - order algebraic polynomial; for the fourth - order format, determine the final reconstructed polynomial based on the first - order algebraic polynomial and the third - order algebraic polynomial.

[0040] (1) Perform spatial discretization by numerical methods and calculate the corresponding numerical fluxes.

[0041] (1) Based on the initial fluid physical parameters in step S2, use the ALW-MR-WENO (the multi-resolution WENO schemes with adaptive linear weights) method to perform high-order reconstruction on physical quantities, obtaining the final reconstructed polynomial poly i (x,y) = [ρ i (x,y), ρu i (x,y), ρv i (x,y), E i (x,y)] T , and the four components respectively represent the density of the fluid, the momentum in the x-direction, the momentum in the y-direction, and the total energy.

[0042] The process of the ALW-MR-WENO method includes the following steps:

[0043] Consider the two-dimensional hyperbolic conservation law equation:

[0044]

[0045] The spatial semi-discrete approximation format of the above equation:

[0046]

[0047]

[0048] is the average value of the fluid at the initial moment, F = (f,g), u = (ρ, ρu, ρv, E) T successively represent the conserved quantities such as the density of the fluid, the momentum in the x and y directions, and the total energy, f(u) = (ρu, ρu 2 +p, ρuv, u(E + p)) T , g(u) = (ρv, ρuv, ρv 2 +p, v(E + p)) T are the corresponding fluxes. ρ, u, v, p, E respectively represent the density of the fluid, the velocities in the x and y directions, the pressure, and the total energy. t represents time. Δ0 represents the target cell, represents the boundary of the target cell in the flow field, |Δ0| represents the area of the target cell in the flow field, u0 represents the values of the density, momentum, and total energy of the fluid at the initial moment, u t represents the derivative of u with respect to time t, f(u) x , g(u) y respectively represent the derivatives of f(u) and g(u) with respect to space x and y, L(u) represents -f(u) x -g(u) yThe semi-discrete form. α represents the maximum absolute value of the eigenvalues of the flux Jacobian matrix in the normal direction of the cell boundary. u + ,u - represent the third- and fourth-order reconstructed values of the conserved quantity u at different Gauss points in the target cell and its neighboring cells. F(u + ), F(u - ) are the corresponding third- and fourth-order numerical fluxes. l represents the three sides of the triangular cell, l1 represents the two Gauss integration points on each side of the triangular cell, represents the side length of the target cell, represents the Gauss integration coefficient corresponding to the Gauss integration point, represents the Gauss integration point, represents the normal vector at the integration point.

[0049] (2) The following details the specific steps to solve for the values of the flux at the Gauss points on the target cell interface using the third- and fourth-order ALW-MR-WENO methods as follows:

[0050] 1) Third-order format. The present invention is based on a small template T1 containing only the target cell and a large template T2 composed of the target cell and its co-edge neighboring cells with no less than six cells. The small template T1 and the large template T2 are as shown in Figure 2 (a) and (b) therein. Using the geometric information of the cells contained in the template and the internal fluid information, reconstruct a first-order algebraic polynomial on T1 and reconstruct a second-order algebraic polynomial on T2

[0051] Obtain the unknown coefficients of the quadratic polynomial q2(x, y) by the least squares method and make q2(x, y) satisfy the same mean value as the target cell Δ0 and can capture the mean values of the cells in the set T2\{Δ0}:

[0052]

[0053] A = {1, 2, 3, 4, 5, 6, 7}.

[0054] 2) Fourth-order format. The present invention is based on a small template T1 containing only the target cell and a large template T3 composed of the target cell and its co-edge neighboring cells with no less than ten cells. The large template T3 is as shown in Figure 2 (c) therein. Using the geometric information of the cells contained in the template and the internal fluid information, reconstruct a first-order algebraic polynomial on T1 and reconstruct a third-order algebraic polynomial on T3:

[0055]

[0056] The unknown coefficients of the cubic polynomial \(q_3(x,y)\) are obtained by the least - squares method, and \(q_3(x,y)\) has the same mean value as the target cell \(\Delta_0\), and can capture the mean values of the cells in the set \(T_3\setminus\{\Delta_0\}\). \(A=\{1,2,3,4,5,6,7,8,9,10,11,12\}\)

[0057] (3) Solve the equivalent forms of the above - mentioned reconstructed polynomials \(q_1(x,y)\), \(q_2(x,y)\), \(q_3(x,y)\). Define \(p_1(x,y)=q_1(x,y)\).

[0058] 1) For the third - order format:

[0059]

[0060] 2) For the fourth - order format:

[0061]

[0062] In the above formulas, \(\gamma\) 1,2 , \(\gamma\) 1,3 , \(\gamma\) 2,2 , \(\gamma\) 3,3 are called linear weights, and the linear weights are solved by the following method: For the third - order format, set the initial value of the unnormalized linear weights The linear weights can be obtained as: For the fourth - order format, we set the initial value of the unnormalized linear weights The linear weights can be obtained as:

[0063] (4) Calculate the smoothness factor on the target cell \(\Delta_0\) to measure the smoothness of the reconstructed polynomials \(q_2(x,y)\), \(q_3(x,y)\). The smaller the value of

[0064]

[0065] is, the smoother the constructed polynomial is. Here, \(k=(k_1,k_2)\) T , \(|k| = k_1 + k_2\). For the third - order format, \(r = 2\); for the fourth - order format, \(r = 3\).

[0066] For \(\beta_1\), since the reconstructed polynomial of the corresponding target cell is a constant, if the derivative is directly calculated, the value of \(\beta_1\) is zero. Therefore, in order not to produce a blurred shock transition when calculating a strong shock or a contact discontinuity, it is calculated by the following method:

[0067] Use the template shown in (b) of Figure 2 to construct three first - order algebraic polynomials and satisfy

[0068] Representation unit Δ j1 , the centroid of j1 = 1, …, 7, apply equation (6) to solve the above The corresponding smoothing factor Let:

[0069]

[0070]

[0071]

[0072] σ = σ1 + σ2 + σ3

[0073] Let ε = 10 -10 Prevent the denominator from being zero.

[0074] Then we can obtain:

[0075]

[0076] (2) Dynamically calculate the linear weight and the corresponding non - linear weight according to the obtained smoothness index.

[0077] First, define a factor that is very important for maintaining accuracy:

[0078] τ η = |β η - β1| 2 , η = 2, 3 (8)

[0079] (1) The non - linear weight defined by the following method Its function is to control the proportion of the corresponding two polynomials, that is, if the fluid does not contain discontinuities, increase the value to improve the accuracy, which helps to capture the complex changes of the fluid in the flow field more accurately; otherwise, reduce its value, which helps to suppress oscillations at the discontinuities and maintain the stability of the method.

[0080]

[0081] We set ε = 10 -10 Prevent the denominator from being zero.

[0082] (2) Obtain a temporary final reconstruction polynomial on the target unit that can represent the density, momentum, and total energy of the fluid respectively:

[0083]

[0084] (3) Provide a simple condition as shown below to make the linear weight During the calculation process, adjustments can be continuously made according to the actual situation to find an optimal value.

[0085]

[0086]

[0087] r represents the minimum value of the circumradius of the triangular elements Δ0, Δ1, Δ2, Δ3. represents the value of the temporary final reconstruction polynomial (10) at the Gaussian integration points on the element boundary. represents the average values of the density, momentum, and total energy of the fluid in the target element and its co-edge neighbor elements.

[0088] (4) Dynamically calculate the linear weight.

[0089] 1) If a2 = 2, 3, the program directly jumps to step S4.

[0090] 2) If the above Condition I is satisfied, reduce the value of the linear weight in the discontinuous region: value:

[0091]

[0092] Then the program returns to step 2.4.1 and continues to execute the subsequent process.

[0093] If this condition is not satisfied, the program directly jumps to step S4.

[0094] Furthermore, step S4 specifically includes:

[0095] Set equation (10) as the final reconstruction polynomial to achieve third-order and fourth-order approximations. Then we can obtain the approximate values at different Gaussian points on the target element boundary: Then substitute it into equation (3) to obtain the value of the numerical flux, and further substitute it into equation (2) to obtain the semi-discrete approximation value L(u) that only depends on time t.

[0096] The process of discretizing the spatial semi-discrete finite volume scheme into a spatio-temporal fully discrete high-precision finite volume scheme using the third-order TVD Runge-Kutta time discretization formula includes:

[0097] Use the third-order TVD Runge-Kutta time discretization formula:

[0098]

[0099] Obtain the spatio-temporal fully discrete finite volume scheme. Where, Δt represents the time step. n represents the nth time level, u (1),u (2) is an intermediate transition value, L(u n ), L(u (1) ), L(u (2) ) are the approximate values of the high-order spatial discretization form of the right-hand side of the equation.

[0100] The value of u at the (n + 1)-th time level can be obtained using equation (12). We compare the residuals δ of the density within element i at the n-th time level and the (n + 1)-th time level. i , and accumulate the residuals of all elements within the region to obtain the total residual δ within the region. If δ exceeds δ max , end the calculation. If δ is within [δ min , δ max and the number of iterations does not exceed N, then continue the calculation until δ exceeds δ max , to obtain the numerical results within the flow field at this moment. Therefore, the aerodynamic characteristic distribution on the wing surface can be obtained, such as the pressure distribution diagram and the pressure contour diagram.

[0101] For traditional methods of the same order, more templates are required to obtain the final reconstructed polynomial. However, in the present invention, regardless of the order format, only two templates are needed, namely a small template and a large template. Traditional methods require more templates to reconstruct high-order polynomials, while the present invention only needs to use two templates, namely a small template and a large template. The linear weights in traditional methods need to be solved artificially, but the obtained values may be negative or even non-existent. In the present invention, there are only two linear weights, and the two can be automatically adjusted to any positive numbers whose sum is 1 according to whether the condition Condition I is satisfied during the calculation process based on the initial values. Therefore, the present invention greatly simplifies the structure of the algorithm, improves the calculation efficiency, has relatively strong robustness, and is also easier to solve high-dimensional and high-order problems. Experiments show that the present invention can also achieve the same calculation results as traditional methods in a shorter time.

[0102] Embodiment 2

[0103] In order to execute the method corresponding to the above Embodiment 1 to achieve the corresponding functions and technical effects, a wing performance test system based on the ALW-MR-WENO algorithm is provided below.

[0104] The above system includes:

[0105] A calculation region determination and division module, used to determine the calculation region and perform grid division on the calculation region.

[0106] An initial fluid physical parameter setting module, used to set the corresponding initial fluid physical parameters within the grid according to the set Mach number and angle of attack; the fluid physical parameters include the average fluid density, the average fluid velocity in the x direction, the average fluid velocity in the y direction, and the average total energy of the fluid.

[0107] A high-order reconstruction module, which is used to perform high-order reconstruction on the initial fluid physical parameters by using the ALW-MR-WENO method to obtain the final reconstruction polynomial; the final reconstruction polynomial includes the final reconstruction polynomial in the third-order format and the final reconstruction polynomial in the fourth-order format.

[0108] A fluid physical parameter determination module, which is used to determine the fluid physical parameters in the calculation area based on the final reconstruction polynomial.

[0109] A performance determination module, which is used to determine the performance of the aircraft wing at different Mach numbers and angles of attack according to the fluid physical parameters in the calculation area.

[0110] Furthermore, the high-order reconstruction module specifically includes:

[0111] A polynomial reconstruction unit, which is used to reconstruct a first-degree algebraic polynomial, a second-degree algebraic polynomial, and a third-degree algebraic polynomial on a small template, a first large template, and a second large template respectively by using the geometric information of the target cell in the flow field and the internal fluid information; the small template only contains the target cell, the first large template includes the target cell and its co-edge neighbor target cells, and the number of cells is not less than six, and the second large template includes the target cell and its co-edge neighbor target cells, and the number of cells is not less than ten.

[0112] A final reconstruction polynomial determination unit in the third-order format, which is used to determine the final reconstruction polynomial in the third-order format based on the first-degree algebraic polynomial and the second-degree algebraic polynomial;

[0113] A final reconstruction polynomial determination unit in the fourth-order format, which is used to determine the final reconstruction polynomial in the fourth-order format based on the first-degree algebraic polynomial and the third-degree algebraic polynomial.

[0114] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. The same or similar parts among the various embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the description in the method part.

[0115] Specific examples are used in this article to elaborate on the principles and implementation manners of the present invention. The descriptions of the above embodiments are only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A wing performance test method based on the ALW-MR-WENO algorithm, characterized in that, Including: Determine the computational domain and perform grid division on the computational domain; Set the corresponding initial fluid physical parameters within the grid according to the set Mach number and angle of attack; the fluid physical parameters include the average fluid density, the average fluid velocity in the x-direction, the average fluid velocity in the y-direction, and the average total fluid energy; specifically, according to the set Mach number M ∞ , angle of attack θ, the medium parameter γ of the fluid, the average density of the fluid and the average pressure to define the average velocity in the x-direction in the unit the average velocity in the y-direction the average momentum in the x-direction the average momentum in the y-direction the average total energy Use the ALW-MR-WENO method to perform high-order reconstruction on the initial fluid physical parameters to obtain the final reconstructed polynomials; the final reconstructed polynomials include the final reconstructed polynomials in third-order format and the final reconstructed polynomials in fourth-order format; Determine the fluid physical parameters within the computational domain based on the final reconstructed polynomials; Determine the performance of the aircraft wing at different Mach numbers and angles of attack according to the fluid physical parameters within the computational domain; Among them, using the ALW-MR-WENO method to perform high-order reconstruction on the initial fluid physical parameters to obtain the final reconstructed polynomials specifically includes: Utilize the geometric information of the target cell in the flow field and the internal fluid information to reconstruct a first-degree algebraic polynomial, a second-degree algebraic polynomial, and a third-degree algebraic polynomial on a small template, a first large template, and a second large template respectively; the small template only contains the target cell, the first large template includes the target cell and its co-edge neighbor target cells, and the number of cells is not less than six, and the second large template includes the target cell and its co-edge neighbor target cells, and the number of cells is not less than ten; Determine the final reconstructed polynomial in third-order format based on the first-degree algebraic polynomial and the second-degree algebraic polynomial; Determine the final reconstructed polynomial in fourth-order format based on the first-degree algebraic polynomial and the third-degree algebraic polynomial.

2. The wing performance test method based on the ALW-MR-WENO algorithm according to claim 1, characterized in that The expression of the first-degree algebraic polynomial q1(x,y) is: The expression of the second-degree algebraic polynomial q2(x,y) is: The expression of the third-degree algebraic polynomial q3(x,y) is: where x and y represent the abscissa and ordinate values of the Gaussian integration points on the cell boundary; represent the average values of the density, momentum, and total energy of the fluid at the initial moment; x0 and y0 represent the abscissa and ordinate values of the center point of the target cell; |Δ0| represents the area of the target cell in the flow field.

3. The wing performance test method based on the ALW-MR-WENO algorithm according to claim 2, characterized in that, The expression of the final reconstructed polynomial Q(x,y) is: p1(x,y) = q1(x,y) For the third-order format: For the fourth-order format: Among them, both represent non-linear weights, and γ 1,2 , γ 1,3 , γ 2,2 , γ 3,3 is a linear weight.

4. The wing performance testing method based on the ALW-MR-WENO algorithm according to claim 1, wherein, Also including: Calculate the smoothness factor on the target cell; The smoothness factor is used to measure the smoothness of the second-degree algebraic polynomial and the third-degree algebraic polynomial.

5. The wing performance testing method based on the ALW-MR-WENO algorithm according to claim 4, characterized in that The calculation formula of the smoothness factor is: where β l is the smoothing factor corresponding to q l (x, y), β1 is the smoothing factor corresponding to ; is a first-order algebraic polynomial; for a third-order scheme, r = 2, and for a fourth-order scheme, r = 3; k represents the k-th derivative of q l (x, y); k1 represents the k1-th partial derivative of q l (x, y) with respect to x; k2 represents the k2-th partial derivative of q l (x, y) with respect to y; k = k1 + k2; q l (x, y) represents a quadratic algebraic polynomial or a cubic algebraic polynomial; Δ0 represents the target element; represents the centroid of the elements Δ1, Δ2, Δ3.

6. An aircraft wing performance testing system based on the ALW-MR-WENO algorithm, characterized in that, Including: A computational domain determination and division module for determining the computational domain and performing grid division on the computational domain; Initial fluid physical parameter setting module, which is used to set corresponding initial fluid physical parameters in the grid according to the set Mach number and angle of attack; the fluid physical parameters include fluid average density, fluid average velocity in the x direction, fluid average velocity in the y direction, and fluid average total energy; specifically, according to the set Mach number M ∞ , angle of attack θ, medium parameter γ of the fluid, and average density of the fluid and average pressure to define the average velocity in the x direction in the unit average velocity in the y direction average momentum in the x direction average momentum in the y direction average total energy A high-order reconstruction module for using the ALW-MR-WENO method to perform high-order reconstruction on the initial fluid physical parameters to obtain the final reconstructed polynomials; the final reconstructed polynomials include the final reconstructed polynomials in third-order format and the final reconstructed polynomials in fourth-order format; A fluid physical parameter determination module for determining the fluid physical parameters within the computational domain based on the final reconstructed polynomials; A performance determination module for determining the performance of the aircraft wing at different Mach numbers and angles of attack according to the fluid physical parameters within the computational domain; Among them, the high-order reconstruction module specifically includes: A polynomial reconstruction unit for utilizing the geometric information of the target cell in the flow field and the internal fluid information to reconstruct a first-degree algebraic polynomial, a second-degree algebraic polynomial, and a third-degree algebraic polynomial on a small template, a first large template, and a second large template respectively; the small template only contains the target cell, the first large template includes the target cell and its co-edge neighbor target cells, and the number of cells is not less than six, and the second large template includes the target cell and its co-edge neighbor target cells, and the number of cells is not less than ten; The final reconstruction polynomial determination unit of the third-order format is used to determine the final reconstruction polynomial of the third-order format based on the first-order algebraic polynomial and the second-order algebraic polynomial; The final reconstruction polynomial determination unit of the fourth-order format is used to determine the final reconstruction polynomial of the fourth-order format based on the first-order algebraic polynomial and the third-order algebraic polynomial.

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