A method, device and equipment for constructing a five-order format smoothing factor of shock wave capture of an aircraft, and a storage medium

Abstract

The application discloses a fifth-order format smooth factor construction method, device and equipment for aircraft shock capturing and a storage medium, relates to the technical field of aerodynamics, and comprises the following steps: discretizing a flow field numerical simulation grid of an aircraft; determining an initial template of a fifth-order format for constructing a smooth factor based on the discrete grid; determining an upwind direction of local flow in the aircraft flow field; splitting the initial template based on the upwind direction to obtain a first sub-template deviated to the upwind side and a second sub-template deviated to the downwind side; constructing corresponding first and second difference expressions based on the first and second sub-templates; determining a dimensionless quantity order function for representing the smooth degree of the flow field based on the first and second difference expressions; constructing a target smooth factor by using the quantity order function; and performing shock capturing on the aircraft by using the target smooth factor, so that the fifth-order precision of an arbitrary order extreme point is maintained.

Description

Technical Field

[0001] This invention relates to the field of aerodynamics, and in particular to a method, apparatus, device, and storage medium for constructing a fifth-order smoothness factor for shock wave capture of aircraft. Background Technology

[0002] Currently, many physical and chemical processes in nature can be described by partial differential equations. However, due to the complexity of real-world problems, these equations often fail to provide analytical solutions. With the development of computers, numerical methods have become the primary means of solving practical engineering problems by obtaining numerical approximate solutions. Numerical solution methods are not limited to one type; finite difference methods, finite volume methods, and finite element methods are among the mainstream methods. To obtain high-resolution approximate solutions for discontinuities, it is necessary to develop nonlinear high-order accuracy schemes that incorporate discontinuity-capturing mechanisms.

[0003] The implementation process of the finite difference method is as follows: First, within the solution domain, the continuous solution domain is approximated as a finite discrete set of points using a difference grid or difference nodes. The simplest difference discretization is the partitioning of a fixed, equidistant difference grid. Then, at each node, each derivative term in the partial differential equation describing the problem is replaced with the corresponding difference expression to reduce its order, thus forming an algebraic equation at each node. Each equation contains the desired quantity at its own node and some neighboring nodes; the points included are called the template, and the number of points is called the template width. Finally, solving the system of algebraic equations formed by all the points yields the desired numerical solution.

[0004] Different finite difference schemes with varying precision can be constructed based on different template widths and algebraic equation forms at template points. The fifth-order precision nonlinear weighted scheme is the most popular high-precision scheme, frequently used in computational fluid dynamics to solve shock wave capture problems. The core idea of ​​nonlinear weighting is to decompose a high-precision template into several low-precision sub-templates. These low-precision sub-templates are assigned dynamic nonlinear weights (nonlinear weighting) based on their smoothness (characterized by a smoothness factor). Smoother sub-templates are assigned larger weights, while those with discontinuities (extreme points) have smaller weights. This approach avoids interpolation across discontinuities, allowing the constructed high-precision scheme to capture discontinuous structures like shock waves with minimal oscillation. The specific form of the nonlinear weights in this weighting concept significantly impacts the scheme's resolution. Numerous studies have shown that the JS nonlinear weights in the most commonly used fifth-order precision nonlinear weighted scheme, WENO-JS, introduce significant nonlinear errors. Even the Z weights, developed based on JS weights, have not completely solved the problem of order reduction at extreme points, primarily due to the inadequate design of the smoothness factor in the nonlinear weight function.

[0005] In addition, many adaptive algorithms have been studied for the design of smoothing factors. A typical example is Yamalev et al., who set the smoothing factor as a power function of the grid spacing, but this would exacerbate the numerical oscillations of discontinuous calculations.

[0006] As can be seen from the above, how to construct a smooth factor that simultaneously satisfies the requirements of no order reduction at arbitrary extrema and good numerical dissipation characteristics during the construction of a fifth-order solvability factor for aircraft shock wave capture is an urgent problem to be solved. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a method, apparatus, device, and storage medium for constructing a fifth-order scheme smoothing factor for aircraft shock wave capture. This method maintains the fifth-order scheme without degrading at any extreme point during the construction of the fifth-order scheme smoothing factor for aircraft shock wave capture, while simultaneously exhibiting good numerical dissipation characteristics. The specific solution is as follows:

[0008] In a first aspect, this application provides a method for constructing a fifth-order format smoothness factor for shock wave capture in aircraft, including:

[0009] The flow field numerical simulation of the aircraft uses a discrete grid to determine an initial template for constructing a fifth-order scheme for the smoothness factor; the initial template includes each continuous grid node in the shock wave region and the smooth flow region of the aircraft flow field.

[0010] The windward direction of the local flow in the aircraft flow field is determined, and the initial template is split based on the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. A first difference expression and a second difference expression are constructed based on the first and second sub-templates, respectively. The number of grid nodes corresponding to the first sub-template is consistent with the number of grid nodes corresponding to the second sub-template. The number of grid nodes corresponding to the first sub-template is less than the number of grid nodes corresponding to the initial template. The first and second sub-templates include overlapping portions. The precision of the first and second difference expressions is the fifth-order precision corresponding to the fifth-order scheme.

[0011] Based on the first difference expression and the second difference expression, a dimensionless order function is determined to characterize the smoothness of the flow field. The target smoothness factor is constructed using the order function, and the target smoothness factor is used to perform fifth-order accuracy shock wave capture on the aircraft. In the smooth region of the aircraft flow field, the target smoothness factor is greater than a preset smoothness factor reference value; in the region containing shock waves or contact discontinuities, the target smoothness factor is less than the preset smoothness factor reference value.

[0012] Optionally, the discrete grid for the numerical simulation of the flow field based on the aircraft, used to determine an initial template for constructing a fifth-order scheme for the smoothness factor, includes:

[0013] The flow field values ​​corresponding to the aircraft are determined, and a mesh is generated based on the flow field values ​​using a preset simulation model to obtain the corresponding discrete mesh. Then, the flow control equations corresponding to the first-order nonlinear hyperbolic conservation law are determined.

[0014] Based on user requirements, the target template width is determined, and then the shock wave region and smooth flow region in the aircraft flow field are determined. The grid nodes corresponding to the shock wave region and the smooth flow region in the discrete grid are determined. Then, based on the target template width and each grid node, and using the flow control equation, the template is constructed to obtain the initial template of the fifth order format.

[0015] Optionally, determining the windward direction of the local flow in the aircraft flow field, and splitting the initial template based on the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side, and constructing corresponding first difference expressions and second difference expressions based on the first sub-template and the second sub-template respectively, includes:

[0016] The windward direction of the local flow in the flow field of the aircraft is determined, and the mesh nodes on both sides of the initial template are expanded based on the windward direction to obtain an expanded template; the expanded template includes seven consecutive mesh nodes.

[0017] The flow field variable values ​​corresponding to the seven grid nodes in the extended template are determined, and the initial template is constructed with sub-templates based on each flow field variable value and the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downwind side; wherein, the first sub-template and the second sub-template include six grid nodes;

[0018] Using a preset linear combination algorithm, difference expressions are constructed for each grid node in the first sub-template and each grid node in the second sub-template, respectively, to obtain the corresponding first difference expression and second difference expression.

[0019] Optionally, determining the dimensionless order function characterizing the smoothness of the flow field based on the first difference expression and the second difference expression includes:

[0020] The flow field variable values ​​corresponding to the grid nodes in the discrete grid are processed using the first difference expression and the second difference expression respectively to obtain the corresponding first difference value and second difference value;

[0021] The difference and result between the first difference value and the second difference value, as well as the difference result between the difference values, are determined. Then, a preset square processing algorithm is used to process the difference and result and the difference result to obtain a dimensionless order function that characterizes the smoothness of the flow field.

[0022] Optionally, the step of constructing a target smoothing factor using the order function and using the target smoothing factor to perform fifth-order accuracy shock wave capture on the aircraft includes:

[0023] The flow field variable values ​​corresponding to each grid node in the discrete grid are processed using the order function to obtain the initial smoothing factor parameter, and the smooth region in the flow field of the aircraft is determined. Then, the initial smoothing factor parameter is increased in the smooth region to obtain the corresponding first smoothing factor parameter.

[0024] The non-smooth regions in the flow field of the aircraft are identified, and the initial smoothing factor parameter is reduced in the non-smooth regions to obtain the corresponding second smoothing factor parameter. The target smoothing factor is determined based on the first smoothing factor parameter and the second smoothing factor parameter, and the target smoothing factor is used to capture the shock wave corresponding to the aircraft with fifth-order accuracy.

[0025] Optionally, after constructing the target smoothness factor using the order function, the method further includes:

[0026] An initial extreme point test function with a variable extreme point order is constructed. Based on the initial extreme point test function, a preset interval, and a preset extreme point order, the target smoothness factor is interpolated under different extreme point order conditions to obtain the correspondence between interpolation accuracy and statistical error.

[0027] The target smoothing factor is adjusted based on the correspondence and the preset weighting algorithm to obtain the adjusted smoothing factor. Then, the dissipation and dispersion characteristics of the adjusted smoothing factor are evaluated using the spectral analysis method to obtain the evaluation result. After the evaluation result indicates that the evaluation is passed, the adjusted smoothing factor is set as the new target smoothing factor.

[0028] Secondly, this application provides a fifth-order solvability factor construction device for aircraft shock wave capture, comprising:

[0029] A template generation module is used to determine an initial template for constructing a fifth-order scheme of smoothness factor based on a discrete grid for numerical simulation of the flow field of an aircraft; the initial template includes each continuous grid node in the shock wave region and the smooth flow region of the aircraft flow field;

[0030] The difference expression generation module is used to determine the windward direction of the local flow in the aircraft flow field, and to split the initial template based on the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. Based on the first and second sub-templates, corresponding first and second difference expressions are constructed respectively. The number of grid nodes corresponding to the first sub-template is consistent with the number of grid nodes corresponding to the second sub-template. The number of grid nodes corresponding to the first sub-template is less than the number of grid nodes corresponding to the initial template. The first and second sub-templates include overlapping portions. The precision of the first and second difference expressions is the fifth-order precision corresponding to the fifth-order format.

[0031] A smoothing factor generation module is used to determine a dimensionless order function to characterize the smoothness of the flow field based on the first difference expression and the second difference expression, so as to construct a target smoothing factor using the order function and use the target smoothing factor to perform fifth-order accuracy shock wave capture on the aircraft; wherein, in the smooth region of the aircraft flow field, the smoothing factor is greater than a preset smoothing factor reference value; in the region containing shock waves or contact discontinuities, the smoothing factor is less than the preset smoothing factor reference value.

[0032] Optionally, the difference expression generation module includes:

[0033] An extended template generation unit is used to determine the windward direction of the local flow in the flow field of the aircraft, and to expand the mesh nodes on both sides of the initial template based on the windward direction to obtain an extended template; the extended template includes seven consecutive mesh nodes.

[0034] The sub-template acquisition unit is used to determine the flow field variable values ​​corresponding to the seven grid nodes in the extended template, and to construct sub-templates for the initial template based on each flow field variable value and the windward direction, thereby obtaining a first sub-template biased towards the windward side and a second sub-template biased towards the downwind side; wherein, the first sub-template and the second sub-template include six grid nodes;

[0035] The difference expression generation sub-unit is used to construct difference expressions for each grid node in the first sub-template and each grid node in the second sub-template using a preset linear combination algorithm, so as to obtain the corresponding first difference expression and second difference expression respectively.

[0036] Thirdly, this application provides an electronic device, comprising:

[0037] Memory, used to store computer programs;

[0038] A processor is used to execute the computer program to implement the aforementioned method for constructing a fifth-order format smooth factor for aircraft shock wave capture.

[0039] Fourthly, this application provides a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned method for constructing a fifth-order format smoothing factor for aircraft shock wave capture.

[0040] As can be seen from the above, before constructing the fifth-order scheme smoothing factor for shock wave capture of an aircraft, this application needs to use a discrete grid based on the numerical simulation of the aircraft's flow field to determine the initial template for constructing the fifth-order scheme smoothing factor. The initial template includes each continuous grid node in the shock wave region and the smooth flow region of the aircraft's flow field. The windward direction of the local flow in the aircraft's flow field is determined, and the initial template is split based on the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. The corresponding first difference expression and second difference expression are constructed based on the first sub-template and the second sub-template, respectively. The dimensionless order function used to characterize the smoothness of the flow field is determined based on the first difference expression and the second difference expression. The target smoothing factor is constructed using the order function, and the target smoothing factor is used to perform fifth-order accurate shock wave capture of the aircraft.

[0041] Therefore, this application first requires a discrete grid based on the numerical simulation of the aircraft's flow field to determine an initial template for constructing a fifth-order scheme for the smoothness factor. Then, the windward direction of the local flow in the aircraft's flow field is determined, and the initial template is split based on this windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. Corresponding first and second difference expressions are then constructed based on these sub-templates. Finally, a dimensionless order function characterizing the smoothness of the flow field is determined based on the first and second difference expressions. This order function is used to construct the target smoothness factor, and the target smoothness factor is used to perform fifth-order accurate shock wave capture of the aircraft. In this way, the construction of the fifth-order scheme smoothness factor for aircraft shock wave capture ensures that the order of extreme points does not decrease, while also exhibiting good numerical dissipation characteristics. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0043] Figure 1This is a flowchart of a fifth-order format smoothness factor construction method for aircraft shock wave capture disclosed in this application;

[0044] Figure 2 This is a schematic diagram illustrating a specific method of performing equidistant differential mesh generation as disclosed in this application;

[0045] Figure 3 This is a schematic diagram of a specific fifth-order precision sub-template disclosed in this application;

[0046] Figure 4 This is a schematic diagram of the format accuracy test results for a specific k=0 smooth region disclosed in this application;

[0047] Figure 5 This is a schematic diagram of the format accuracy test results corresponding to a specific first-order extreme point k=1 disclosed in this application;

[0048] Figure 6 This is a schematic diagram of the format accuracy test results corresponding to a specific second-order extremum point k=2 disclosed in this application;

[0049] Figure 7 This is a schematic diagram of a specific format precision real part result disclosed in this application;

[0050] Figure 8 This is a schematic diagram of a specific format precision imaginary part result disclosed in this application;

[0051] Figure 9 This is a schematic diagram of a fifth-order format smooth factor construction device for aircraft shock wave capture disclosed in this application;

[0052] Figure 10 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] Currently, many physical and chemical processes in nature can be described by partial differential equations. However, due to the complexity of real-world problems, these equations often fail to provide analytical solutions. With the development of computers, numerical methods have become the primary means of solving practical engineering problems by obtaining numerical approximate solutions. Therefore, this application provides a method for constructing a fifth-order scheme smoothing factor for shock wave capture in aircraft. This method ensures that the extrema of any order do not decrease in order during shock wave capture, while the corresponding scheme exhibits good numerical dissipation characteristics.

[0055] See Figure 1 As shown, this embodiment of the invention discloses a method for constructing a fifth-order format smoothness factor for aircraft shock wave capture, comprising:

[0056] Step S11: Based on the discrete grid of the flow field numerical simulation of the aircraft, determine the initial template of the fifth-order scheme for constructing the smoothness factor based on the discrete grid; the initial template includes each continuous grid node in the shock wave region and the smooth flow region in the flow field of the aircraft.

[0057] In this embodiment, the first step is to determine the template points. A schematic diagram of the equidistant differential mesh division is shown below. Figure 2 As shown. Furthermore, for a first-order nonlinear hyperbolic equation, this embodiment requires at least 5 template points when constructing the quantities of the 5th-order precision half-nodes. However, to ensure its upwind characteristics, this embodiment requires the use of the values ​​of the left and right half-nodes, involving at least 6 template points. The expression corresponding to the template used for the interior point JS weight is shown below:

[0058] ;

[0059] Furthermore, considering the quantity of each half-node, this embodiment requires at least two adjacent nodes. Therefore, this embodiment can calculate the smoothing factor on a template of seven points. The template for calculating the smoothing factor can be set as follows: The 7-point template.

[0060] Specifically, the discrete mesh for numerical simulation of the flow field of an aircraft, and the initial template for constructing a fifth-order scheme based on the discrete mesh, can include: determining the flow field values ​​corresponding to the aircraft, generating a mesh using a preset simulation model and based on the flow field values ​​to obtain the corresponding discrete mesh, and then determining the flow control equations corresponding to the first-order nonlinear hyperbolic conservation law; determining the target template width based on user requirements, then determining the shock wave region and smooth flow region in the aircraft flow field, determining the mesh nodes in the discrete mesh corresponding to the shock wave region and smooth flow region, and then constructing the template based on the target template width and each mesh node and using the flow control equations to obtain the initial template of the fifth-order scheme.

[0061] Step S12: Determine the windward direction of the local flow in the aircraft flow field, and split the initial template based on the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. Construct corresponding first difference expressions and second difference expressions based on the first sub-template and the second sub-template, respectively. The number of grid nodes corresponding to the first sub-template is consistent with the number of grid nodes corresponding to the second sub-template. The number of grid nodes corresponding to the first sub-template is less than the number of grid nodes corresponding to the initial template. The first sub-template and the second sub-template include overlapping parts. The precision of the first difference expression and the second difference expression are respectively the fifth-order precision corresponding to the fifth-order format.

[0062] In this embodiment, the present application requires the construction of a difference expression related to the 5th derivative. First, the present application requires the 7-point template... It is split into two 6-point templates, and the expressions are as follows:

[0063] ;

[0064] Subsequently, in this embodiment of the application, a difference expression related to the fifth derivative needs to be constructed on the 6-point template. This represents the difference expression on the left side. The right-hand side difference expression is represented as follows:

[0065] ;

[0066] ;

[0067] in, This represents the parameter value at node j. This represents the parameter value at node j+1; similar values ​​are used for other nodes. To calculate the grid scale, i.e., the distance from j+1 to j, it is usually a small quantity, therefore The larger n is, the smaller the overall value. and This is the set of coefficients for the expression, usually a constant. Specific values ​​do not need to be given here, as this term is... Item, relative to The item is a small quantity; In error analysis, the order sign indicates that the magnitude of the remainder term does not exceed [a certain value]. .

[0068] Specifically, the windward direction of the local flow in the aircraft's flow field is determined. Based on this windward direction, the initial template is split to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. Corresponding first and second difference expressions are then constructed based on the first and second sub-templates, respectively. This process includes: determining the windward direction of the local flow in the aircraft's flow field and expanding the grid nodes on both sides of the initial template based on this windward direction to obtain an expanded template; the expanded template includes seven consecutive grid nodes; determining the flow field variable values ​​corresponding to the seven grid nodes in the expanded template, and constructing sub-templates based on each flow field variable value and the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side; wherein the first and second sub-templates each include six grid nodes; and using a preset linear combination algorithm to construct difference expressions for each grid node in the first sub-template and each grid node in the second sub-template, respectively, to obtain corresponding first and second difference expressions.

[0069] Step S13: Based on the first difference expression and the second difference expression, determine a dimensionless order function to characterize the smoothness of the flow field, so as to construct a target smoothness factor using the order function, and use the target smoothness factor to perform fifth-order accuracy shock wave capture on the aircraft; wherein, in the smooth region of the aircraft flow field, the target smoothness factor is greater than a preset smoothness factor reference value; in the region containing shock waves or contact discontinuities, the target smoothness factor is less than the preset smoothness factor reference value.

[0070] In this embodiment, the present application requires the construction of a dimensionless order function. The dimensionless order function can be obtained from the following relationship:

[0071] ;

[0072] in, The order of the extreme point.

[0073] Specifically, determining the dimensionless order function used to characterize the smoothness of the flow field based on the first difference expression and the second difference expression can include: processing the flow field variable values ​​corresponding to the grid nodes in the discrete grid using the first difference expression and the second difference expression respectively to obtain the corresponding first difference value and second difference value; determining the difference value and result between the first difference value and the second difference value, and then using a preset square processing algorithm and processing based on the difference value and result to obtain the dimensionless order function used to characterize the smoothness of the flow field.

[0074] Subsequently, embodiments of this application can utilize dimensionless order functions to construct adaptive weights in JS. The specific form of the original JS permission is as follows:

[0075] ;

[0076] ;

[0077] ;

[0078] in, This represents the value of the parameter at the j+1 / 2 half node in the JS weighted format; For nonlinear weights, it is a function, and the subscript k corresponds to different template points, such as... Figure 3 As shown, Figure 3 This is a schematic diagram of a sub-template with fifth-order precision, which includes three templates: 0, 1, and 2. This represents the value of the half-node constructed on template k, since template k only has three nodes. Only second-order precision; The weight function corresponding to template k; The smoothing factor corresponding to template k; It is a small positive number; It is a positive integer; The smoothing factor corresponding to template 0. The smoothing factor corresponding to template 1, This is the smoothing factor corresponding to template 2. For the ideal right, , , , , Let be a positive integer, where:

[0079] ;

[0080] Among them, for the three 3-point sub-templates The smoothness factor of the k-th sub-template is determined by the base part of the sub-template. Adaptive smoothing factor of full template The composition is as follows:

[0081] ;

[0082] It is worth mentioning that the adaptive system constructed in the embodiments of this application... The following conditions must be met: When in the smooth region, When the sub-template contains discontinuities ,therefore, The corresponding expression is as follows:

[0083] ;

[0084] in, , which is a small positive quantity, ensures that the overall quantity value is not 0.

[0085] Specifically, constructing a target smoothing factor using a magnitude function and then using the target smoothing factor to capture shock waves of the aircraft with fifth-order accuracy can include: processing the flow field variable values ​​corresponding to each grid node in the discrete grid using a magnitude function to obtain initial smoothing factor parameters, determining smooth regions in the aircraft flow field, increasing the initial smoothing factor parameters in the smooth regions to obtain corresponding first smoothing factor parameters; determining non-smooth regions in the aircraft flow field, decreasing the initial smoothing factor parameters in the non-smooth regions to obtain corresponding second smoothing factor parameters, determining the target smoothing factor based on the first and second smoothing factor parameters, and then using the target smoothing factor to capture the shock waves of the aircraft with fifth-order accuracy.

[0086] Subsequently, this embodiment of the application needs to be tested using the standard extreme point test function to prove the accuracy and dissipation properties of the smoothness factor design method at discontinuities, and the corresponding expression is as follows:

[0087] ;

[0088] in, , , For the argument of the test function, This is the second argument of the test function. The set of natural numbers is represented by mathematical symbols.

[0089] In one specific implementation, the test interval is... ,when When, test function It is a monotonic, smooth function with no extreme points; when When, the test function is place as The extreme point of order.

[0090] in, The corresponding interpolation test results are as follows: Figure 4 As shown, the horizontal axis represents the grid density, the vertical axis represents the statistical error, and the slope of the curve represents the interpolation accuracy. This represents a smooth region that does not contain extreme points. Figure 4 It can be seen that the format in this embodiment has good 5th-order precision, consistent with the precision of the linear format. In the figure, JS represents the original JS weight, and its statistical error is greater than the statistical error corresponding to the embodiment in this application. The corresponding interpolation test results are as follows: Figure 5 As shown, and the conclusions obtained are... Consistent. Furthermore, The corresponding interpolation test results are as follows: Figure 6 As shown, further, when there is a second-order extreme point in the embodiment of this application, the embodiment of this application still maintains the same interpolation accuracy and statistical error as the linear format, while the interpolation accuracy of the original JS weight format is reduced to the fourth order, and the statistical error is greater than the statistical error corresponding to the embodiment of this application.

[0091] Furthermore, embodiments of this application employ the Adr spectrum analysis method to analyze the dissipation and dispersion characteristics of the format, wherein, Figure 7 This is a schematic diagram of the real part results of Amplitude-Duration-Rate Spectrum Analysis. Figure 8 This is a schematic diagram of the imaginary part of the format accuracy results. The real part represents the dispersion characteristics of the format, and the imaginary part represents the dissipation characteristics. The horizontal axis represents the waveband, and the closer the curve is to the theoretical value (Exact), the better. From... Figure 7 and Figure 8 As can be seen from this, the spectral characteristics in the embodiments of this application are close to the fifth-order linear format, which is superior to the original JS weighted format.

[0092] Specifically, after constructing the target smoothing factor using the order function, the process may further include: constructing an initial extreme point test function with variable extreme point orders; performing interpolation tests on the target smoothing factor based on the initial extreme point test function, a preset interval, and a preset extreme point order under different extreme point order conditions to obtain the correspondence between interpolation accuracy and statistical error; adjusting the target smoothing factor based on the correspondence and a preset weighting algorithm to obtain the adjusted smoothing factor; then using spectral analysis to evaluate the dissipation and dispersion characteristics of the adjusted smoothing factor to obtain the evaluation result; and setting the adjusted smoothing factor as the new target smoothing factor after the evaluation result indicates that the evaluation has passed.

[0093] As can be seen from the above, the embodiments of this application first require a discrete grid based on the numerical simulation of the flow field of the aircraft to determine an initial template for constructing a fifth-order scheme for the smoothing factor. Then, the windward direction of the local flow in the aircraft's flow field is determined, and the initial template is split based on this windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. Corresponding first and second difference expressions are then constructed based on these sub-templates. Finally, a dimensionless order function characterizing the smoothness of the flow field is determined based on the first and second difference expressions. This order function is used to construct the target smoothing factor, and the target smoothing factor is used to perform fifth-order accurate shock wave capture of the aircraft. In this way, the construction of the fifth-order scheme smoothing factor for aircraft shock wave capture ensures that the order of extreme points does not decrease, while also exhibiting good numerical dissipation characteristics.

[0094] Accordingly, see Figure 9 As shown, this application also provides a fifth-order solvability factor construction device for aircraft shock wave capture, comprising:

[0095] Template generation module 11 is used to determine an initial template for constructing a fifth-order format for the smoothness factor based on the discrete grid of the flow field numerical simulation of the aircraft; the initial template includes each continuous grid node in the shock wave region and the smooth flow region in the flow field of the aircraft.

[0096] The difference expression generation module 12 is used to determine the windward direction of the local flow in the aircraft flow field, and to split the initial template based on the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. Based on the first sub-template and the second sub-template, corresponding first difference expressions and second difference expressions are constructed respectively. The number of grid nodes corresponding to the first sub-template is consistent with the number of grid nodes corresponding to the second sub-template. The number of grid nodes corresponding to the first sub-template is less than the number of grid nodes corresponding to the initial template. The first sub-template and the second sub-template include overlapping portions. The precision of the first difference expression and the second difference expression are respectively the fifth-order precision corresponding to the fifth-order format.

[0097] The smoothing factor generation module 13 is used to determine a dimensionless order function to characterize the smoothness of the flow field based on the first difference expression and the second difference expression, so as to construct a target smoothing factor using the order function and use the target smoothing factor to perform fifth-order accuracy shock wave capture on the aircraft; wherein, in the smooth region of the aircraft flow field, the smoothing factor is greater than a preset smoothing factor reference value; in the region containing shock waves or contact discontinuities, the smoothing factor is less than the preset smoothing factor reference value.

[0098] In some specific embodiments, the template generation module 11 may specifically include:

[0099] Discrete mesh generation unit is used to determine the flow field values ​​corresponding to the aircraft, so as to generate a mesh based on the flow field values ​​using a preset simulation model, obtain the corresponding discrete mesh, and then determine the flow control equations corresponding to the first-order nonlinear hyperbolic conservation law.

[0100] The grid node determination unit is used to determine the corresponding target template width based on user requirements, then determine the shock wave region and smooth flow region in the aircraft flow field, and determine the grid nodes in the discrete grid corresponding to the shock wave region and the smooth flow region. Then, based on the target template width and each grid node, and using the flow control equation, the template is constructed to obtain the initial template of the fifth order format.

[0101] In some specific embodiments, the difference expression generation module 12 may specifically include:

[0102] An extended template generation unit is used to determine the windward direction of the local flow in the flow field of the aircraft, and to expand the mesh nodes on both sides of the initial template based on the windward direction to obtain an extended template; the extended template includes seven consecutive mesh nodes.

[0103] The sub-template acquisition unit is used to determine the flow field variable values ​​corresponding to the seven grid nodes in the extended template, and to construct sub-templates for the initial template based on each flow field variable value and the windward direction, thereby obtaining a first sub-template biased towards the windward side and a second sub-template biased towards the downwind side; wherein, the first sub-template and the second sub-template include six grid nodes;

[0104] The difference expression generation sub-unit is used to construct difference expressions for each grid node in the first sub-template and each grid node in the second sub-template using a preset linear combination algorithm, so as to obtain the corresponding first difference expression and second difference expression respectively.

[0105] In some specific embodiments, the difference expression generation module 12 may specifically include:

[0106] An extended template generation unit is used to determine the windward direction of the local flow in the flow field of the aircraft, and to expand the mesh nodes on both sides of the initial template based on the windward direction to obtain an extended template; the extended template includes seven consecutive mesh nodes.

[0107] A flow field variable value determination unit is used to determine the flow field variable values ​​corresponding to the seven grid nodes in the extended template, and to construct sub-templates for the initial template based on each flow field variable value and the windward direction, to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downwind side; wherein, the first sub-template and the second sub-template include six grid nodes;

[0108] The difference expression construction unit is used to construct difference expressions for each grid node in the first sub-template and each grid node in the second sub-template using a preset linear combination algorithm, so as to obtain the corresponding first difference expression and second difference expression respectively.

[0109] In some specific embodiments, the smoothing factor generation module 13 may specifically include:

[0110] The difference value generation unit is used to process the flow field variable values ​​corresponding to the grid nodes in the discrete grid using the first difference expression and the second difference expression respectively to obtain the corresponding first difference value and second difference value.

[0111] The order function determination unit is used to determine the difference value and result between the first difference value and the second difference value, as well as the difference value difference result. Then, it uses a preset square processing algorithm and processes the difference value and result and the difference value difference result to obtain a dimensionless order function that characterizes the smoothness of the flow field.

[0112] In some specific embodiments, the smoothing factor generation module 13 may specifically include:

[0113] The smooth region determination unit is used to process the flow field variable values ​​corresponding to each grid node in the discrete grid using the order function to obtain the initial smooth factor parameter, and to determine the smooth region in the flow field of the aircraft. Then, the initial smooth factor parameter is increased in the smooth region to obtain the corresponding first smooth factor parameter.

[0114] A smoothing factor generation subunit is used to determine the non-smooth regions in the flow field of the aircraft, and to reduce the initial smoothing factor parameter in the non-smooth regions to obtain the corresponding second smoothing factor parameter. Based on the first smoothing factor parameter and the second smoothing factor parameter, a target smoothing factor is determined, and the target smoothing factor is used to capture the shock wave corresponding to the aircraft with fifth-order accuracy.

[0115] In some specific embodiments, the fifth-order solvability factor construction device for aircraft shock wave capture may further include:

[0116] The smoothing factor interpolation test unit is used to construct an initial extreme point test function with a variable extreme point order, and to perform interpolation tests on the target smoothing factor based on the initial extreme point test function, a preset interval, and a preset extreme point order under different extreme point order conditions, so as to obtain the correspondence between interpolation accuracy and statistical error.

[0117] The evaluation result determination unit is used to adjust the target smoothing factor based on the correspondence and the preset weighting algorithm to obtain the adjusted smoothing factor, and then use the spectrum analysis method to evaluate the dissipation and dispersion characteristics of the adjusted smoothing factor to obtain the evaluation result. After the evaluation result indicates that the evaluation is passed, the adjusted smoothing factor is set as the new target smoothing factor.

[0118] Furthermore, embodiments of this application also disclose an electronic device, Figure 10 This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the fifth-order format smoothing factor construction method for aircraft shock wave capture disclosed in any of the foregoing embodiments. Furthermore, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0119] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0120] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0121] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the fifth-order format smooth factor construction method for aircraft shock wave capture disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0122] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned disclosed method for constructing a fifth-order format smoothing factor for aircraft shock wave capture. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0123] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0124] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0125] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0126] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0127] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for constructing a fifth-order solvability factor for shock wave capture in aircraft, characterized in that, include: The flow field numerical simulation of the aircraft is based on a discrete grid, and an initial template for a fifth-order scheme for constructing a smoothness factor is determined based on the discrete grid. The initial template includes continuous grid nodes in the shock wave region and the smooth flow region of the aircraft flow field; The windward direction of the local flow in the aircraft flow field is determined, and the initial template is split based on the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. A first difference expression and a second difference expression are constructed based on the first and second sub-templates, respectively. The number of grid nodes corresponding to the first sub-template is consistent with the number of grid nodes corresponding to the second sub-template. The number of grid nodes corresponding to the first sub-template is less than the number of grid nodes corresponding to the initial template. The first and second sub-templates include overlapping portions. The precision of the first and second difference expressions is the fifth-order precision corresponding to the fifth-order scheme. Based on the first difference expression and the second difference expression, a dimensionless order function is determined to characterize the smoothness of the flow field. The target smoothness factor is constructed using the order function, and the target smoothness factor is used to perform fifth-order accuracy shock wave capture on the aircraft. In the smooth region of the aircraft flow field, the target smoothness factor is greater than a preset smoothness factor reference value; in the region containing shock waves or contact discontinuities, the target smoothness factor is less than the preset smoothness factor reference value. The smoothing factor generation module determines a dimensionless order function to characterize the smoothness of the flow field based on the first difference expression and the second difference expression, and uses the order function to construct a target smoothing factor, including: The flow field variable values ​​corresponding to the grid nodes in the discrete grid are processed using the first difference expression and the second difference expression respectively to obtain the corresponding first difference value and second difference value; The difference and result between the first difference value and the second difference value, as well as the difference result, are determined. Then, a preset square processing algorithm is used to process the difference and result and the difference result to obtain a dimensionless order function that characterizes the smoothness of the flow field. The flow field variable values ​​corresponding to each grid node in the discrete grid are processed using the order function to obtain the initial smoothing factor parameter, and the smooth region in the flow field of the aircraft is determined. Then, the initial smoothing factor parameter is increased in the smooth region to obtain the corresponding first smoothing factor parameter. The non-smooth regions in the flow field of the aircraft are identified, and the initial smooth factor parameter is reduced in the non-smooth regions to obtain the corresponding second smooth factor parameter, so as to determine the target smooth factor based on the first smooth factor parameter and the second smooth factor parameter; Among them, dimensionless order functions Obtained from the following relation: ； in, Let the order of the extreme point be . This represents the difference expression on the left side. This represents the difference expression on the right. To calculate the grid scale, i.e. the distance from j+1 to j, where j+1 and j are both nodes.

2. The method for constructing a fifth-order sonicated smoothness factor for shock wave capture of an aircraft according to claim 1, characterized in that, The discrete grid for the numerical simulation of the flow field based on the aircraft, used to determine an initial template for constructing a fifth-order scheme for the smoothness factor, includes: The flow field values ​​corresponding to the aircraft are determined, and a mesh is generated based on the flow field values ​​using a preset simulation model to obtain the corresponding discrete mesh. Then, the flow control equations corresponding to the first-order nonlinear hyperbolic conservation law are determined. Based on user requirements, the target template width is determined, and then the shock wave region and smooth flow region in the aircraft flow field are determined. The grid nodes corresponding to the shock wave region and the smooth flow region in the discrete grid are determined. Then, based on the target template width and each grid node, and using the flow control equation, the template is constructed to obtain the initial template of the fifth order format.

3. The method for constructing a fifth-order solvability factor for shock wave capture of aircraft according to claim 1, characterized in that, The process involves determining the windward direction of the local flow in the aircraft's flow field, splitting the initial template based on this windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side, and constructing corresponding first and second difference expressions based on the first and second sub-templates, respectively, including: The windward direction of the local flow in the flow field of the aircraft is determined, and the mesh nodes on both sides of the initial template are expanded based on the windward direction to obtain an expanded template; the expanded template includes seven consecutive mesh nodes. The flow field variable values ​​corresponding to the seven grid nodes in the extended template are determined, and the initial template is constructed with sub-templates based on each flow field variable value and the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downwind side; wherein, the first sub-template and the second sub-template include six grid nodes; Using a preset linear combination algorithm, difference expressions are constructed for each grid node in the first sub-template and each grid node in the second sub-template, respectively, to obtain the corresponding first difference expression and second difference expression.

4. The method for constructing a fifth-order sonicated smoothness factor for shock wave capture of an aircraft according to claim 1, characterized in that, After constructing the target smoothness factor using the order function, the method further includes: An initial extreme point test function with a variable extreme point order is constructed. Based on the initial extreme point test function, a preset interval, and a preset extreme point order, the target smoothness factor is interpolated under different extreme point order conditions to obtain the correspondence between interpolation accuracy and statistical error. The target smoothing factor is adjusted based on the correspondence and the preset weighting algorithm to obtain the adjusted smoothing factor. Then, the dissipation and dispersion characteristics of the adjusted smoothing factor are evaluated using the spectral analysis method to obtain the evaluation result. After the evaluation result indicates that the evaluation is passed, the adjusted smoothing factor is set as the new target smoothing factor.

5. A fifth-order scheme smoothing factor construction device for aircraft shock wave capture, characterized in that, include: A template generation module is used for discrete mesh-based numerical simulation of flow field of aircraft to determine an initial template for constructing a fifth-order scheme of smoothness factor based on the discrete mesh; The initial template includes continuous grid nodes in the shock wave region and the smooth flow region of the aircraft flow field; The difference expression generation module is used to determine the windward direction of the local flow in the aircraft flow field, and to split the initial template based on the windward direction to obtain a first sub-template biased towards the windward side and a second sub-template biased towards the downstream side. Based on the first and second sub-templates, corresponding first and second difference expressions are constructed respectively. The number of grid nodes corresponding to the first sub-template is consistent with the number of grid nodes corresponding to the second sub-template. The number of grid nodes corresponding to the first sub-template is less than the number of grid nodes corresponding to the initial template. The first and second sub-templates include overlapping portions. The precision of the first and second difference expressions is the fifth-order precision corresponding to the fifth-order format. A smoothing factor generation module is used to determine a dimensionless order function characterizing the smoothness of the flow field based on the first difference expression and the second difference expression, so as to construct a target smoothing factor using the order function and use the target smoothing factor to perform fifth-order accuracy shock wave capture on the aircraft; wherein, in the smooth region of the aircraft flow field, the smoothing factor is greater than a preset smoothing factor reference value; in the region containing shock waves or contact discontinuities, the smoothing factor is less than the preset smoothing factor reference value. Specifically, the smoothing factor generation module is used for: The flow field variable values ​​corresponding to the grid nodes in the discrete grid are processed using the first difference expression and the second difference expression respectively to obtain the corresponding first difference value and second difference value; The difference and result between the first difference value and the second difference value, as well as the difference result, are determined. Then, a preset square processing algorithm is used to process the difference and result and the difference result to obtain a dimensionless order function that characterizes the smoothness of the flow field. The flow field variable values ​​corresponding to each grid node in the discrete grid are processed using the order function to obtain the initial smoothing factor parameter, and the smooth region in the flow field of the aircraft is determined. Then, the initial smoothing factor parameter is increased in the smooth region to obtain the corresponding first smoothing factor parameter. The non-smooth regions in the flow field of the aircraft are identified, and the initial smooth factor parameter is reduced in the non-smooth regions to obtain the corresponding second smooth factor parameter, so as to determine the target smooth factor based on the first smooth factor parameter and the second smooth factor parameter; Among them, dimensionless order functions Obtained from the following relation: ； in, Let the order of the extreme point be . This represents the difference expression on the left side. This represents the difference expression on the right. To calculate the grid scale, i.e. the distance from j+1 to j, where j+1 and j are both nodes.

6. The fifth-order solvability factor construction device for aircraft shock wave capture according to claim 5, characterized in that, The difference expression generation module includes: An extended template generation unit is used to determine the windward direction of the local flow in the flow field of the aircraft, and to expand the mesh nodes on both sides of the initial template based on the windward direction to obtain an extended template; the extended template includes seven consecutive mesh nodes. The sub-template acquisition unit is used to determine the flow field variable values ​​corresponding to the seven grid nodes in the extended template, and to construct sub-templates for the initial template based on each flow field variable value and the windward direction, thereby obtaining a first sub-template biased towards the windward side and a second sub-template biased towards the downwind side; wherein, the first sub-template and the second sub-template include six grid nodes; The difference expression generation sub-unit is used to construct difference expressions for each grid node in the first sub-template and each grid node in the second sub-template using a preset linear combination algorithm, so as to obtain the corresponding first difference expression and second difference expression respectively.

7. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the fifth-order format smoothing factor construction method for aircraft shock wave capture as described in any one of claims 1 to 4.

8. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the fifth-order format smoothing factor construction method for aircraft shock wave capture as described in any one of claims 1 to 4.

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