A method, apparatus, device, and storage medium for optimizing wing geometry parameters.

Abstract

This application discloses a method, apparatus, device, and storage medium for optimizing wing geometry parameters, relating to the field of fluid numerical simulation technology. The method includes: determining the computational domain grid corresponding to the wing's geometry parameters, and determining the equivalent gas constants and pressure matching constants related to a low Mach number compressible fluid equivalent to air; performing numerical simulation based on the computational domain grid using a compressible solver to obtain aerodynamic performance data; the governing equations of the compressible solver are compressible Navier-Stokes equations constructed based on a conserved state equation compatible with the fully gas form and the sound speed formula; and optimizing the wing's geometry parameters based on the aerodynamic performance data to obtain a wing geometry model that meets preset aerodynamic performance conditions. This constructs a conserved compressible solver compatible with the fully gas form and requiring no solution to the Poisson equations, and improves the optimization efficiency of wing geometry parameters by combining numerical simulation of low Mach number compressible fluids.

Description

Technical Field

[0001] This invention relates to the field of fluid numerical simulation technology, and in particular to a method, apparatus, equipment and storage medium for optimizing wing geometry parameters. Background Technology

[0002] In the optimization of wing geometry parameters, repeated numerical simulations of the flow field are required to obtain aerodynamic performance data; therefore, the efficiency of the flow field solution directly affects the optimization efficiency. For aircraft takeoff, landing, and low-speed cruise, the incoming Mach number is typically no greater than 0.1, and the airflow can be approximated as incompressible. Existing incompressible flow solution methods usually require solving the pressure Poisson equation at each time step to satisfy the velocity field divergence constraint. As the mesh size or Reynolds number increases, the solution cost of the pressure Poisson equation increases significantly, becoming a major factor affecting computational efficiency. Furthermore, since the pressure Poisson equation is a globally coupled equation, its parallel computation efficiency is limited. Existing research shows that low-Mach number incompressible flow can be approximated as low-Mach number compressible flow and solved using the compressible Navier-Stokes equations, thus avoiding the solution of the pressure Poisson equation. However, traditional compressible solvers based on the ideal gas equation of state are difficult to directly apply to the simulation of low-Mach number incompressible flow.

[0003] Therefore, how to avoid solving the Poisson equation and achieve efficient numerical simulation of incompressible fluids at low Mach numbers is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method, apparatus, device, and storage medium for optimizing wing geometry parameters, constructing a conserved compressible solver compatible with completely gaseous forms and requiring no solution to the Poisson equations; and realizing a numerical model for low Mach number compressible fluids, which can improve the efficiency of wing geometry parameter tuning. The specific scheme is as follows: In a first aspect, this application provides a method for optimizing wing geometry parameters, including: The computational domain mesh corresponding to the geometric parameters of the wing is determined, and the equivalent gas constant and pressure matching constant related to the low Mach number compressible fluid equivalent to air are determined; the low Mach number is defined as a Mach number not greater than 0.1. Based on the computational domain grid, a compressible solver is used to perform numerical simulation of the low Mach number compressible fluid to obtain the aerodynamic performance data of the wing. The governing equations of the compressible solver are the compressible Navier-Stokes equations, which are constructed based on the conservation equations of state compatible with the complete gas form and the corresponding sound speed formula, and are used to adapt to the numerical simulation of the low Mach number compressible fluid. The geometric parameters of the wing are optimized based on the aerodynamic performance data until a wing geometric model that meets the preset aerodynamic performance conditions is obtained.

[0005] Optionally, determining the equivalent gas constant and pressure matching constant related to the low Mach number compressible fluid equivalent to air includes: Based on the rigid gas model, determine the equation of state framework for air that is compatible with the complete gas form; The equivalent gas constant corresponding to the state equation framework is determined by combining the environmental conditions, and the pressure matching constant corresponding to the state equation framework is determined by combining the pressure conditions at low Mach numbers. Accordingly, the conservation equation of state is the equation of state obtained by substituting the equivalent gas constant and the pressure matching constant into the equation of state framework.

[0006] Optionally, the numerical simulation of the low Mach number compressible fluid using a compressible solver includes: Based on the low Mach number compressible fluid, the finite volume method is used to spatially discretize the control equations of the compressible solver to obtain the corresponding discretized control equations. The discretized control equations are explicitly integrated using an explicit third-order time integration method to achieve numerical simulation of the low Mach number compressible fluid.

[0007] Optionally, the calculation process of the inviscid flux corresponding to the spatial discretization operation includes: The original variable vectors corresponding to the current grid cells of the computational domain grid are reconstructed on the target interface using a fifth-order weighted essentially non-oscillating scheme to obtain the state on the left side and the state on the right side of the interface. Estimate the left wave velocity, right wave velocity, and middle wave velocity based on the states on the left and right sides of the interface. The wave system region where the target interface is located is determined based on the numerical signs of the left wave velocity, the right wave velocity, and the middle wave velocity. Conserved variables and physical channels are selected from the state on the left side of the interface and the state on the right side of the interface to calculate the inviscid flux.

[0008] Optionally, the discretization process of the viscous flux corresponding to the spatial discretization operation includes: The velocity gradient tensor is obtained by calculating the original variable data corresponding to the current grid cell of the computational domain grid using a 14th-order central difference scheme. The divergence of the viscous flux constructed from the velocity gradient tensor is calculated using a 10th-order central difference scheme to obtain the corresponding viscous stress divergence.

[0009] Optionally, the discretization process of the viscous flux corresponding to the spatial discretization operation includes: The original variable data corresponding to the current grid cell of the computational domain grid are calculated using a 14th-order central difference scheme, and the viscous flux is constructed using the calculated velocity gradient tensor. A global Lax-Friedrichs flux split is performed on the viscous flux to obtain the corresponding positive flux component and negative flux component; The positive flux component and the negative flux component are reconstructed using a fifth-order weighted essentially non-oscillatory scheme, and the divergence value of the viscous flux is calculated based on the reconstructed flux components.

[0010] Optionally, the step of using an explicit third-order time integration method to explicitly integrate the discrete control equations to achieve numerical simulation of the low Mach number compressible fluid includes: Determine the right-hand side terms of the governing equations for the current time level; Based on the right-hand side and the time step, a third-order Runge-Kutta scheme with decreasing total variation is used to perform conservation variable updates, thereby realizing the numerical simulation of the low Mach number compressible fluid; the time step is a time step determined based on a preset Courant number.

[0011] Secondly, this application provides a wing geometry parameter optimization device, comprising: The data determination module is used to determine the computational domain grid corresponding to the geometric parameters of the wing, and to determine the equivalent gas constant and pressure matching constant related to the low Mach number compressible fluid equivalent to air; the low Mach number is Mach number not greater than 0.1; The numerical simulation module is used to perform numerical simulation of the low Mach number compressible fluid based on the computational domain grid and a compressible solver to obtain the aerodynamic performance data corresponding to the wing. The governing equations of the compressible solver are the compressible Navier-Stokes equations, which are constructed based on the conservation equations of state compatible with the completely gas form and the corresponding sound speed formula, and are used to adapt to the numerical simulation of the low Mach number compressible fluid. The tuning module is used to tune the geometric parameters of the wing based on the aerodynamic performance data until a wing geometric model that meets the preset aerodynamic performance conditions is obtained.

[0012] Thirdly, this application provides an electronic device, comprising: Memory, used to store computer programs; A processor for executing the computer program to implement the wing geometry optimization method described above.

[0013] Fourthly, this application provides a computer-readable storage medium for storing a computer program that, when executed by a processor, implements the wing geometry parameter optimization method described above.

[0014] Therefore, this application first determines the computational domain grid corresponding to the wing's geometric parameters, and determines the equivalent gas constant and pressure matching constant related to the low Mach number compressible fluid equivalent to air; the low Mach number is defined as a Mach number not greater than 0.1; then, based on the computational domain grid, a compressible solver is used to numerically simulate the low Mach number compressible fluid to obtain the aerodynamic performance data corresponding to the wing; the governing equation of the compressible solver is the compressible Navier-Stokes equation, and the compressible Navier-Stokes equation is constructed based on a conservation-type state equation compatible with the fully gas form and the corresponding sound speed formula, used to adapt to the numerical simulation of the low Mach number compressible fluid; then, based on the aerodynamic performance data, the wing's geometric parameters are optimized until a wing geometric model that meets the preset aerodynamic performance conditions is obtained. In this way, this application can equate air to a low Mach number compressible fluid, and construct a conserved compressible solver that is compatible with the completely gaseous form and does not require solving the Poisson equation; thus, numerical simulation of low Mach number compressible fluids is realized, which effectively improves computational efficiency; and the wing geometry parameters are dynamically adjusted and optimized based on the numerical simulation results, thereby improving overall efficiency. Attached Figure Description

[0015] 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.

[0016] Figure 1 This is a flowchart of a wing geometry parameter optimization method disclosed in this application; Figure 2 This is a schematic diagram of a specific viscous flux discretization scheme disclosed in this application; Figure 3 This is a schematic diagram of another specific viscous flux discretization scheme disclosed in this application; Figure 4This is a flowchart of a numerical simulation method for incompressible flow without Poisson equations based on a rigid gas model disclosed in this application. Figure 5 This application discloses a velocity distribution diagram in the x-direction of a top-cover driven cavity flow. Figure 6 This is another velocity distribution diagram in the cross-x direction of the top cover driven cavity flow disclosed in this application; Figure 7 This is another type of velocity distribution diagram in the cross-x direction of the top cover driven cavity flow disclosed in this application; Figure 8 This is a cross-sectional velocity distribution diagram in the x-direction of a top cover driven cavity flow disclosed in this application; Figure 9 This is a comparison of CPU time between Riemann DNS and Vortex DNS solvers at different Reynolds numbers as disclosed in this application; Figure 10 This is a comparison diagram of the U-component velocity distribution under different grid resolutions disclosed in this application; Figure 11 This is a comparison of CPU times between Riemann DNS and Vortex DNS solvers at different grid resolutions, as disclosed in this application. Figure 12 This is a comparison chart of the computational errors of the Riemann DNS and Vortex DNS solvers at different grid resolutions disclosed in this application; Figure 13 This is a schematic diagram of a wing geometry parameter optimization device disclosed in this application; Figure 14 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0017] 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.

[0018] See Figure 1 As shown, this embodiment of the invention discloses a method for optimizing wing geometry parameters, including: Step S11: Determine the computational domain grid corresponding to the geometric parameters of the wing, and determine the equivalent gas constant and pressure matching constant related to the low Mach number compressible fluid equivalent to air; the low Mach number is Mach number not greater than 0.1.

[0019] It should be noted that during takeoff, landing, or low-speed cruise, the incoming Mach number of an aircraft is typically no greater than 0.1, at which point the airflow can be approximated as incompressible. To achieve efficient numerical simulation of low-Mach number airflow, this application uses a rigid gas equation of state instead of the ideal gas equation of state, and maps the rigid gas equation of state to a form compatible with the complete gas form, so as to be compatible with commonly used compressible solvers.

[0020] In a specific embodiment, to adapt the rigid gas model to a compressible solver built on the ideal gas equation of state, a state equation framework compatible with the complete gas form is first constructed based on the rigid gas model, and the fluid compressibility is adjusted by introducing stiffness parameters and equivalent specific heat ratio. Then, the equivalent gas constant and pressure matching constant corresponding to the state equation framework are determined according to the reference environmental conditions. Furthermore, the equivalent gas constant and the pressure matching constant are substituted into the state equation framework to construct a conserved state equation. Based on the conserved state equation and the corresponding sound velocity relationship, a compressible solver suitable for numerical simulation of low Mach number flows can be constructed.

[0021] Step S12: Based on the computational domain grid, a compressible solver is used to perform numerical simulation of the low Mach number compressible fluid to obtain the aerodynamic performance data corresponding to the wing; the governing equation of the compressible solver is the compressible Navier-Stokes equation, and the compressible Navier-Stokes equation is constructed based on the conservation-type state equation compatible with the completely gas form and the corresponding sound speed formula, which is used to adapt to the numerical simulation of the low Mach number compressible fluid.

[0022] In this application, the computational domain grid corresponding to the wing and the equivalent gas constants and pressure matching constants related to equating air to a low Mach number compressible fluid can be obtained through the above steps. Further combining the equivalent gas constants and pressure matching constants yields the governing equations for numerical simulation of low Mach number compressible fluids, namely the compressible Navier-Stokes equations. It should be noted that the compressible Navier-Stokes equations are constructed based on a conservation-type equation of state compatible with the fully gaseous form and the corresponding sound velocity formula. The conservation-type equation of state establishes a direct mapping relationship between pressure and conserved variables, allowing pressure to be directly calculated from local conserved variables without constructing and solving the pressure Poisson equation, thus adapting to the numerical simulation of low Mach number compressible fluids. Furthermore, a compressible solver based on these compressible Navier-Stokes equations is used to perform numerical simulations of low Mach number compressible fluids within the computational domain grid; thus, aerodynamic performance data related to the wing can be obtained through numerical simulation of the flow field around the wing. Aerodynamic performance data may include wing surface pressure distribution, boundary layer velocity profile, lift coefficient, drag coefficient, etc.

[0023] In one specific embodiment, during the numerical simulation of the low Mach number compressible fluid using a compressible solver, the control equations of the compressible solver are first spatially discretized using the finite volume method based on the low Mach number compressible fluid, resulting in the corresponding discretized control equations. Then, an explicit third-order time integration method is used to explicitly integrate the discretized control equations in time, thus achieving the numerical simulation of the low Mach number compressible fluid. Specifically, the finite volume method can be used to discretize on a Cartesian uniform grid, involving inviscid flux discretization and viscous flux discretization; viscous flux involves the first derivative (velocity gradient) and the second derivative (divergence). After spatial discretization, time progression is performed using an explicit third-order time integration method, updating the conserved variables of all grid cells in each time step to achieve the numerical simulation of the low Mach number compressible fluid.

[0024] In one specific embodiment, the calculation process of inviscid flux corresponding to spatial discretization operations first reconstructs the original variable vector corresponding to the current grid cell of the computational domain grid at the target interface using a fifth-order weighted essentially non-oscillatory scheme, obtaining the state on the left and right sides of the interface. Then, the left, right, and middle wave velocities are estimated based on these states. Next, the wave system region where the target interface is located is determined based on the numerical signs of the left, right, and middle wave velocities. Conserved variables and physical channels are selected from the left and right states to calculate the inviscid flux. It is understood that by selecting a fifth-order weighted essentially non-oscillatory scheme to reconstruct the original variable vector at the common boundary of adjacent grid cells, using five candidate templates, and calculating the interpolation polynomial and its smoothness metric on each template, the states on the left and right sides of the interface can be obtained through weighted combination, i.e., the states on the left and right sides of the interface. It is understood that weighting allows for automatic selection of the optimal combination to achieve fifth-order accuracy in smooth regions, and can automatically reduce the order near discontinuities to avoid overshooting due to fixed-amplitude oscillations. Next, density, pressure, and normal velocity data are extracted from the states on the left and right sides of the interface to calculate the sound velocity on the left and right sides, as well as the wave velocity on the left, right, and center. Finally, during numerical flux calculation, the wave system region in which the interface is located is determined based on the numerical signs of the left, right, and center wave velocities. Corresponding conserved variables and physical fluxes are then selected from the states on the left and right sides of the interface to calculate the inviscid flux. This inviscid flux is used for subsequent updates to the conserved variables.

[0025] In one specific embodiment, the discretization process of the viscous flux corresponding to the spatial discretization operation involves the first derivative (velocity gradient) and the second derivative (divergence), which can be achieved using an alternating-order central difference method or a hybrid central difference method. Specifically, the alternating-order central difference method involves using a 14th-order central difference scheme to calculate the original variable data corresponding to the current grid cell of the computational domain grid to obtain the velocity gradient tensor; then, a 10th-order central difference scheme is used to calculate the divergence of the viscous flux constructed from the velocity gradient tensor to obtain the corresponding viscous stress divergence. Specifically, the first derivative is used to construct the viscous stress tensor; the velocity gradient is calculated using a 14th-order central difference scheme, and the output is the velocity gradient tensor; the obtained velocity gradient tensor can then be used to construct the viscous stress tensor; finally, a 10th-order central difference scheme is used to calculate the divergence of the viscous stress tensor. It is understood that using different orders in the viscous flux discretization process can avoid the problem of severe oscillations near discontinuities in all-order central difference methods. Furthermore, the hybrid central difference method refers to using a 14th-order central difference scheme to calculate the original variable data corresponding to the current grid cell of the computational domain grid, and constructing a viscous flux using the calculated velocity gradient tensor; then, performing global Lax-Friedrichs flux splitting on the viscous flux to obtain the corresponding positive and negative flux components; then, using a fifth-order weighted essentially non-oscillatory scheme to reconstruct the positive and negative flux components respectively, and calculating the divergence value of the viscous flux based on the reconstructed flux components. It can be seen that the moderate central difference still uses a 14th-order central difference to calculate the velocity gradient to obtain the viscous flux; then, global Lax-Friedrichs flux splitting is performed, with the viscous flux as input and the positive and negative flux components as output; compared with local Lax-Friedrichs (taking the local maximum characteristic velocity at each interface), global Lax-Friedrichs is simpler, has less computational cost, and avoids point-by-point calculation of eigenvalues. Subsequently, a fifth-order weighted, inherently non-oscillatory scheme is used to reconstruct the positive and negative flux components separately, yielding two reconstructed flux components, which can also be combined to obtain the interface flux component. The divergence is approximated by the interface flux difference quotient, i.e., the divergence value of the viscous flux is calculated; specifically, the divergence is approximated by dividing the difference in interface flux by the grid spacing. This method more naturally matches the "flux balance" concept of the finite volume method. Understandably, discretizing the viscous flux using a 14th-order central difference scheme, global Lax-Friedrichs flux splitting, and a fifth-order weighted, inherently non-oscillatory scheme can maintain high accuracy while better suppressing numerical oscillations near flow discontinuities.

[0026] In another specific embodiment, during the time-progression of the discretized state equations to achieve numerical simulation of low Mach number compressible fluids, at the current time level, the right-hand side of the governing equations is assembled based on the inviscid flux, viscous flux, and source terms calculated in the aforementioned spatial discretization steps. The time step is determined according to a pre-set Courant-Friedrichs-Lewy (CFL), which can be set to 0.1. It is understood that the CFL is a numerical stability criterion, quantifying whether the time step meets the numerical stability requirements. Then, a third-order Runge-Kutta scheme with decreasing total variation is used to update the conserved variables, propelling them from the current time level to the next, thus achieving numerical simulation of low Mach number compressible fluids. Furthermore, the time-progression process can repeat the above steps until a preset termination time is reached or the convergence criterion is met. It is understandable that the third-order TVD Runge-Kutta (Third-order Runge-Kutta Total Variation Diminishing) scheme satisfies the property that the total variation does not increase. That is, for any time step, when the CFL condition is met, the total variation of the numerical solution will not increase with time, thus ensuring the stability of the calculation process.

[0027] Step S13: Optimize the geometric parameters of the wing based on the aerodynamic performance data until a wing geometric model that meets the preset aerodynamic performance conditions is obtained.

[0028] This application, through the aforementioned steps, can obtain aerodynamic performance data related to the wing through numerical simulation of low Mach number compressible fluids. This aerodynamic performance data can then be used as an evaluation basis, with the optimization objectives of suppressing boundary layer separation or improving the lift-to-drag ratio, to fine-tune the wing's geometric parameters. For example, gradient descent or adjoint algorithms can be used to calculate corrections for parameters such as airfoil curvature and wingtip shape, thereby achieving the fine-tuning of the wing's geometric parameters. By repeating the above parameter tuning steps until the changes in the continuously obtained aerodynamic performance data are less than a certain threshold and the flow field residuals meet the convergence criteria, the tuning can be considered complete, and the final optimized wing geometric model can be output.

[0029] Therefore, this application can equate air to a low Mach number compressible fluid, constructing a conserved compressible solver compatible with the completely gaseous form that does not require solving the Poisson equation. This avoids the problem of the condition number deteriorating with mesh refinement and Reynolds number increases. The computational cost per time step is fixed and linearly related only to the mesh size. It realizes numerical simulation of low Mach number compressible fluids, eliminates the need for global Poisson communication, and performs only local mesh calculations in a single step, resulting in a large-scale parallel efficiency improvement. Furthermore, it dynamically adjusts and optimizes the wing geometry parameters based on the numerical simulation results, further enhancing overall efficiency.

[0030] The above embodiments, combined with wing geometry parameter optimization, introduce the numerical simulation process of incompressible flow without Poisson's equations. This is applicable to engineering optimization scenarios requiring repeated flow field calculations, such as wing shape optimization for civil aviation aircraft or low-speed UAVs, or engineering scenarios involving incompressible flow, such as ship hull drag reduction optimization, low-speed aerodynamic design of wind turbine blades, and hydraulic flood discharge flow field simulation. The following embodiments will detail the numerical simulation process of incompressible flow without Poisson's equations from six aspects: mathematical model, key transformations, spatial discretization, time progression, implementation steps, and verification cases. Specifically, this includes: In mathematical modeling, this actually refers to constructing the governing equations in a conserved form; solving the conserved form of the three-dimensional compressible Navier-Stokes equations: ; in, For a vector of conserved variables, ,in Let be density, u, v, w be velocity components, E be total energy per unit volume, and t be time. , , Let x, y, and z be the inviscid fluxes, respectively. For viscous flux, it includes the velocity gradient term; It is a viscous dissipation source term that acts only on the energy equation and includes heat conduction and viscous dissipation work.

[0031] It should be noted that this application uses the same governing equations as the standard compressible solver, but replaces the ideal gas equation of state with a rigid gas equation of state. Furthermore, regarding the dimensional transformation between the rigid gas model and the complete gas model: it is necessary to map the rigid gas (air) to the complete gas form required by the conservation solver, i.e., to find an equivalent... (Specific heat ratio), equivalent gas constant R, and additional pressure offset constant Specifically, from the formula for the speed of sound of a perfect gas... Inverse calculation of equivalent reference pressure (Taking room temperature and pressure water as an example): ; in, For equivalent specific heat ratio, For density.

[0032] Accordingly, take the ambient temperature From the ideal gas law The equivalent gas constant can be obtained: ; Given the gas constant of air ,but: ; Right now .

[0033] Furthermore, a pressure matching constant is introduced. To meet the pressure conditions at low Mach numbers, so that... ,temperature At that time, the calculated pressure equals the ambient pressure. : ; Finally, the state equation in the form of conserved variables is derived. Total energy. ,in Let be the kinetic energy and e be the specific internal energy. The internal energy relationship of a perfect gas is: ; However, here the pressure needs to be adjusted by offset. ,Right now , can be obtained This equation is the rigid gas equation of state used in compressible solvers. It should be noted that, similar to the Tait-type rigid gas model, it can realize that "a small change in density causes a significant change in pressure" and can be converted to... All of these equations can be used to replace the ideal gas law.

[0034] Accordingly, for rigid gases, the speed of sound needs to be corrected to: ; We can obtain: ; Understandably, the solver only needs to know the conserved variables. Pressure p and sound velocity c can be calculated directly without any iteration.

[0035] The next step is the spatial discretization stage of the numerical simulation; specifically, the finite volume method is used for discretization on a Cartesian uniform grid. Conserved variables are stored at the center (i, j, k) of each grid cell. Integrating at the center of the unit yields the semi-discrete form of the conserved variables.

[0036] For inviscid flux calculation in a discrete process, taking the x-direction as an example (the y and z directions are similar), the original variables are first reconstructed, specifically the original variable vector. A fifth-order WENO (Weighted Essentially Non-Oscillatory, referring to fifth-order spatial reconstruction) reconstruction is performed at interface i+1 / 2, where T is the transpose. It should be noted that besides WENO5, WENO7, WENO-Z, and linear reconstruction (in smooth flow) can also be used. WENO5 uses five candidate templates (each containing three elements), calculates the interpolation polynomial and its smoothness metric (oscillation index) on each template, and then obtains the states on the left and right sides of the interface through nonlinear weighted combination. and The weighting coefficients enable automatic selection of the optimal combination to achieve fifth-order accuracy in smooth regions, and automatic reduction of order near discontinuities to avoid overshooting during fixed-amplitude oscillations. Then, wave velocity estimation is performed, with the left wave velocity... and right wave speed as follows: ; intermediate wave speed as follows: ; in, For the speed of sound The superscripts L and R represent the states on the left and right sides of the interface, respectively. Normal velocity; Density; For pressure.

[0037] Based on wave velocity partitioning, numerical flux can be defined as: ; Among them, intermediate flux The compact expression of Johnsen & Colonius (2006) is adopted. It should be noted that the HLLC (Harten-Lax-van Leer Contact) approximate Riemann solver can be used to calculate the interface numerical flux, or the Roe format, HLL format, and AUSM+ series formats can be used to calculate the interface numerical flux.

[0038] Furthermore, the discretization of viscous flux involves the first derivative (velocity gradient) and the second derivative (divergence). This embodiment introduces two high-order schemes, both of which avoid numerical oscillations and achieve high accuracy. Scheme A is an alternating-order central difference method, where the order of the central difference can be adjusted according to accuracy requirements. Specifically, it includes 14th-order and 10th-order central differences, such as... Figure 2 In (a), the template is of order 14 (N=7, nodes i-7 to i+7). Figure 2 In example (b), the template is a 10th-order template (N=5, nodes i-5 to i+5). Specifically, the first derivative (used to construct the viscous stress tensor) uses a 14th-order central difference, and the second derivative (viscous stress divergence) uses a 10th-order central difference. This scheme A has approximate spectral accuracy in smooth flow fields, and due to the different orders, it avoids the problem of severe oscillations near discontinuities that occur in all central differences of the same order.

[0039] Correspondingly, Scheme B is a hybrid central difference + GLF (using a splitting method with global maximum wave velocity) - WENO5, specifically including 14th-order central difference, global Lax-Friedrichs flux splitting, and fifth-order weighted essentially non-oscillatory (WENO5) reconstruction, such as... Figure 3 In the template (a), the central difference template of order 14 is shown. Figure 3 (b) in the diagram represents the WENO5 reconstruction template. This scheme B is suitable for regions with weak discontinuities or high gradients. The specific steps are as follows: The velocity gradient is calculated using the 14th-order central difference method to obtain the viscous flux. GLF splitting of viscous flux: ; in, Take the maximum characteristic velocity of the entire computational domain (global Lax-Friedrichs).

[0040] Then use WENO5 to reconstruct the interface. and ,right Using a right-skewed template (WENO5+), for A left-skewed template (WENO5-) is used. It should be noted that GLF splitting can be replaced by Steger-Warming splitting (eigenvalue splitting based on the flux Jacobian matrix) or Van Leer splitting (splitting based on the Mach number); WENO5 (a fifth-order weighted essentially non-oscillatory scheme) can be replaced by ENO4 (a fourth-order essentially non-oscillatory scheme) or a compact scheme.

[0041] Finally, the divergence of viscous flux is approximated by the quotient of the interfacial flux difference. It is understandable that Scheme B, while maintaining high accuracy, can better suppress numerical oscillations near flow discontinuities.

[0042] Furthermore, during the time-stepping phase of the numerical simulation, a third-order TVD Runge-Kutta scheme (RK3-TVD) can be used for explicit time integration, balancing stability and accuracy. Time step size. Controlled by CFL number: Take here This is to ensure the stability of flows at low Mach numbers (Ma≤0.1). It should be noted that in addition to the third-order TVD Runge-Kutta scheme, second-order TVD Runge-Kutta, fourth-order explicit Runge-Kutta, low-storage Runge-Kutta (such as third-order 3-step), and even implicit schemes (such as LU-SGS, but care should still be taken to avoid the Poisson equation) can also be used.

[0043] It should be noted that compressible flow asymptotically converges to incompressible flow at low Mach numbers. Quantitatively, when At that time, density perturbation Pressure disturbance The density tends to a constant, and the velocity divergence tends to zero. Therefore, as long as the Mach number in the simulation is ≤0.1, the error between the solution of the compressible solver and the incompressible equation is within an acceptable range. Furthermore, in addition to Cartesian uniform grids, it can also be extended to curvilinear coordinates or unstructured grids, and the discretization of inviscid and viscous fluxes maintains the aforementioned high-order accuracy processing method.

[0044] In one specific embodiment, such as Figure 4 The flowchart shown is a numerical simulation method for incompressible flow without Poisson equations based on a rigid gas model. Taking room temperature water as an example, the method first initializes the parameters by setting the rigid gas parameters according to the room temperature water. Calculate the equivalent gas constant Pressure matching constant Set the computational domain size and the number of grid cells. Reynolds number (Re) and CFL number. Given an initial velocity field. and temperature field (or pressure field). Calculate the initial density using the equation of state. and total energy During the numerical simulation, each time step is iterated: Update boundary conditions (such as the moving wall velocity of the top cover driving cavity); Calculate the inviscid flux (WENO5+HLLC); Calculate the viscous flux (choose option A or B); Calculate the source terms (thermal conduction and viscous dissipation); Perform RK3-TVD time advance and update the conserved variables of all grid cells. ; Calculating pressure using the rigid gas law. ; Check if the termination time has been reached; if not, continue.

[0045] The final output includes velocity field, pressure field, vorticity field, etc.

[0046] In another specific embodiment, taking the top cover driving cavity flow as an example, the computational domain is: , grid Top cover speed Other walls are stationary; Reynolds numbers Re = 100, 400, 1000, 3200; Initial conditions: global velocity is zero, pressure is uniform p = A (ambient pressure); CFL = 0.1; total simulation time... The flow was brought to a steady state; the results were compared with benchmark data such as those from Ghia et al. (1982) (a paper in computational fluid dynamics, referred to as the benchmark data in that paper) to verify accuracy. The corresponding verification results show a comparison of the velocity distribution in the x-direction of the flow driven by the top cover in the cavity. Figure 5 (Re=100) Figure 6 (Re=400) Figure 7 (Re=1000) and Figure 8 As shown in (Re=3200); a comparison of CPU (Central Processing Unit) times for Riemann DNS (solving the Riemann problem and calculating numerical flux, denoted as Riemann numerical simulation) and Vortex DNS (solving the vortex equation and calculating velocity from vortex, denoted as vortex numerical simulation) solvers at different Reynolds numbers. Figure 9 As shown, DNS refers to Direct Numerical Simulation. It can be seen that in the top-cover driven cavity flow (128² mesh, Re=3200), the CPU time of the proposed solution is only 6.1% of that of the traditional incompressible solver VortexDNS. Compared with the Ghia benchmark solution and analytical solution, the L1 error at the 128² mesh is on the same order of magnitude as the traditional high-precision solver, and shows a monotonically converging trend with mesh refinement.

[0047] In yet another specific embodiment, taking the Taylor-Green vortex as an example, the computational domain Periodic boundary; initial velocity field , The Reynolds number Re=100 was used for numerical simulation up to t=0.5. The error was compared with the analytical solution to verify the mesh convergence. The velocity distribution of the U component was compared under different mesh resolutions, such as... Figure 10 As shown; Figure 11A comparison of the computational errors of the Riemann DNS and Vortex DNS solvers at different grid resolutions, such as Figure 12 The figure shows a comparison of CPU time between the Riemann DNS and Vortex DNS solvers at different mesh resolutions. It can be seen that in the Taylor-Green vortex (512² mesh), the CPU time of the proposed solution is only 7.7% of that of the traditional incompressible solver VortexDNS. The denser the mesh and the higher the Reynolds number, the more significant the advantage.

[0048] Therefore, the technical solution of this application can be equivalent to a low Mach number compressible fluid, constructing a conserved compressible solver compatible with the completely gaseous form and requiring no solution of the Poisson equation. This avoids the problem of condition number deteriorating with mesh refinement and Re, and the computational cost at each time step is fixed, linearly related only to the mesh size. It achieves numerical simulation of low Mach number compressible fluids, eliminates the need for Poisson global communication, and performs only local mesh calculations in a single step, resulting in significant improvements in large-scale parallel efficiency. Furthermore, it proposes two high-order schemes: a 14th-order + 10th-order central difference scheme and a 14th-order central difference scheme + GLF-WENO5 scheme, meeting the accuracy requirements of direct numerical simulation. In this embodiment, Ma is constrained to ≤0.1, and convergence is verified through classical incompressible examples (top-cover driven cavity flow, Taylor-Green vortex).

[0049] like Figure 13 As shown, this embodiment discloses a wing geometry parameter optimization device, including: The data determination module 11 is used to determine the computational domain grid corresponding to the geometric parameters of the wing, and to determine the equivalent gas constant and pressure matching constant related to the low Mach number compressible fluid equivalent to air; the low Mach number is a Mach number not greater than 0.1. The numerical simulation module 12 is used to perform numerical simulation of the low Mach number compressible fluid based on the computational domain grid and a compressible solver to obtain the aerodynamic performance data corresponding to the wing; the governing equation of the compressible solver is the compressible Navier-Stokes equation, and the compressible Navier-Stokes equation is constructed based on the conservation equation of state compatible with the completely gas form and the corresponding sound speed formula, which is used to adapt to the numerical simulation of the low Mach number compressible fluid; The tuning module 13 is used to tune the geometric parameters of the wing based on the aerodynamic performance data until a wing geometric model that meets the preset aerodynamic performance conditions is obtained.

[0050] Therefore, this application can be equivalent to air as a low Mach number compressible fluid, and constructs a conserved compressible solver that is compatible with the completely gas form and does not require solving the Poisson equation; thus, a numerical model of low Mach number compressible fluid is realized, which effectively improves the computational efficiency; and the wing geometry parameters are dynamically adjusted and optimized based on the numerical simulation results, thereby improving the overall efficiency.

[0051] In one specific embodiment, the data determination module 11 may include: The equation of state framework determination unit is used to determine the equation of state framework for air that is compatible with the complete gas form, based on the rigid gas model. The constant calibration unit is used to determine the equivalent gas constant corresponding to the state equation framework in combination with the environmental conditions, and to determine the pressure matching constant corresponding to the state equation framework in combination with the pressure conditions at low Mach numbers; accordingly, the conservation state equation is the state equation obtained by substituting the equivalent gas constant and the pressure matching constant into the state equation framework.

[0052] In one specific embodiment, the numerical simulation module 12 may include: The spatial discretization submodule is used to perform spatial discretization on the control equations of the compressible solver based on the low Mach number compressible fluid using the finite volume method, so as to obtain the corresponding discretized control equations. The time integration submodule is used to perform explicit time integration on the discrete control equations using an explicit third-order time integration method, thereby realizing the numerical simulation of the low Mach number compressible fluid.

[0053] In one specific embodiment, the spatial discrete submodule may include: The variable vector reconstruction unit is used to reconstruct the original variable vector corresponding to the current grid cell of the computational domain grid on the target interface using a fifth-order weighted essentially non-oscillating scheme, so as to obtain the state on the left side of the interface and the state on the right side of the interface. An estimation unit is used to estimate the left wave velocity, right wave velocity, and middle wave velocity based on the state of the left side of the interface and the state of the right side of the interface. The inviscid flux calculation unit is used to determine the wave system region where the target interface is located based on the numerical signs of the left wave velocity, the right wave velocity, and the middle wave velocity, and to select conserved variables and physical channels from the state on the left side of the interface and the state on the right side of the interface to calculate the inviscid flux.

[0054] In another specific embodiment, the spatial discrete submodule may include: The velocity gradient calculation unit is used to calculate the original variable data corresponding to the current grid cell of the computational domain grid using a 14th-order central difference scheme to obtain the velocity gradient tensor. The viscous stress divergence calculation unit is used to calculate the divergence of the viscous flux constructed from the velocity gradient tensor using a 10th-order central difference scheme to obtain the corresponding viscous stress divergence.

[0055] In yet another specific embodiment, the spatially discrete submodule may include: The viscous flux construction unit is used to calculate the original variable data corresponding to the current grid cell of the computational domain grid using a 14th-order central difference scheme, and to construct the viscous flux using the calculated velocity gradient tensor. The flux splitting unit is used to perform global Lax-Friedrichs flux splitting on the viscous flux to obtain corresponding positive flux components and negative flux components; The divergence value calculation unit is used to reconstruct the positive flux component and the negative flux component using a fifth-order weighted essentially non-oscillatory scheme, and to calculate the divergence value of the viscous flux based on the reconstructed flux components.

[0056] In one specific embodiment, the numerical simulation module 12 may include: The right-hand side term determination unit is used to determine the right-hand side terms of the governing equations at the current time level; The numerical simulation unit is used to perform conservation variable update operations using the third-order Runge-Kutta scheme with decreasing total variation based on the right-hand side and the time step, thereby realizing the numerical simulation of the low Mach number compressible fluid; the time step is a time step determined based on a preset Courant number.

[0057] Furthermore, embodiments of this application also disclose an electronic device, Figure 14 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.

[0058] Figure 14 This is a schematic diagram of the structure of an electronic device 20 provided in an embodiment 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 wing geometry parameter optimization method disclosed in any of the foregoing embodiments. Alternatively, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0059] 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.

[0060] 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.

[0061] 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 wing geometry parameter optimization method executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0062] 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 wing geometry parameter optimization method. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0063] 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.

[0064] 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.

[0065] 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.

[0066] 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.

[0067] 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 intended to help 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 optimizing wing geometry parameters, characterized in that, include: The computational domain mesh corresponding to the geometric parameters of the wing is determined, and the equivalent gas constant and pressure matching constant related to the low Mach number compressible fluid equivalent to air are determined; the low Mach number is defined as a Mach number not greater than 0.

1. Based on the computational domain grid, a compressible solver is used to perform numerical simulation of the low Mach number compressible fluid to obtain the aerodynamic performance data of the wing. The governing equations of the compressible solver are the compressible Navier-Stokes equations, which are constructed based on the conservation equations of state compatible with the complete gas form and the corresponding sound speed formula, and are used to adapt to the numerical simulation of the low Mach number compressible fluid. The geometric parameters of the wing are optimized based on the aerodynamic performance data until a wing geometric model that meets the preset aerodynamic performance conditions is obtained. The determination of the equivalent gas constant and pressure matching constant related to the low Mach number compressible fluid equivalent to air includes: Based on the rigid gas model, determine the equation of state framework for air that is compatible with the complete gas form; The equivalent gas constant corresponding to the state equation framework is determined by combining the environmental conditions, and the pressure matching constant corresponding to the state equation framework is determined by combining the pressure conditions at the low Mach number. The conservation equation of state is the equation of state obtained by substituting the equivalent gas constant and the pressure matching constant into the equation of state framework. The conservation equation of state is as follows: ； Where p is the pressure, This is the equivalent specific heat ratio, where E is the total energy per unit volume and K is the kinetic energy. This is the pressure matching constant; The speed of sound is: ； Where c is the speed of sound For density.

2. The wing geometry parameter optimization method according to claim 1, characterized in that, The numerical simulation of the low Mach number compressible fluid using a compressible solver includes: Based on the low Mach number compressible fluid, the finite volume method is used to spatially discretize the control equations of the compressible solver to obtain the corresponding discretized control equations. The discretized control equations are explicitly integrated using an explicit third-order time integration method to achieve numerical simulation of the low Mach number compressible fluid.

3. The wing geometry parameter optimization method according to claim 2, characterized in that, The calculation process of the inviscid flux corresponding to the spatial discretization operation includes: The original variable vectors corresponding to the current grid cells of the computational domain grid are reconstructed on the target interface using a fifth-order weighted essentially non-oscillating scheme to obtain the state on the left side and the state on the right side of the interface. Estimate the left wave velocity, right wave velocity, and middle wave velocity based on the states on the left and right sides of the interface. The wave system region where the target interface is located is determined based on the numerical signs of the left wave velocity, the right wave velocity, and the middle wave velocity. Conserved variables and physical channels are selected from the state on the left side of the interface and the state on the right side of the interface to calculate the inviscid flux.

4. The wing geometry parameter optimization method according to claim 2, characterized in that, The discretization process of the viscous flux corresponding to the spatial discretization operation includes: The velocity gradient tensor is obtained by calculating the original variable data corresponding to the current grid cell of the computational domain grid using a 14th-order central difference scheme. The divergence of the viscous flux constructed from the velocity gradient tensor is calculated using a 10th-order central difference scheme to obtain the corresponding viscous stress divergence.

5. The wing geometry parameter optimization method according to claim 2, characterized in that, The discretization process of the viscous flux corresponding to the spatial discretization operation includes: The original variable data corresponding to the current grid cell of the computational domain grid are calculated using a 14th-order central difference scheme, and the viscous flux is constructed using the calculated velocity gradient tensor. A global Lax-Friedrichs flux split is performed on the viscous flux to obtain the corresponding positive flux component and negative flux component; The positive flux component and the negative flux component are reconstructed using a fifth-order weighted essentially non-oscillatory scheme, and the divergence value of the viscous flux is calculated based on the reconstructed flux components.

6. The wing geometry parameter optimization method according to any one of claims 2 to 5, characterized in that, The method of explicitly integrating the discrete control equations using an explicit third-order time integration method to achieve numerical simulation of the low Mach number compressible fluid includes: Determine the right-hand side terms of the governing equations for the current time level; Based on the right-hand side and the time step, a third-order Runge-Kutta scheme with decreasing total variation is used to perform conservation variable updates, thereby realizing the numerical simulation of the low Mach number compressible fluid; the time step is a time step determined based on a preset Courant number.

7. A wing geometry parameter optimization device, characterized in that, include: The data determination module is used to determine the computational domain grid corresponding to the geometric parameters of the wing, and to determine the equivalent gas constant and pressure matching constant related to the low Mach number compressible fluid equivalent to air; the low Mach number is Mach number not greater than 0.1; The numerical simulation module is used to perform numerical simulation of the low Mach number compressible fluid based on the computational domain grid and a compressible solver to obtain the aerodynamic performance data corresponding to the wing. The governing equations of the compressible solver are the compressible Navier-Stokes equations, which are constructed based on the conservation equations of state compatible with the completely gas form and the corresponding sound speed formula, and are used to adapt to the numerical simulation of the low Mach number compressible fluid. The tuning module is used to tune the geometric parameters of the wing based on the aerodynamic performance data until a wing geometric model that meets the preset aerodynamic performance conditions is obtained. The data determination module includes: The equation of state framework determination unit is used to determine the equation of state framework for air that is compatible with the complete gas form, based on the rigid gas model. A constant calibration unit is used to determine the equivalent gas constant corresponding to the state equation framework in combination with the environmental conditions, and to determine the pressure matching constant corresponding to the state equation framework in combination with the pressure conditions at low Mach numbers; wherein, the conserved state equation is the state equation obtained by substituting the equivalent gas constant and the pressure matching constant into the state equation framework. The conservation equation of state is as follows: ； Where p is the pressure, This is the equivalent specific heat ratio, where E is the total energy per unit volume and K is the kinetic energy. This is the pressure matching constant; The speed of sound is: ； Where c is the speed of sound For density.

8. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the wing geometry parameter optimization method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, Used to store a computer program, which, when executed by a processor, implements the wing geometry parameter optimization method as described in any one of claims 1 to 6.

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