Variable-density low-speed flow mesoscopic numerical calculation method and apparatus

Abstract

The present invention relates to the technical field of fluid mechanics. Disclosed is a variable-density low-speed flow mesoscopic numerical calculation method, comprising: determining a computational domain, and dividing or reading grid information, fluid parameters and control parameters in the computational domain; on the basis of the read information, allocating arrays, initializing corresponding parameters of the computational domain, and entering a time step loop upon completion; setting boundary conditions, and assigning all boundary macroscopic quantities in a flow field; under a finite volume framework, deriving a numerical flux of the flow field by means of a BGK equation to solve a Navier-Stokes equation of the flow field; calculating pressure and velocity fluxes at cell interfaces of the flow field, and updating boundary macroscopic quantity information on the basis of flux information; determining whether there is an external force, and if so, applying the external force by means of splitting, and updating the boundary macroscopic quantities; determining whether a time step meets a loop condition; if so, re-entering setting boundary conditions, and assigning all boundary macroscopic quantities in the flow field; and if not, outputting flow field data, and ending simulation. The present invention has the advantages of high algorithm accuracy and simple programming.

Description

Numerical calculation method and device for variable density low-speed flow medium TECHNICAL FIELD

[0001] The present application relates to the technical field of fluid mechanics, and in particular to a numerical calculation method and device for variable density low-speed flow medium. BACKGROUND

[0002] Computational fluid dynamics has been widely used in many related industrial fields such as automobiles, ships, aerospace, etc. In order to solve the problems in the engineering field, various commercial software has been developed at home and abroad to simulate fluid mechanics phenomena. At present, most of the computational fluid dynamics methods are based on the macroscopic Navier-Stokes equation of the traditional numerical format, and these methods usually adopt the calculation strategy of decoupling the viscous term and the inviscid term, and it is difficult to consider the tangential gradient in the finite volume method framework. However, the gas kinetic scheme (GKS) based on the mesoscopic Boltzmann equation can simultaneously couple the viscous term and the inviscid term, and consider the influence of the tangential gradient. The GKS method has the advantages of clear object image, low dissipation, and being suitable for high-speed flow, and has been widely used in compressible flow. There is also a corresponding promotion and application in the solution of constant density incompressible flow. However, in the low-speed flow problem with large spatial variation of the density field, such as the low-density region caused by heat release in the combustion process, or the case where the density difference between the liquid phase and the gas phase is large in two-phase flow such as cavitation and boiling, the gas kinetic scheme based on constant density is not applicable. This limits the application of the method in the fields of multi-component flow, multiphase flow and turbulent combustion simulation.

[0003] Therefore, a numerical calculation method and device for variable density low-speed flow medium are provided to solve the above problems. SUMMARY

[0004] The main purpose of the present application is to solve the problem in the prior art that in the low-speed flow problem with large spatial variation of the density field, such as the low-density region caused by heat release in the combustion process, or the case where the density difference between the liquid phase and the gas phase is large in two-phase flow such as cavitation and boiling, the gas kinetic scheme based on constant density is not applicable; this limits the application of the method in the fields of multi-component flow, multiphase flow and turbulent combustion simulation.

[0005] The first aspect of the present application provides a numerical calculation method for variable density low-speed flow medium, which comprises:

[0006] determining a calculation region, dividing or reading grid information, fluid parameters and control parameters in the calculation region;

[0007] opening an array according to the read information, initializing the corresponding parameters of the calculation region, and after completion, entering a time part loop;

[0008] Setting boundary conditions, assigning all boundary macroscopic quantities in the flow field;

[0009] Solving the Navier-Stokes equation of the flow field, calculating the pressure and velocity flux of the flow field unit interface; updating the boundary macroscopic quantity information through the flux information, judging whether there is an external force, if yes, then applying the external force through the splitting method, and updating the boundary macroscopic quantity at the same time;

[0010] Judging whether the time step meets the loop condition; if yes, re-entering the setting of boundary conditions, assigning all boundary macroscopic quantities in the flow field; if not, outputting the flow field data and ending the simulation.

[0011] Further, the division or reading of the grid information, fluid parameters and control parameters in the calculation region comprises:

[0012] Dividing the calculation region into different grids, reading the grid information, fluid parameter information and control parameter information of each grid in the calculation region;

[0013] Or reading the grid information, fluid parameter information and control parameter information of the grid already divided in the calculation region.

[0014] Further, the grid information includes grid length information, grid width information, grid number information, unit grid length information and grid coordinate information.

[0015] Further, the fluid parameters include density information, velocity information, pressure information and viscosity parameter information; the control parameter information includes time step information, CFL number information and Mach number information.

[0016] Further, the Navier-Stokes equation is:

[0017] Force, τ ν is the deviatoric stress tensor, and F is the external force term acting on the fluid;

[0018] The deviatoric stress tensor containing volume viscosity includes:

[0019] In the formula, μ is the hydrodynamic viscosity, ξ ν is the volume viscosity coefficient, d is the dimension, and I is the unit vector.

[0020] Further, the calculation of the pressure and velocity flux of the flow field comprises:

[0021] The flux form based on momentum is:

[0022] The flux form based on velocity is:

[0023] Further, the splitting mode for applying external force includes:

[0024] Wherein, u * Solved by Navier-Stokes equation.

[0025] The second aspect of the present application provides a variable density low-speed flow medium numerical calculation device, comprising:

[0026] The data reading module is configured to determine a calculation region, and divide or read grid information, fluid parameters and control parameters in the calculation region.

[0027] The time step cycle entering module is configured to open an array according to the read information, initialize corresponding parameters of the calculation region, and enter a time step cycle after completion.

[0028] The boundary condition setting module is configured to set a boundary condition, and assign all boundary macroscopic quantities in a flow field.

[0029] The boundary macroscopic quantity updating module is configured to solve a flow field Navier-Stokes equation, calculate pressure and velocity fluxes of a flow field unit interface, update boundary macroscopic quantity information through the flux information, judge whether there is an external force, and if so, apply the external force through a splitting mode and update the boundary macroscopic quantity.

[0030] The cycle / ending judgment module is configured to judge whether a time step meets a cycle condition, and if so, re-enter the setting of the boundary condition and the assignment of all boundary macroscopic quantities in the flow field, and if not, output flow field data and end simulation.

[0031] The third aspect of the present application provides an electronic device, comprising a memory and at least one processor, wherein the memory stores instructions.

[0032] The at least one processor invokes the instructions in the memory, so that the electronic device performs each step of the variable density low-speed flow medium numerical calculation method.

[0033] The fourth aspect of the present application provides a computer readable storage medium, wherein the computer readable storage medium stores instructions, and the instructions are executed by a processor to realize each step of the variable density low-speed flow medium numerical calculation method.

[0034] The present application is based on continuous Boltzmann-BGK equation, constructs low Mach approximate numerical flux in the framework of finite volume, the flux constructed by Chapman-Enskog expansion analysis can restore to macroscopic control equation (Navier-Stokes equation), according to the assumption of constant density near incompressible flow, the momentum-based flux can be simplified to the form of velocity-based flux, after the form of flux is obtained, the numerical algorithm based on gas dynamics format can be constructed. The algorithm directly evolves and updates the macroscopic quantity in the flow field, the calculation program is simple, the calculation precision is high, and the physical process of low-speed flow can be efficiently simulated by numerical simulation.

[0035] The innovation of the low Mach numerical algorithm of the present application lies in that the low Mach numerical flux which can restore to macroscopic control equation is constructed by Chapman-Enskog analysis, the algorithm based on gas dynamics format is developed, and the accuracy of the algorithm in solving unsteady flow process is verified. BRIEF DESCRIPTION OF DRAWINGS

[0036] Fig. 1 is a schematic diagram of cell interface flux under finite volume format;

[0037] Fig. 2 is a flow chart of the variable density low-speed flow medium numerical algorithm of the present application;

[0038] Fig. 3 is a schematic diagram of gas dynamics format interface;

[0039] Fig. 4 is a comparison diagram of Taylor Green vortex pressure field and velocity field and analytical solution;

[0040] Fig. 5 is a cloud chart of Taylor Green vortex pressure field and velocity field;

[0041] Fig. 6 is a schematic diagram of Taylor Green vortex velocity field accuracy;

[0042] Fig. 7 is a schematic diagram of the structure of the variable density low-speed flow medium numerical calculation device provided by the embodiment of the present application;

[0043] Fig. 8 is a schematic diagram of the structure of the electronic device provided by the embodiment of the present application. DETAILED DESCRIPTION

[0044] The embodiment of the present application provides a variable-density low-speed flow medium numerical calculation method, which comprises determining a calculation region, dividing or reading grid information, fluid parameters and control parameters in the calculation region; opening an array according to the read information, initializing corresponding parameters of the calculation region, and entering a time part loop after completion; setting a boundary condition, and assigning all boundary macro-quantities in a flow field; solving a flow field Navier-Stokes equation, and calculating pressure and velocity flux of a flow field unit interface; updating boundary macro-quantity information through flux information, judging whether an external force exists, if yes, applying the external force through a splitting mode, and updating the boundary macro-quantity at the same time; judging whether a time step meets a loop condition; if yes, re-entering the setting of the boundary condition, and assigning all boundary macro-quantities in the flow field; if not, outputting flow field data, and ending simulation, and the present application solves the problems in the prior art, such as that a gas dynamics format based on a constant density is not applicable in a low-speed flow problem with a large spatial variation of a density field, such as a low-density area caused by heat release in a combustion process, or a large difference between liquid and gas densities in two-phase flow such as cavitation and boiling, and limits the application of the method in the fields of multi-component flow, multiphase flow and turbulent combustion simulation and the like.

[0045] The terms "first", "second", "third", "fourth" and the like in the description, claims, and drawings of the present application, and those above (if any) are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the use of such terms, if any, are not construed to limit the scope of the application, except as outlined in the claims. Moreover, the terms "comprise" or "have", and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, product, or apparatus that comprises a list of elements is not necessarily limited to those elements, but can include other elements not expressly listed or inherent to such process, method, system, product, or apparatus.

[0046] For the convenience of understanding, the specific flow of the embodiment of the present application is described below, and the first embodiment of the variable-density low-speed flow medium numerical calculation method in the embodiment of the present application comprises the following steps.

[0047] Determining a calculation region, dividing or reading grid information, fluid parameters and control parameters in the calculation region;

[0048] Opening an array according to the read information, initializing corresponding parameters of the calculation region, and entering a time part loop after completion;

[0049] Setting a boundary condition, and assigning all boundary macro-quantities in a flow field;

[0050] Solving the Navier-Stokes equation of the flow field, calculating the pressure and velocity flux of the flow field unit interface; updating the boundary macroscopic quantity information through the flux information, judging whether there is an external force, if yes, applying the external force through the splitting method, and updating the boundary macroscopic quantity at the same time;

[0051] Judging whether the time step meets the cycle condition; if yes, re-entering the setting of the boundary condition, assigning values to all boundary macroscopic quantities in the flow field; if not, outputting the flow field data and ending the simulation.

[0052] Since the method proposed in the current embodiment supports variable density low-speed flow under the GKS format in the finite volume framework, first, the GKS method is introduced, then the improvement thereof and the connection with the macroscopic variable density incompressible NS equation are described, and it is explained that the mesoscopic format proposed in the embodiment can be used for low-speed variable density flow problems.

[0053] The existing GKS method is based on the original Boltzmann-BGK equation,

[0054] Where f(t,x,ξ) represents the probability density function of the molecular velocity distribution at time t and position x, f eq is the distribution function, τ is the relaxation time, which is related to the gas viscosity through the pressure. The standard Boltzmann-BGK can obtain the standard compressible Navier-Stokes equation through Chapman-Enskog expansion analysis. If the temperature T or the gas constant in the equilibrium distribution function is selected as a given fixed parameter, then the sound speed of the fluid can be controlled, which is called the pseudo sound speed. At this time, the Chapman-Enskog analysis expansion can obtain the weakly compressible Navier-Stokes equation. If in the finite volume framework, according to the macroscopic quantity information on both sides of the fluid grid unit interface, the time-space integral solution of the distribution function f on the grid unit interface can be constructed analytically, f eq -τDf eq +O(τ 2 ) (2)

[0055] Where D represents the total derivative. The above expression and the original BGK equation are expanded and analyzed to obtain the Navier-Stokes equation,

[0056] Where ρ is the fluid density, u is the fluid density, p is the fluid pressure, τ ν is the fluid viscous stress.

[0057] The GKS method obtained by using the above method can be used for simulating low-speed flow, the calculation time step of which is not limited to the real flow speed, and the energy / temperature equation does not need to be solved, which is a mesoscopic artificial compression method. However, the method requires that the spatial variation of the real density of the fluid is small, and thus cannot be applied to multi-component flow such as component density gap, multiphase flow, and combustion.

[0058] The technical scheme provided in the embodiment is to modify the original Boltzmann-BGK equation, and add a fictitious external force term to ensure that the macroscopic equation obtained by Chapman-Enskog expansion analysis corresponds to the NS equation of the low Mach number approximation, that is, the Low Mach Number Approximation (LMNA) method. Although the LMNA method is widely used in traditional NS equations, the standard GKS method does not support it. The modification method provided in the embodiment is as follows. First, extend the BGK equation and add an external force term:

[0059] Wherein, a is an analog external force, P h is the hydrodynamic pressure, RT is a parameter for controlling compressibility, and represents the equilibrium distribution function. Can be expressed as:

[0060] is a normal distribution function. The moment of the equilibrium state is

[0061] A variable density low-speed flow mesoscopic numerical algorithm process is divided into the following steps. Steps 1-6 first introduce the general flow process of the finite volume based on the traditional NS equation, and the subsequent steps derive the GKS method which can restore to the above equation

[0062] Step 1: Determine the calculation region, divide or read the grid information, fluid parameters and control parameters, and enter Step 2.

[0063] Step 2: According to the read information, open an array, initialize the corresponding parameters of the calculation region, and after completion, enter the time step loop and enter Step 3.

[0064] Step 3: Set the boundary conditions, assign values to all boundary macroscopic quantities in the flow field, and enter Step 4.

[0065] Step4: Derive the flow field numerical flux according to the BGK equation in the limited volume framework, solve the flow field Navier-Stokes equation, first calculate the pressure and velocity (or momentum) flux of the flow field unit interface, then update the macroscopic quantity in the unit through the flux information of the interface, if there is external force, apply the external force through the splitting method, update the macroscopic quantity, enter Step5.

[0066] Step5: Determine whether the time step meets the loop condition, if yes, enter Step3, if no, enter Step6.

[0067] Step6: Output the flow field data and end the simulation.

[0068] The grid information in Step1 includes grid length, width, grid number, unit grid length and grid coordinates; fluid parameters include density, velocity, pressure and viscosity parameters of each grid point; control parameters include time step, CFL number and Mach number and other dimensionless parameters.

[0069] The Navier-Stokes equation in Step4 above is:

[0070] In formula (8), ρ is the fluid density, t is the time, u is the fluid velocity, p h is the fluid dynamic pressure, τ ν is the deviatoric stress tensor, F is the external force term acting on the fluid. The deviatoric stress tensor containing the volume viscosity can be expressed as:

[0071] In the formula, μ is the fluid dynamic viscosity, ξ ν is the volume viscosity coefficient, d is the dimension, and I is the unit vector.

[0072] The interface flux in Step4 includes the flux of pressure and velocity (or momentum), and the interface flux of unit (i, j) is shown in Figure 1, wherein and respectively represent the flux in x and y directions, and the macroscopic quantity information in the unit can be updated by using the unit interface flux.

[0073] The splitting method in Step4 is implemented as follows:

[0074] The velocity u * can be obtained by solving the first formula in formula (3), and the velocity u n+1 of the next time step can be obtained according to the splitting method to apply external force.

[0075] Figure 2 describes the key in solving the Navier-Stokes equation under the limited volume framework is the solution of the flow field interface flux, the following will be from the BGK (Bhatnagar-Gross-Krook) equation, the derivation of the flow field interface flux, and through the Chapman-Enskog approximation expansion to restore the macroscopic control equation [3].

[0076] First, the BGK equation with force term can be expressed as:

[0077] Where f is the distribution function, The equilibrium distribution function is represented by f, ξ is the micro velocity, τ is the relaxation time, and the gas density and momentum are: <f>, pu = 0 <uf>,

[0078] The expression of force term F is

[0079] where P h The moment of equilibrium state is

[0080] The moment of source term is

[0081] The BGK equation can be rewritten as

[0082] Therefore, the distribution function can be expressed in terms of equilibrium state and source term, and the form of Chapman-Enskog approximation expansion is given as

[0083] The second order moment of f (1) is

[0084] <ξ α ξ β ,f (1) > = <ξ α ξ β ,-Df eq +F> = RTρS + O(τ 2 )+O(u 3 ) (18)

[0085] where The zeroth order moment and first order moment of BGK equation are given as

[0086] Up to now, the kinetic model can be derived as Navier-Stokes equation of the original BGK equation.

[0087] In order to further derive the expression of interface flux, the numerical flux of low Mach approximation will be derived based on the model of Lee[4] et al. below.

[0088] Firstly, a new distribution function is defined as where The expression of f

[0089] The equilibrium expression of the above distribution function is

[0090] The BGK equation with source term can be expressed as​​

[0091] The expression of the source term is:

[0092] Take the moment of the equilibrium distribution function in equation (21):

[0093] Take the moment of the source term in equation (23):

[0094] Rewrite the BGK equation in equation (22) to give the expression of the distribution function:

[0095] g = g eq - τDg eq + τG+ O(τ 2 ) (26)

[0096] Chapman-Enskog approximation expansion is performed on the distribution function:

[0097] The Taylor expansion of the distribution function at time t n and x jk at second-order time accuracy is performed in the finite volume framework, see Figure 3:

[0098] First-order moments are taken for the distribution functions g (0) and g (1) in equation (27) respectively:

[0099] Second-order moments are taken for the distribution functions g (0) and g (1) in equation (27) respectively:

[0100] The velocity integral of the distribution function with time in equation (28) is taken:

[0101] The time integral of F jk (t) in the above equation can obtain the flux of pressure:

[0102] Second-order moments are taken for the distribution function with time in equation (28):

[0103] The time integral of H jk (t) in the above equation can obtain the flux of momentum:

[0104] For the incompressible flow with constant density: The pressure flux and the velocity flux can be expressed as:

[0105] Through the above derivation process, two kinds of low Mach number fluxes based on momentum and velocity are obtained, and the numerical fluxes described above are applied to the variable density low speed flow medium numerical algorithm, which can be used to simulate low speed flow.

[0106] The gas-kinetic scheme (GKS) is a mesoscopic method under the finite volume framework, and its main advantages include: the flow field information is evolved and updated by macroscopic quantities, and most of the effective processing methods in traditional numerical methods based on macroscopic quantities, such as reconstruction of physical quantities in cells or interfaces, boundary conditions, acceleration techniques in steady flow, etc. can be directly applied, and the gas-kinetic scheme is based on the continuous Boltzmann equation, which does not need to be discretized in velocity space and does not need to store the distribution function, so that the computational amount and storage amount of the method are greatly reduced, which is much smaller than the overhead of directly solving the BGK equation.

[0107] Referring to FIGS. 1-6, the second embodiment of the variable density low speed flow medium numerical calculation method in the embodiment of the application comprises:

[0108] The flow process of the variable density low speed flow medium numerical algorithm comprises the following steps:

[0109] Step 1: determine the calculation region, divide or read the grid information, fluid parameters and control parameters, and enter Step 2.

[0110] Step 2: open an array according to the read information, initialize the corresponding parameters of the calculation region, and enter the time step loop after completion, and enter Step 3.

[0111] Step 3: set the boundary conditions, assign values to the corresponding macroscopic quantities of all boundaries in the flow field, and enter Step 4.

[0112] Step 4: derive the flow field numerical flux according to the BGK equation under the finite volume framework, solve the flow field Navier-Stokes equation, first calculate the pressure and velocity (or momentum) fluxes of the flow field cell interface, then update the macroscopic quantities in the cell through the flux information of the interface, if there is an external force, the external force is applied through the splitting method, and the macroscopic quantities are updated, and enter Step 5.

[0113] Step 5: determine whether the time step meets the loop condition, if yes, enter Step 3, otherwise, enter Step 6.

[0114] Step 6: output the flow field data and end the simulation.

[0115] To verify the correctness of the algorithm proposed in the present application, the following example is verified.

[0116] The implementation example is two-dimensional Taylor-Green vortex simulation. In a square cavity with four periodic boundaries, a given time-dependent pressure field and velocity field are initialized. The pressure and velocity in the calculation region evolve over time. By comparing with the analytical solution, the correctness of the algorithm can be verified.

[0117] The example parameter settings include: calculation region: LxL=64x64, Mach number Ma=0.01, fluid viscosity v=2e-4, CFL number is set to: 0.01408, and the calculation step number is 4x10 5 The initialization of the pressure field and the velocity field is as follows:

[0118] Wherein, the velocity U0=Ma.

[0119] For the constant density incompressible flow of this example, the algorithm based on velocity flux can be used, and the pressure and velocity flux are as follows:

[0120] By deriving the low Mach number value flux based on velocity, the numerical algorithm for variable density low speed flow medium can be applied to the flow process of this example.

[0121] As shown in FIG. 4, the comparison chart of the pressure field and the velocity field with the analytical solution shows that the results of the algorithm are in good agreement with the analytical solution. Meanwhile, FIG. 5 shows the pressure field and velocity field cloud chart at the corresponding time.

[0122] According to the double logarithmic curve of FIG. 6, it can be seen that the algorithm for calculating the velocity field has a spatial accuracy higher than the second order.

[0123] The variable density low speed flow medium numerical calculation method in the embodiment of the present application is described above, and the variable density low speed flow medium numerical calculation device in the embodiment of the present application is described below. Please refer to FIG. 7. The variable density low speed flow medium numerical calculation device in the embodiment of the present application includes the following for the above-mentioned embodiment:

[0124] The data reading module 701 is used to determine the calculation region, divide or read the grid information, fluid parameters and control parameters in the calculation region;

[0125] The time step cycle entering module 702 is used to open an array according to the read information, initialize the corresponding parameters of the calculation region, and enter the time step cycle after completion;

[0126] The boundary condition setting module 703 is used to set the boundary condition and assign values to all boundary macroscopic quantities in the flow field.

[0127] The boundary macroscopic quantity updating module 704 is configured to solve the Navier-Stokes equation of the flow field, calculate the pressure and velocity flux of the flow field unit interface, update the boundary macroscopic quantity information through the flux information, and determine whether there is an external force. If yes, the external force is applied through a splitting method, and the boundary macroscopic quantity is updated.

[0128] The cycle / ending determining module 705 is configured to determine whether the time step meets a cycle condition. If yes, the boundary condition is set again, and all the boundary macroscopic quantities in the flow field are assigned values. If no, the flow field data is output, and the simulation is ended.

[0129] The above Fig. 7 describes the variable-density low-speed flow medium numerical calculation device in the embodiment of the application in detail from the perspective of modular functional entities. The electronic device in the embodiment of the application is described in detail from the perspective of hardware processing.

[0130] Fig. 8 is a structural schematic diagram of an electronic device provided by the embodiment of the application. The electronic device 700 can be quite different due to different configurations or performances, and can include one or more processors (central processing units, CPUs) 710 (for example, one or more processors) and a memory 720, one or more storage media 730 (for example, one or more mass storage devices) storing application programs 733 or data 732. The memory 720 and the storage media 730 can be temporary storage or persistent storage. The programs stored in the storage media 730 can include one or more modules (not shown in the figure), and each module can include a series of instruction operations in the electronic device 700. Further, the processor 710 can be configured to communicate with the storage media 730 and execute the series of instruction operations in the storage media 730 on the electronic device 700.

[0131] The electronic device 700 can further include one or more power supplies 740, one or more wired or wireless network interfaces 750, one or more input / output interfaces 750, and / or one or more operating systems 731, such as Windows Serve, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art can understand that the electronic device structure shown in Fig. 8 does not constitute a limitation based on the electronic device, and can include more or fewer components than shown in the figure, or combine certain components, or different component arrangements.

[0132] The application further provides a computer readable storage medium, which can be a nonvolatile computer readable storage medium or a volatile computer readable storage medium, and the computer readable storage medium stores instructions, and the instructions make a computer execute the steps of the numerical calculation method of the variable-density low-speed flow medium when the instructions are run on the computer.

[0133] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described system or device, unit can refer to the corresponding processes in the foregoing method embodiments, and will not be described here.

[0134] The integrated unit, if implemented in the form of a software function unit and sold or used as an independent product, can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the application essentially or the part that contributes to the prior art or the whole or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for making a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the method described in each embodiment of the application. The foregoing storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various program code storage media.

[0135] The above-described embodiments are only used to illustrate the technical solutions of the application, rather than limit them; although the application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for some technical features; and these modifications or replacements do not make the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the application.< / uf> < / f>

Claims

1. A method for numerical calculation of a variable-density low-speed flow medium, characterized by, The variable-density low-speed flow medium numerical calculation method comprises the following steps: determining a calculation region, dividing or reading grid information, fluid parameters and control parameters in the calculation region; opening an array according to the read information, initializing corresponding parameters of the calculation region, and entering a time step cycle after completion; setting boundary conditions and assigning all boundary macro-quantities in the flow field; deriving a flow field numerical flux according to a BGK equation under a finite volume framework to solve a flow field Navier-Stokes equation; calculating pressure and velocity fluxes of a flow field unit interface, updating boundary macro-quantity information through flux information, and judging whether there is an external force; if yes, the external force is applied through a splitting method, and the boundary macro-quantity is updated; judging whether the time step meets a cycle condition; if yes, the boundary conditions are set again, and all boundary macro-quantities in the flow field are assigned; if not, flow field data is output, and the simulation is ended.

2. The numerical calculation method of the variable density low speed flow medium according to claim 1, characterized in that, The dividing or reading grid information, fluid parameters and control parameters in the calculation region comprises the following steps: dividing the calculation region into different grids, and reading grid information, fluid parameter information and control parameter information of each grid in the calculation region; or reading grid information, fluid parameter information and control parameter information of the already divided grids in the calculation region.

3. The numerical calculation method of the variable density low speed flow medium according to claim 2, characterized in that, The grid information comprises grid length information, grid width information, grid number information, unit grid length information and grid coordinate information.

4. The numerical calculation method of the variable density low speed flow medium according to claim 2, characterized in that, The fluid parameters comprise density information, velocity information, pressure information and viscosity parameter information; and the control parameter information comprises time step length information, CFL number information and Mach number information.

5. The numerical calculation method of the variable density low speed flow medium according to claim 1, characterized in that, The Navier-Stokes equation is: where p is the fluid density, t is time, u is the fluid velocity, p h is the hydrodynamic pressure, τ ν is the deviatoric stress tensor, F is the external force term acting on the fluid; where the bulk viscous deviatoric stress tensor includes: where μ is the hydrodynamic viscosity, ξ ν is the volume viscosity coefficient, d is the dimension, and I is the unit vector.

6. The numerical calculation method of the variable density low speed flow medium according to claim 5, characterized in that, The calculating pressure and velocity fluxes of the flow field comprises the following steps: The momentum-based flux form is: The flux form based on velocity is:

7. The numerical calculation method of the variable density low speed flow medium according to claim 6, characterized in that, The external force is applied by splitting, and the splitting includes: where u * Obtained by solving the Navier-Stokes equation.

8. A device for numerical calculation of a variable-density low-speed flow medium, characterized by comprising: comprising: a data reading module for determining a calculation region, dividing or reading grid information, fluid parameters and control parameters in the calculation region; a time step cycle entering module for opening an array according to the read information, initializing corresponding parameters of the calculation region, and entering a time step cycle after completion; a boundary condition setting module for setting boundary conditions and assigning all boundary macro-quantities in the flow field; a boundary macro-quantity updating module for solving a flow field Navier-Stokes equation, calculating pressure and velocity fluxes of a flow field unit interface, updating boundary macro-quantity information through flux information, and judging whether there is an external force; if yes, the external force is applied through a splitting method, and the boundary macro-quantity is updated; a cycle / ending judging module for judging whether the time step meets a cycle condition; if yes, the boundary conditions are set again, and all boundary macro-quantities in the flow field are assigned; if not, flow field data is output, and the simulation is ended. 9.An electronic device comprising a memory and at least one processor, wherein the memory stores instructions; the at least one processor invokes the instructions in the memory to enable the electronic device to perform each step of the variable-density low-speed flow medium numerical calculation method according to any one of claims 1-7.

10. A computer-readable storage medium having stored thereon instructions, the instructions comprising, the instructions are executed by the processor to implement each step of the variable-density low-speed flow medium numerical calculation method according to any one of claims 1-7.

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