阅读说明：本技术 一种应用于高精度间断迦辽金流体仿真的粘性项处理方法 (Viscous item processing method applied to high-precision Galegac Liaojin fluid simulation ) 是由 赵辉 陈江涛 杨悦悦 张耀冰 吴晓军 贾洪印 李欢 张培红 周桂宇 崔鹏程 陈洪 于 2021-08-11 设计创作，主要内容包括：本发明公开了一种应用于高精度间断迦辽金流体仿真的粘性项处理方法,用于解决迦辽金方法在计算Navier-Stokes方程时出现的计算精度低于理论精度的问题,从而精确捕捉流场中用于工程应用的升力、阻力、速度、密度和压力等信息。包括如下步骤：对空间进行剖分得到计算网格,采用高精度间断迦辽金框架对Navier-Stokes方程进行处理,得到半离散形式的控制方程；定义新的提升算子,采用新的提升算子计算粘性通量,积分后获得粘性项的计算结果；采用迭代方式进行方程的求解计算,获得仿真结果。本发明在节省计算量的同时,有效保持了高阶格式的计算精度,计算精度高于理论精度。(The invention discloses a viscosity term processing method applied to high-precision Galerkin fluid simulation, which is used for solving the problem that the calculation precision of a Galerkin method in calculating a Navier-Stokes equation is lower than the theoretical precision, so that information such as lifting force, resistance, speed, density, pressure and the like applied to engineering in a flow field can be accurately captured. The method comprises the following steps: dividing the space to obtain a computational grid, and processing a Navier-Stokes equation by adopting a high-precision intermittent Galerkin frame to obtain a semi-discrete control equation; defining a new lifting operator, calculating the viscosity flux by adopting the new lifting operator, and obtaining a calculation result of the viscosity term after integration; and solving and calculating the equation by adopting an iteration mode to obtain a simulation result. The invention saves the calculation amount, effectively keeps the calculation precision of the high-order format, and the calculation precision is higher than the theoretical precision.)

1. A viscosity item processing method applied to high-precision Galois gold fluid simulation is characterized in that a high-precision Galois gold frame is adopted to subdivide a space to generate a calculation grid, a viscosity flux is calculated through iterative integration, and a grid for acquiring a lift force, a resistance force, a speed, a density and a pressure is generated, and the specific steps are as follows:

s1: the method comprises the following steps of subdividing the space to obtain a computational grid, processing a Navier-Stokes equation by adopting a high-precision intermittent Galois frame to obtain a semi-discrete control equation, and specifically comprises the following steps:

s11, mesh division is carried out on the calculation area to obtain different mesh discrete units,

s12, the compressed Navier-Stokes equation is as follows:

s13, processing the Navier-Stokes equation by adopting a high-precision interrupted Galerkin frame to obtain a semi-discrete control equation in an integral form:

wherein:in order to be a conservative quantity in the equation,in order to be a convection term,is composed ofThe derivative with respect to the time t,in order to be a divergence of the flow term,in the case of the sticky term,is the divergence of the viscous term or terms,in order to be the basis function(s),is the gradient of the basis function for which,is composed ofThe volume within the grid cell K is divided,is composed ofVolume in grid cell K, ": "represents a contraction of the vector(s),is composed ofAt the boundary surface of the grid cellThe surface integral of the above-mentioned object,andrespectively a non-viscous flux and a viscous flux,is composed ofAt the boundary surface of the grid cellThe surface integral of the above-mentioned object,is a dyadic of the tensor and is,is the normal vector of the boundary surface of the grid cell,flux, which is a conservative variable;

s2, defining a new lifting operator, calculating the viscosity flux by adopting the new lifting operator, and obtaining the calculation result of the viscosity term after integration, wherein the calculation result specifically comprises the following steps:

s21, defining a new lifting operator L as follows:

s22, defining the viscous flux as follows:

s23, calculating the integral quantity in the step S13 through the new lifting operator defined in S21 and the viscous flux defined in S22;

wherein:taking the number of faces of the grid unit as a penalty factor,andrespectively are the analytical values of the viscosity terms of the cells at the two sides of the grid surface, p is the algebraic order of the discrete polynomial,andis the volume of the two-sided unit,the area of the contact surface of the grid unit;

and S3, on the basis of the integral relation obtained in S23, solving a control equation through iterative calculation to obtain a simulated aerodynamic force result and density, speed and pressure information in the flow field.

Technical Field

The invention relates to a watershed of computational fluid mechanics technology, in particular to a viscous item processing method applied to high-precision Galois gold fluid simulation.

Background

The high-precision Galerkin simulation calculation is used as an important branch of computational fluid dynamics, has good dispersion and dissipation characteristics, is suitable for solving multi-scale complex problems, and can capture fine flow field calculation information by using less calculation resources, thereby gaining more and more attention of scholars.

The high-precision intermittent Galerkin method can only solve a hyperbolic conservation equation containing a first-order partial derivative, such as an Euler equation, at the earliest, but most problems faced by fluid simulation are based on a Navier-Stokes equation, in order to solve the Navier-Stokes equation and acquire information of lift force, resistance, speed, density, pressure and the like in a flow field, an original second-order equation can be reduced into two first-order systems by introducing the gradient of a control variable and the derivative of the gradient in the Navier-Stokes equation as intermediate variables, and then discrete processing is carried out according to an intermittent Galerkin framework. The traditional method needs to calculate and store variable gradients and derivatives of the gradients, and the calculation accuracy under the high-accuracy condition can be reduced while the number of calculation equations and the actual calculation amount are increased.

Disclosure of Invention

The invention aims to effectively remove the calculation process of the gradient and the gradient derivative in the calculation of the viscosity term by adopting a new lifting operator mode, thereby saving the calculation amount, improving the efficiency and effectively keeping the calculation precision of a high-order format.

In order to achieve the purpose, the invention adopts the following technical scheme:

a viscous item processing method applied to high-precision Galois gold fluid simulation is characterized in that a high-precision Galois gold frame is adopted to subdivide a space to generate a calculation grid, viscous flux is calculated through iterative integration, and the grid for acquiring lift force, resistance, speed, density and pressure is generated, and the method specifically comprises the following steps:

the method comprises the following steps: and (3) subdividing the space to obtain a computational grid, and processing a Navier-Stokes equation by adopting a high-precision intermittent Galerkin frame to obtain a semi-discrete control equation.

Step two: and defining a new lifting operator, calculating the viscosity flux by adopting the new lifting operator, and obtaining a calculation result of the viscosity term after integration.

Step three: and solving and calculating the equation by adopting an iteration mode to obtain a simulation result.

Compared with the prior art, the invention has the beneficial effects that:

1. compared with the prior method, the method can obtain the calculation result of the viscosity term only by calculating the lifting operator, saves the calculation of the gradient and the gradient derivative, simplifies the calculation process and improves the calculation efficiency.

2. Compared with the prior method, the method keeps the calculation precision of the high-order format, and the whole calculation precision is greatly improved compared with the prior method.

Drawings

The invention will now be described, by way of example, with reference to the accompanying drawings, in which:

FIG. 1 is a schematic flow diagram of the present invention;

FIG. 2 is a schematic representation of a density contour obtained using the method of the present invention;

FIG. 3 is a schematic illustration of a density contour obtained using conventional methods;

FIG. 4 is a comparison table comparing the error and accuracy of the method of the present invention with those of the conventional method.

Detailed Description

All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.

Any feature disclosed in this specification (including any accompanying claims, abstract and drawings), may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.

As shown in fig. 1, in this embodiment, a high-precision seqvier gold frame is used to subdivide a space to generate a computational grid, and a viscous flux is calculated by iterative integration to generate a grid for acquiring a lift force, a resistance, a speed, a density, and a pressure, and the specific process is as follows:

s1: the method comprises the following steps of subdividing the space to obtain a computational grid, processing a Navier-Stokes equation by adopting a high-precision intermittent Galois frame to obtain a semi-discrete control equation, and specifically comprises the following steps:

s11, mesh division is carried out on the calculation area to obtain different mesh discrete units,

s12, the compressed Navier-Stokes equation is as follows:

s13, processing the Navier-Stokes equation by adopting a high-precision interrupted Galerkin frame to obtain a semi-discrete control equation in an integral form:

wherein:in order to be a conservative quantity in the equation,in order to be a convection term,is composed ofThe derivative with respect to the time t,in order to be a divergence of the flow term,in the case of the sticky term,is the divergence of the viscous term or terms,in order to be the basis function(s),is the gradient of the basis function for which,is composed ofThe volume within the grid cell K is divided,is composed ofVolume in grid cell K, ": "represents a contraction of the vector(s),is composed ofAt the boundary surface of the grid cellThe surface integral of the above-mentioned object,andrespectively a non-viscous flux and a viscous flux,is composed ofAt the boundary surface of the grid cellThe surface integral of the above-mentioned object,is a dyadic of tensor, is a normal vector of a boundary surface of a grid unit,flux, which is a conservative variable;

s2, defining a new lifting operator, calculating the viscosity flux by adopting the new lifting operator, and obtaining the calculation result of the viscosity term after integration, wherein the calculation result specifically comprises the following steps:

s21, defining a new lifting operator L as follows:

s22, defining the viscous flux as follows:

s23, calculating the integral quantity in the step S13 through the new lifting operator defined in S21 and the viscous flux defined in S22;

wherein:taking the number of faces of the grid unit as a penalty factor,andrespectively are the analytical values of the viscosity terms of the cells at the two sides of the grid surface, P is the algebraic order of the discrete polynomial,andis the volume of the two-sided unit,the area of the contact surface of the grid unit;

and S3, on the basis of the integral relation obtained in S23, solving a control equation through iterative calculation to obtain a simulated aerodynamic force result and density, speed and pressure information in the flow field.

As shown in fig. 2 and fig. 3, the method of the present embodiment is compared with the conventional method, and the problem of the cylindrical bypass flow at a low speed is analyzed, and mainly flow field information such as density, pressure, speed and the like around the bypass flow is calculated, theoretically, the obtained result should be symmetric from top to bottom, and the density contour map obtained by calculation in the conventional method has non-physical characteristics (greatly deviates from a correct result) due to precision loss.

As shown in fig. 4, the method of the present embodiment is used to compare the calculation accuracy with the conventional method, and the standard couette example is used to perform accuracy analysis, wherein when the theoretical accuracy is known, the error is calculated mainly by using the density results of different grids to obtain the corresponding density calculation accuracy, which is then compared with the theoretical accuracy, so as to determine the difference between the accuracy obtained by different methods and the theoretical accuracy.

The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed.