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Intermittent Galerkin finite element numerical solution method of Euler equation

A numerical solution, Euler equation technology, applied in the field of computational fluid dynamics numerical solution, can solve the problems of large calculation time and memory consumption, too many degrees of freedom, etc., to achieve the effect of reducing time and memory consumption

Active Publication Date: 2020-06-05
UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Problems solved by technology

[0005] In view of the above-mentioned problems or deficiencies, in order to solve the problem of a large amount of calculation time and memory consumption caused by too many degrees of freedom in the process of solving the Euler equation by the DG method, and to improve the calculation efficiency, the invention provides a discontinuous Galerkin solution to the Euler equation. Finite element numerical solution method, that is, a discontinuous Galerkin (DG) finite element numerical method based on Proper Orthogonal Decomposition (POD) model reduction

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  • Intermittent Galerkin finite element numerical solution method of Euler equation
  • Intermittent Galerkin finite element numerical solution method of Euler equation
  • Intermittent Galerkin finite element numerical solution method of Euler equation

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[0078] Using a sphere with a radius of 0.5 and an air box of [-20,20]×[-20,20]×[-20,20] as models to verify the effectiveness of the POD model reduction, consider a subsonic flow problem, Its Mach number is M ∞ =0.2, the calculation is performed on a simple sphere flow model with 7893 elements. The result comparison of its field diagram is as follows image 3 Shown:

[0079] image 3 -a is the pressure field diagram of the original DG, image 3 -b is the pressure field map after POD dimension reduction, and it can be seen from the figure that the results of the field map obtained by the two are consistent; Figure 4 is the comparison of the change of surface field pressure coefficient before and after POD dimensionality reduction, Figure 5 It is the relative error change of the surface field before and after POD dimension reduction. It can be seen from the figure that the relative error before and after dimension reduction is controlled at about 0.2%, which does not affe...

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Abstract

The invention belongs to the field of computational fluid mechanics numerical solution, and relates to an intermittent Galerkin finite element numerical solution method of an Euler equation, which isbased on orthogonal decomposition model order reduction. According to the invention, the discontinuous Galerkin finite element (DG) method and the orthogonal decomposition (POD) method are combined; solving variables are approximated by constructing a POD base so as to reduce the model dimension; the POD model is used for order reduction to perform low-dimensional approximate description on a multi-dimensional physical process, and the model dimension is reduced, so that in the calculation process of the DG algorithm, the degree of freedom of the calculation model is reduced while the acceptable precision is maintained, the calculation cost is reduced, and the time and memory consumption is reduced. Finally, the advantages of the finite element and the finite volume are kept, and the defects of the finite element and the finite volume are overcome.

Description

technical field [0001] The invention belongs to the numerical solution field of computational fluid dynamics, and relates to a numerical solution method of a discontinuous Galerkin finite element for the Euler equation, which is based on an orthogonal decomposition model for order reduction. Background technique [0002] Computational fluid dynamics (Computational fluid dynamics, CFD) is an important branch of modern fluid mechanics, which is the product of the combination of computer science, fluid mechanics, computational mathematics and computational physics. In the process of using CFD to solve practical problems, the practical problem must first be described as a corresponding mathematical model. Generally, it is a partial differential equation system with given initial values ​​and boundary conditions. The model of the constant solution is Euler / Navier-Stokes( N-S) equation. In the field of CFD, numerical methods have become one of the most important methods for solvi...

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Application Information

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IPC IPC(8): G06F30/23
CPCY02T90/00
Inventor 徐立朱兰杨中海李斌
Owner UNIV OF ELECTRONICS SCI & TECH OF CHINA
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