High-order element Euler equation numerical simulation method based on non-Jacobian matrix

A Jacobian matrix and numerical simulation technology, applied in the field of numerical solution of three-dimensional fluid mechanics, which can solve problems such as low computational efficiency of high-order elements

Active Publication Date: 2020-04-14
UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Problems solved by technology

[0004] In view of the above-mentioned problems or deficiencies, in order to solve the problem of low computational efficiency of high-order units; the present invention provides a numerical simulation method for Euler equations of high-order units based on no Jacobian matrix. The cross product of normal and surface tangent vectors is used to obtain high-order element integrals, and on this basis, corresponding high-precision numerical simulation methods are developed

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  • High-order element Euler equation numerical simulation method based on non-Jacobian matrix
  • High-order element Euler equation numerical simulation method based on non-Jacobian matrix
  • High-order element Euler equation numerical simulation method based on non-Jacobian matrix

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[0034] The technical solution of the present invention will be described in detail below in conjunction with the drawings and embodiments.

[0035] In the aerodynamic analysis of aircraft, it is generally necessary to analyze and calculate the aerodynamic parameters when the gas flows through the aircraft. Taking the flow around a three-dimensional sphere as an example, refer to the attached figure 1 , a numerical simulation method for higher-order element Euler equations based on Jacobian-free matrix, including the following steps:

[0036] A. Establish the geometric model of the spherical structure, and then establish the fluid calculation domain. The structural cross-sectional view is as attached figure 2 shown.

[0037] B. The fluid calculation domain built in step A is subdivided by high-order tetrahedral elements, and transformed into a discrete space model.

[0038] The fluid computational domain established in step A of subdivision of high-order tetrahedral elements...

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Abstract

The invention belongs to the technical field of three-dimensional fluid mechanics numerical solution, and relates to a high-order element Euler equation numerical simulation method based on a non-Jacobian matrix. According to the method, the curved surface object surface is accurately fitted through an unstructured high-order element, then the Euler equation is dispersed on the basis of the high-order element, finally, the cross multiplication relation between the unit outer normal vector and the surface tangent vector of Gaussian points is solved through the object surface, curved surface integral is simplified, a Jacobian matrix is eliminated and a corresponding high-efficiency numerical simulation method is developed accordingly.

Description

technical field [0001] The invention belongs to the technical field of numerical solution of three-dimensional fluid mechanics, and relates to a numerical simulation method of Euler equation of higher-order elements based on Jacobian-free matrix. Background technique [0002] Computational fluid dynamics (referred to as CFD) has been widely used in automobile manufacturing, civil engineering, environmental engineering, shipbuilding industry and aviation industry, etc. It helps to explain and understand the results of theory and experiments, and is indispensable for fluid mechanics analysis. Methods. [0003] With the development of CFD, the application of corresponding numerical algorithms in CFD has also been developed, such as finite difference, finite volume and finite element method. With the advancement of industrial technology, fluid dynamics has put forward higher requirements for the accuracy of numerical algorithms, so high-precision numerical simulation methods ar...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/23G06F30/28G06F111/10
Inventor 徐立尹俊辉杨中海李斌
Owner UNIV OF ELECTRONICS SCI & TECH OF CHINA
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