Analytic Riemann resolving method for multi-dimensional Euler equation

A multi-dimensional, equation technology, applied in the field of analytical Riemann solution for multi-dimensional Euler equations, can solve problems such as large numerical dissipation, and achieve the effect of small format dissipation, reduced numerical dissipation, and simple form

Active Publication Date: 2021-05-07
四川京航天程科技发展有限公司
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Problems solved by technology

Studies have shown (Li Zuowu, Acta Mechanics, 2008) that the numerical format based on the approximate Riemann solution algorithm has large numerical dissipation and is not suitable for calculating boundary layer problems, such as hypersonic aerodynamic heat, etc.

Method used

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  • Analytic Riemann resolving method for multi-dimensional Euler equation
  • Analytic Riemann resolving method for multi-dimensional Euler equation
  • Analytic Riemann resolving method for multi-dimensional Euler equation

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Embodiment Construction

[0030] The present invention will be further described in detail below in conjunction with the accompanying drawings, so that those skilled in the art can implement it with reference to the description.

[0031] The present invention proposes a numerical calculation method based on analytical Riemann solution for multidimensional Euler equations, the calculation process of which is actually to solve the flow field of a one-dimensional shock tube. If the flow is two-dimensional or three-dimensional, according to the mathematical equations, the eigenvalues ​​and eigenvectors of the multidimensional equations should be calculated, and then the wave system decomposition should be calculated. This calculation process is complicated. In actual calculation, according to the physical laws of flow, we transform the multidimensional problem into a one-dimensional shock tube problem, and decompose the multidimensional velocity component into the motion of the wave system and the motion of...

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Abstract

The invention discloses an analytic Riemannian solution method aiming at a multi-dimensional Euler equation, which is characterized in that a multi-dimensional problem is converted into a one-dimensional shock tube problem based on a flowing physical law, a multi-dimensional velocity component is decomposed into a wave system-generating motion and a wave system-following motion, and a one-dimensional analytic Riemannian solution is applied in a normal direction based on velocity decomposition, the tangential velocity is kept unchanged through a wave system, so that the analysis Riemannian solution method is popularized to multi-dimensional flux calculation by utilizing the physical law, and the analysis Riemannian solution numerical solution of the multi-dimensional Euler equation is achieved. Compared with a general vector flux splitting method, the Riemann resolving method for analyzing the multi-dimensional Euler equation is small in format dissipation, and for viscous boundary layer calculation, a good result can be obtained by adopting a small number of grids or sparse grid distribution.

Description

technical field [0001] The invention relates to the field of computational fluid dynamics. More specifically, the present invention relates to an analytic Riemann solution method for multidimensional Euler equations used in computational fluid dynamics (Computational Fluid Dynamics, CFD) numerical solutions of hypersonic flow fields. Background technique [0002] In the field of aerospace, the design of aircraft is firstly the shape design of the aircraft, that is, to meet the requirements of aerodynamic and thermal characteristics. The aerodynamic and thermal characteristics of the aircraft can be obtained through wind tunnel experiments, and can also be obtained through numerical simulation calculations using computational fluid dynamics (Computational Fluid Dynamics, CFD) software. [0003] When calculating the computational fluid dynamics (Computational Fluid Dynamics, CFD) numerical solution of the hypersonic flow field, if the viscous effect is not considered, the inv...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F30/15G06F30/23G06F30/28G06F17/11
CPCG06F30/15G06F30/23G06F30/28G06F17/11Y02T90/00
Inventor 黎作武
Owner 四川京航天程科技发展有限公司
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