Analytic Riemann resolving method for multi-dimensional Euler equation

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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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.

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