Numerical method for solving two-dimensional Riemannian problem and simulating subsonic non-viscous stream

Abstract

The invention belongs to the field of computational fluid mechanics, in particular to a numerical method for solving a two-dimensional Riemannian problem, and is applied to solve an Euler equation and perform the numerical simulation of subsonic non-viscous stream. By the numerical method, the Euler equation on an Euler plane is transformed to a stream function plane; in a two-dimensional Cartesian grid, the Riemannian problem of a translational stream line and the Riemannian problem along the stream line are solved, so that the error of a numerical solution is reduced.

Description

1. Technical Field [0001] The invention belongs to the field of computational fluid mechanics, and specifically is a numerical method for solving two-dimensional Riemann problems, which is applied to the numerical simulation of subsonic and inviscid flow. 2. Background technology [0002] The Riemann Problem was first proposed in the field of aerodynamics, originally referring to a special flow phenomenon of compressible fluid in a one-dimensional shock tube. Specifically, it means that a compressible fluid, such as air, is compressed in a one-dimensional pipe until a shock wave appears. The appearance of shock waves indicates that the flow of fluid is discontinuous. Across the shock wave, the velocity, density, pressure, and entropy of the fluid all undergo jump changes. In 1858, Riemann studied the characteristics of this discontinuous flow phenomenon, and proposed and solved one of the simplest initial value problems of the one-dimensional Euler equation, which was later cal...

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Problems solved by technology

Obviously, violating the entropy increase principle of the shock wave will cause a certain error in the numerical solution

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