Numerical Solution of Compressible Euler and Magnetohydrodynamic flow past an infinite cone

TL;DR

This paper develops a numerical scheme for solving the Euler and Magnetohydrodynamic equations on curved manifolds, specifically applied to conical flows, ensuring accurate modeling of tensorial relationships in high-speed aerodynamics.

Contribution

It introduces the first numerical solver for conical ideal MHD equations that preserves tensorial transformations on curved manifolds.

Findings

Successfully applied to conical Euler and MHD equations

Preserves tensorial relationships in curved space

First demonstration of a solver for conical ideal MHD

Abstract

A numerical scheme is developed for systems of conservation laws on manifolds which arise in high speed aerodynamics and magneto-aerodynamics. The systems are presented in an arbitrary coordinate system on the manifold and involve source terms which account for the curvature of the domain. In order for a numerical method to accurately capture the behavior of the system it is solving, the equations must be discretized in a way that is not only consistent in value, but also models the appropriate character of the system. Such a discretization is presented in this work which preserves the tensorial transformation relationships involved in formulating equations in a curved space. A numerical method is then developed and applied to the conical Euler and Ideal Magnetohydrodynamic equations. To the author's knowledge, this is the first demonstration of a numerical solver for the conical Ideal MHD equations.