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A numerical scheme is developed for systems of conservation laws on manifoldswhich arise in high speed aerodynamics and magneto-aerodynamics. The systemsare presented in an arbitrary coordinate system on the manifold and involvesource terms which account for the curvature of the domain. In order for anumerical method to accurately capture the behavior of the system it issolving, the equations must be discretized in a way that is not only consistentin value, but also models the appropriate character of the system. Such adiscretization is presented in this work which preserves the tensorialtransformation relationships involved in formulating equations in a curvedspace. A numerical method is then developed and applied to the conical Eulerand Ideal Magnetohydrodynamic equations. To the author's knowledge, this is thefirst demonstration of a numerical solver for the conical Ideal MHD equations.

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