TVD scheme to deal with acoustic points in ideal madnetogasdynamics equations.

Abstract

The computational magnetogasdynamics is an important tool for the development of the interdisciplinary technologies for aerospace design. Principally, because the numerical simulations generate parametric studies often impossible to do experimentally. For the magnetogasdynamics flows, the numerical evaluations always are limited by the ability to analyze and to solve accurately the hyperbolic non-linear differential equations system. In this work is presented a modification of the original Harten-Yee TVD scheme by incorporating a new sonic fix for the acoustic causality points using the finite volume technique. The proposed sonic fix is implemented to solve time-dependent, two-dimensional, ideal magnetogasdynamics equations. Two test cases were simulated: magnetogasdynamics Riemann problem and the Hartmann flow. Magnetogasdynamics Riemann flow is compressible and non-steady; however Hartmann flow is incompressible and steady test. The numerical results obtained using the new sonic fix have shown to reduce the oscillations compared with the results calculated by the traditional Harten-Yee TVD scheme. The results also show that the new scheme is robust.