Pseudo-wave decomposition high-order method for magnetogasdynamics

A new characteristics-based decomposition of the ideal magnetogasdynamic equations is derived. This formulation consists in representing the temporal variation of the physical quantities pressure, velocity, magnetic field and entropy as a linear combination of the generic advective terms corresponding to each wave type occurring in the medium. The flux terms can then be handled with existing high-order upwind dispersion relation preserving schemes; those being specifically chosen in our case to increase numerical accuracy and improve stability. Another feature of the new formulation of the non-ideal governing equations is that the boundary conditions are exactly satisfied at the frontiers of the computational domain. The accuracy of the method is assessed by comparison between numerical and exact solutions. Good agreement is obtained between computed and exact solutions.