Abstract
This paper reports our recent development of our Riemann-solver free space-time discontinuous Galerkin method to solve the ideal compressible magnetohydrodynamics (MHD) equations. The preliminary results we have for 1-D 7 × 7 and 2-D 8 × 8 MHD equations show that the method is able to capture the complex MHD waves correctly without the need of any type of Riemann solvers or other flux functions, which makes our method very promising in solving systems where accurate and reliable Riemann solvers are difficult to design.
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