Chapter

Spectral and High Order Methods for Partial Differential Equations

Volume 76 of the series Lecture Notes in Computational Science and Engineering pp 357-364

Date:

An Explicit Discontinuous Galerkin Scheme with Divergence Cleaning for Magnetohydrodynamics

  • Christoph AltmannAffiliated withInstitut für Aerodynamik und Gasdynamik, Universität Stuttgart Email author 

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Abstract

The explicit space-time expansion discontinuous Galerkin scheme (Gassner et al., J. Sci. Comp. 34(3):260–286, 2008) is applied for solving ideal and viscous magnetohydrodynamic equations. Based on a Taylor expansion in space and time about the barycenter of each cell at the old time level, this predictor-corrector strategy enables each cell to have its own time step whereas the high order of accuracy in time is retained. Thus, it may significantly speed up computations. The discontinuous Galerkin method together with the local time-stepping algorithm allows for an efficient local sub-cycling for a divergence cleaning using a hyperbolic transport correction (Dedner et al., J. Comput. Phys. 175(2):645–673, 2002). Convergence tests and test problems are performed to challenge the capabilities of the space-time expansion scheme.