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An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations: Continuous analysis and GLM divergence cleaning. (arXiv:1711.05576v1 [math.NA])
来源于:arXiv
This work presents an extension of discretely entropy stable discontinuous
Galerkin (DG) methods to the resistive magnetohydrodynamics (MHD) equations.
Although similar to the compressible Navier-Stokes equations at first sight,
there are some important differences concerning the resistive MHD equations
that need special focus. The continuous entropy analysis of the ideal MHD
equations, which are the advective parts of the resistive MHD equations, shows
that the divergence-free constraint on the magnetic field components must be
incorporated as a non-conservative term in a form either proposed by Powell or
Janhunen. Consequently, this non-conservative term needs to be discretized,
such that the approximation is consistent with the entropy. As an extension of
the ideal MHD system, we address in this work the continuous analysis of the
resistive MHD equations and show that the entropy inequality holds. Thus, our
first contribution is the proof that the resistive terms are symmetric and
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