Hall magnetohydrodynamics on block-adaptive grids

Details Hall magnetohydrodynamics on block-adaptive grids Hall magnetohydrodynamics on block-adaptive grids

Jul 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008jcoph.227.6967t&link_type=abstract

Journal of Computational Physics, Volume 227, Issue 14, p. 6967-6984.

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Scientific paper

We present a conservative second order accurate finite volume discretization of the magnetohydrodynamics equations including the Hall term. The scheme is generalized to three-dimensional block-adaptive grids with Cartesian or generalized coordinates. The second order accurate discretization of the Hall term at grid resolution changes is described in detail. Both explicit and implicit time integration schemes are developed. The stability of the explicit time integration is ensured by including the whistler wave speed for the shortest discrete wave length into the numerical dissipation, but then second order accuracy requires the use of symmetric limiters in the total variation diminishing scheme. The implicit scheme employs a Newton Krylov Schwarz type approach, and can achieve significantly better efficiency than the explicit scheme with an appropriate preconditioner. The second order accuracy of the scheme is verified by numerical tests. The parallel scaling and robustness are demonstrated by three-dimensional simulations of planetary magnetospheres.

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