Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
A solution-adaptive upwind scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Adaptive blocks: a high performance data structure
SC '97 Proceedings of the 1997 ACM/IEEE conference on Supercomputing
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
A parallel explicit/implicit time stepping scheme on block-adaptive grids
Journal of Computational Physics
Adaptive numerical algorithms in space weather modeling
Journal of Computational Physics
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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.