High-order finite-volume integration schemes for subsonic magnetohydrodynamics

Abstract

We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented up to tenth order of accuracy. This method requires only one reconstructed value per face for each computational cell. A passage through high-order point values leads to a modest growth of computational cost with increasing discretization order. At a given resolution, these high-order schemes present significantly less numerical dissipation than commonly employed lower-order approaches. Thus, results of comparable accuracy are achievable at a substantially coarser resolution, yielding overall performance gains. We also present a way to include physical dissipative terms: viscosity, magnetic diffusivity and cooling functions, respecting the finite-volume and constrained-transport frameworks.

Submitted to JCP. In version 1, the use of a global smoothness indicator: mass density+average of magnetic field components, suitable in supersonic flows, lead to difficulties in the convergence test (MHD vortex) and spurious oscillations for S6 and S8 in the hydro case. Version 2 uses individual smoothness indicators

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