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Title:
A Divergence-free Upwind Code for Multidimensional Magnetohydrodynamic Flows
Authors:
Ryu, Dongsu; Miniati, Francesco; Jones, T. W.; Frank, Adam
Publication:
The Astrophysical Journal, Volume 509, Issue 1, pp. 244-255. (ApJ Homepage)
Publication Date:
12/1998
Origin:
APJ
ApJ Keywords:
METHODS: NUMERICAL, MAGNETOHYDRODYNAMICS: MHD
DOI:
10.1086/306481
Bibliographic Code:
1998ApJ...509..244R

Abstract

A description is given for preserving ∇ ˙ B = 0 in a magnetohydrodynamic (MHD) code that employs the upwind, total variation diminishing (TVD) scheme and Strang type operator splitting for multidimensionality. The method is based on the staggered mesh technique to constrain the transport of magnetic field: the magnetic field components are defined at grid interfaces with their advective fluxes on grid edges, while other quantities are defined at grid centers. The magnetic field at grid centers for the upwind step is calculated by interpolating the values from grid interfaces. The advective fluxes on grid edges for the magnetic field evolution are calculated from the upwind fluxes at grid interfaces. Then the magnetic field can be maintained with ∇ ˙ B = 0 exactly, if this is so initially, while the upwind scheme is used for the update of fluid quantities. The correctness of the code is demonstrated through tests comparing numerical solutions either with analytic solutions or with numerical solutions from a code using an explicit divergence-cleaning method. Also, the robustness is shown through tests involving realistic astrophysical problems.
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