Open AccessA multidimensional upwind scheme for magnetohydrodynamics
Author(s) -
S. A. E. G. Falle,
S. S. Komissarov,
P. S. Joarder
Publication year - 1998
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1998.01506.x
Subject(s) - physics , upwind scheme , magnetohydrodynamics , scheme (mathematics) , mathematics , dissipation , riemann problem , riemann solver , order (exchange) , riemann hypothesis , mechanics , statistical physics , classical mechanics , mathematical analysis , plasma , discretization , thermodynamics , quantum mechanics , finite volume method , finance , economics
This paper describes a second‐order upwind scheme for multidimensional magnetohydrodynamics, which uses a linear approximation for all Riemann problems except those involving strong rarefactions. This enables it to cope with initial data for which previously published schemes might fail. The condition ▽⊙ B = 0 is not enforced in multidimensions, but the numerical problems associated with this are dealt with by adding source terms to the equations, as suggested by Powell. We also show that there are advantages to adding second‐order artificial dissipation at shocks.