Hyperbolic theory of the "shallow water" magnetohydrodynamics equations

Authors
Citation
H. De Sterck, Hyperbolic theory of the "shallow water" magnetohydrodynamics equations, PHYS PLASMA, 8(7), 2001, pp. 3293-3304
Citations number
41
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
PHYSICS OF PLASMAS
ISSN journal
1070-664X → ACNP
Volume
8
Issue
7
Year of publication
2001
Pages
3293 - 3304
Database
ISI
SICI code
1070-664X(200107)8:7<3293:HTOT"W>2.0.ZU;2-5
Abstract
Recently the shallow water magnetohydrodynamic (SMHD) equations have been p roposed for describing the dynamics of nearly incompressible conducting flu ids for which the evolution is nearly two-dimensional (2D) with magnetohydr ostatic equilibrium in the third direction. In the present paper the proper ties of the SMHD equations as a nonlinear system of hyperbolic conservation laws are described. Characteristics and Riemann invariants are studied for 1D unsteady and 2D steady flow. Simple wave solutions are derived, and the nonlinear character of the wave modes is investigated. The del.(h B)=0 con straint and its role in obtaining a regularized Galilean invariant conserva tion law form of the SMHD equations is discussed. Solutions of the Rankine- Hugoniot relations are classified and their properties are investigated. Th e derived properties of the wave modes are illustrated by 1D numerical simu lation results of SMHD Riemann problems. A Roe-type linearization of the SM HD equations is given which can serve as a building block for accurate shoc k-capturing numerical schemes. The SMHD equations are presently being used in the study of the dynamics of layers in the solar interior, but they may also be applicable to problems involving the free surface flow of conductin g fluids in laboratory and industrial environments. (C) 2001 American Insti tute of Physics.