Finite volume TVD scheme on an unstructured grid system for three-dimensional MHD simulation of inhomogeneous systems including strong background potential fields

Journal Article · Fri Apr 01 00:00:00 EST 1994 · Journal of Computational Physics; (United States)

DOI:https://doi.org/10.1006/jcph.1994.1071· OSTI ID:6971384

Tanaka, T ^[1]

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1. Communication Research Lab., Tokyo (Japan)

A three-dimensional (3D) high-resolution MHD simulation scheme on an unstructured grid system is developed for inhomogeneous systems, including strong background potential fields. The scheme is based on the finite volume method (FVM) with an upwinding numerical flux by the linearized Riemann solver. Upwinding on an unstructured grid system are realized from the fact that the MHD equations are symmetric with the rotation of the space. The equation system is modified to avoid direct inclusions of the background potential field as a dependent variable, through the use of changed dependent variables. Despite such a change of the equation system, the eigenvectors in the mode-synthesis matrix that are necessary for the evaluation of the upwinding numerical flux vectors can still be written analytically. The eigenvalues of the MHD flux Jacobian matrix that are also necessary for the upwinding calculations are derived from the well-known Alfven, fast and slow, velocities. The calculations of the eigen vectors is done with special care when the wave propagations become parallel or perpendicular to the ambient magnetic field, because degeneration of the eigenvalues occurs in these cases. To obtain a higher order of accuracy, the upwinding flux is extended to the second-order TVD numerical flux in the calculation of FVM, through the MUSCL approach and Van Leer's differential limiter. In order to show the efficiency of the above scheme, a numerical example is given for the interaction process of high-[beta] supersonic plasma flow with the region of a strong dipole field, including magnetized low-[beta] plasma. 16 refs., 5 figs.

• OSTI ID: 6971384
• Journal Information: Journal of Computational Physics; (United States), Vol. 111:2; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
MAGNETOHYDRODYNAMICS
COMPUTERIZED SIMULATION
THREE-DIMENSIONAL CALCULATIONS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
MESH GENERATION
FLUID MECHANICS
HYDRODYNAMICS
MECHANICS
SIMULATION
665510* - Magnetohydrodynamics- (1992-)
990200 - Mathematics & Computers