FINITE-VOLUME TVD SCHEME ON AN UNSTRUCTURED GRID SYSTEM FOR 3-DIMENSIONAL MHD SIMULATION OF INHOMOGENEOUS SYSTEMS INCLUDING STRONG BACKGROUND POTENTIAL FIELDS

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. Upwindings 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 differentiable 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-fl plasma. (C) 1994 Academic Press, Inc.