An Approximate Riemann Solver for Magnetohydrodynamics (That Works More Than One Dimension)
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics MHD. The Riemann solver has an eight- wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eight wave is not immediately obvious from the governing equations as they are usually written, but arises from the modification of the equations that is presented in this paper. The addition of the eighth wave allows multi-dimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one of the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two- dimensional code yields answers consistent with one-dimensional methods developed previously.
- Numerical Mathematics
- Plasma Physics and Magnetohydrodynamics