An adaptive grid finite difference method for time-dependent Magnetohydrodynamic (MHD) flows and its astrogeophysical applications
Abstract
An adaptive grid finite difference method for solving time dependent, magnetohydrodynamic (MHD) equations is developed. The method is capable of solving problems that include high gradients due to geometry, propagation of shock waves and unsteady boundary conditions. The grid generation technique is based on variational principles with direct control over grid concentration, smoothness and skewness. Studies of one dimensional MHD wave propagation in the subsonic, sub-Alfvenic flow region in the solar corona and the propagation of finite amplitude disturbances in the supersonic, super-Alfvenic flow region of the solar wind are used to demonstrate the technique's accuracy and versatility. The adaptive grid method was used to study the propagation of solar generated disturbances through the solar wind critical points. The physical parameters of the steady state solar wind vary rapidly near the solar surface. The adaptive grid enables the circumvention of these difficulties by placing an extensive number of grid points near the solar surface and around the shock fronts. The method is shown to give a significant increase in accuracy and stability in the computation of this problem.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- December 1987
- Bibcode:
- 1987PhDT........12P
- Keywords:
-
- Astrophysics;
- Finite Difference Theory;
- Geophysics;
- Magnetohydrodynamic Flow;
- Time Dependence;
- Computational Fluid Dynamics;
- Computational Grids;
- Grid Generation (Mathematics);
- Shock Waves;
- Solar Corona;
- Solar Wind;
- Steady State;
- Wave Propagation;
- Plasma Physics