MmB: A new class of accurate high resolution schemes for conservation laws in two dimensions
Abstract
The MmB schemes, which preserve the local maximum and minimum bounds of the initial data in the smallest union of mesh elements of the previous time step containing the domain of dependence of the solution on the mesh element with center at point P under consideration are presented. In 1D, the MmB schemes are almost identical with Total Variation Diminishing (TVD) schemes. There is no secondorder TVD scheme in 2D. Nevertheless, researchers present here two classes of 2D secondorder accurate MmB schemes. It is proved that 1D discrete MmB (or TVD) and 1D semidiscrete TVD schemes may have secondorder accuracy at (nonsonic) critical points, but cannot be uniformly secondorder accurate in the whole neighborhood of the critical point. New accurate high resolution flux limiters are suggested. Numerical results for 1D and 2D test problems are given.
 Publication:

Tokyo Symposium on Mechanics for Space Flight 1989
 Pub Date:
 March 1990
 Bibcode:
 1990tmsf.proc..115W
 Keywords:

 Computational Grids;
 Conservation Laws;
 Flow Distribution;
 Fluid Dynamics;
 High Resolution;
 Hypersonic Flow;
 Spheres;
 Tvd Schemes;
 Accuracy;
 Algorithms;
 Critical Point;
 Functions (Mathematics);
 Traveling Waves;
 Fluid Mechanics and Heat Transfer