The exact region of stability for MacCormack scheme |
| |
Authors: | H Hong |
| |
Affiliation: | 1. Research Institute for Symbolic Computation, Johannes Kepler University, A-4040, Linz, Austria
|
| |
Abstract: | Let the two dimensional scalar advection equation be given by $$\frac{{\partial u}}{{\partial t}} = \hat a\frac{{\partial u}}{{\partial x}} + \hat b\frac{{\partial u}}{{\partial y}}.$$ We prove that the stability region of the MacCormack scheme for this equation isexactly given by $$\left( {\hat a\frac{{\Delta _t }}{{\Delta _x }}} \right)^{2/3} + \left( {\hat b\frac{{\Delta _t }}{{\Delta _x }}} \right)^{2/3} \leqslant 1$$ where Δ t , Δ x and Δ y are the grid distances. It is interesting to note that the stability region is identical to the one for Lax-Wendroff scheme proved by Turkel. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|