A model study for the steady state error of numerical approximations of inviscid flow equations on Cartesian grid

Abstract

SUMMARYThe widely used locally adaptive Cartesian grid methods involve a series of abruptly reÿned interfaces. In this paper we consider the in uence of the reÿned interfaces on the steady state errors for second-order three-point di erence approximations of ow equations. Since the various characteristic components of the Euler equations should behave similarly on such grids with regard to reÿnement-induced errors, it is su cient enough to conduct the analysis on a scalar model problem. The error we consider is a global error, di erent to local truncation error, and re ects the interaction between multiple interfaces. The steady state error will be compared to the errors on smooth reÿnement grids and on uniform grids. The conclusion seems to support the numerical ÿndings of Yamaleev and Carpenter (J. Comput. Phys. 2002; 181:280-316) that reÿnement does not necessarily reduce the numerical error.