Ghost-Cell Method for Inviscid Two-Dimensional Flows on Cartesian Grids

Abstract

A new approach to the computation of inviscid flows using Cartesian grid methods is presented. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids and reviewed here. The method introduces ghost cells near the boundaries whose values are developed from an assumed flowfield model in the vicinity of the wall consisting of a vortex flow that satisfies the normal momentum equation and the nonpenetration condition. The CCST boundary condition was shown to be substantially more accurate than traditional boundary-condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation that we term the ghost body-cell method. In this method, all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges. There is no need for special treatment corresponding to cut cells, which complicate other Cartesian mesh methods. The merits of the method are indicated by the computation of the compressible flow about basic circular cylinders as well as of airfoil applications and detailed comparisons to body-fitted grid computations