Accuracy Assessment of the Cartesian grid method for compressible inviscid flows using a simplified ghost point treatment

Abstract

We introduce a new approach to treat ghost points near embedded boundaries tosolve the 2D compressible Euler equations on a Cartesian grid. Solid wall boundary conditionsare imposed by our new approach called simplified ghost pointtreatment for compressible invis-cid flows with embedded boundaries. In the simplified ghost point treatment, we assume the solidboundary to lie in the middle between two grid points in they-direction. Symmetry conditionsare used to determine density, pressure, wall tangential, and wall normal velocity componentsat the ghost points. A cell-vertex finite volume formulationhas been used to calculate transonicinternal flows over a circular arc bump in a channel.