Second order accurate boundary treatment for Cartesian grid methods

Abstract

The Euler equations describe the flow phenomena of compressible inviscid gas dynamics. We simulate such flows using a higher order Cartesian grid method together with a special treatment for the cells cut by the boundary of a body. We describe a new method for the treatment of the boundary where these cut boundary cells are maintained as whole cells rather than as cut cells, thus avoiding stability problems. The method is second order accurate but not strictly conservative, but we can show that this error in the conservation does not lead to spurious phenomena on some representative test calculations. The advantages of the new boundary treatment are that it is second order accurate, that it is independent of the applied method, and that it can easily be extended to three-dimensional calculations.