A HIGHER-ORDER BOUNDARY TREATMENT FOR CARTESIAN-GRID METHODS

The Euler equations describe the flow phenomena of compressible invisc id gas dynamics, We simulate such flows using a higher-order Cartesian -grid method, together with a special treatment for the cells cut by t he boundary of an object, A new method for the treatment of the bounda ry is described 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 in one dimension and higher-order acc urate in two dimensions I,ut not strictly conservative; however, we sh ow that this error in the conservation does not lead to spurious pheno mena on some representative test calculations, The advantages of the n ew boundary treatment are that it is higher-order accurate, that it is independent of the applied method, and that it is simple. (C) 1998 Ac ademic Press.