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.