Numerical solutions of two dimensional Euler equations are obtained for
transonic and supersonic flows. The shock capturing method is employed to solve
compressible Euler equations by using MacCormack's time marching method that
an explicit finite-difference technique. The test case chosen is that of a transonic
and supersonic flow through a channel with a circular arc bump on the lower wall,
half wedge and extended compression corner. Computational results accurately
reproduced the flow field. In three cases, contour plots showing the important
features of the flow-field are presented. The algorithm is tested for steady-state
inviscid flows at different Mach numbers ranging from the transonic to the supersonic
regime and the results are compared with the existing numerical solutions. The
method incorporates bounded high resolution of discontinuities and is therefore well
suited to all flow regimes ranging from transonic to supersonic.