Abstract: A fourth-order semi-discrete central-upwind scheme for multidimensional inviscid compressible Euler equations is presented in this paper. Based on the local speeds of nonlinear wave propagation at grids boundaries, the width of the local Riemann fans are calculated more accurately. Thus the scheme enjoys a much smaller numerical viscosity, and the staggering between two sets of grids is avoided. Since the location of the interface can be tracked by Level Set function implicitly and the boundary conditions are implicitly captured by the construction of a ghost fluid, the scheme is combined with the Level Set method and the ghost fluid method. In this way, the non-reacting shock problems and detonation discontinuities in multimaterial flows are tracked successfully.