A method for the calculation of unsteady, axisymmetric compressible flows i
nvolving both fixed and separating bodies is presented. The method uses a C
artesian cut-cell mesh approach and high resolution upwind finite volume sc
heme. A stationary background Cartesian mesh is generated on the computatio
nal domain with complex solid geometries represented by different types of
cut cell. Solid bodies are allowed to move across the mesh using a finite v
olume scheme modified to deal with moving boundary problems. The flow solve
r employed is a MUSCL-Hancock Godunov-type scheme in conjunction with an ap
proximate Riemann solver of the Harten, Lax, and van Leer type (for flow in
terfaces) and an exact Riemann solver for a moving piston (for fixed or mov
ing solid faces). A cell merging technique is used to maintain numerical st
ability in the presence of arbitrarily small cut cells and to retain strict
conservation at moving boundaries. The method is applied to a muzzle blast
flow and muzzle break problems involving both fixed and separating bodies.