Computing interface motion in compressible gas dynamics

An analysis is conducted of the coupling of Osher and Sethian's (1988) 'Hamilton-Jacobi' level set formulation of the equations of motion for propagating interfaces to a system of conservation laws for compressible gas dynamics, giving attention to both the conservative and nonconservative differencing of the level set function. The capabilities of the method are illustrated in view of the results of numerical convergence studies of the compressible Rayleigh-Taylor and Kelvin-Helmholtz instabilities for air-air and air-helium boundaries.