Reflection and transmission of plane waves at an interface between two fluids

The propagation, reflection, and transmission of a plane wave through a column of two fluids with a material discontinuity is studied by three methods: a mixed finite element formulation with both pressure and velocity at a point taken as independent variables, and a scaled and an un-scaled acoustic pressure formulation in which only the pressure at a point is taken as an independent variable. It is found that when mass densities of two fluids are close to each other, the un-scaled acoustic pressure formulation gives reasonable results. However, when the speeds of sound in two fluids are close to each other but their mass densities are quite different, and for cases where the first fluid has high impedance relative to that of the second fluid, a mixed or scaled pressure formulation is necessary. Without the mixed or scaled pressure formulation, the continuity conditions at the interface between two fluids are not well satisfied for the un-scaled pressure formulation. The consideration of viscosity of the two fluids and using a dispersion correction method in the time integration scheme in the mixed formulation slightly improves results.