Accurate computation of convective transport in transient two-phase flow

The Van Leer method for the computation of convective fluxes is extended to two-phase flow. By preventing spurious undershoots and overshoots, the scheme preserves physical realism while maintaining high-order accuracy. This is particulary important for two-phase flows, since phase exchange terms are typically a function of volume fraction products and numerical diffusion can incorrectly mix the two phases. The scheme described here is constructed to guarantee that the sum of the volume fractions is always unity and that the volume fractions are always greater than or equal to zero. Various test problems are computed to demonstrate the accuracy of the method and to show how the scheme might be incorporated in existing computational methods. In addition to multiphase flow applications, setting equal phase velocities results in a volume marker scheme that is well suited to single-phase interface tracking problems.