Riemann-problem and level-set approaches for two-fluid flow computations I. Linearized Godunov scheme

A finite-volume method is presented for the computation of compressible flows of two immiscible fluids at very different densities. The novel ingredient in the method is a two-fluid linearized Godunov scheme, allowing for flux computations in case of different fluids (e.g., water and air) left and right of a cell face. A level-set technique is employed to distinguish between the two fluids. The level-set equation is incorporated into the system of hyperbolic conservation laws