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The ghost fluid method allows a propagating interface to remain sharp duringa numerical simulation. The solution of the Riemann problem at the interfaceprovides proper information to determine interfacial fluxes as well as thevelocity of the phase boundary. Then considering two-material problems, theinitial states of the Riemann problem belong to different fluids, which mayhave different equations of states. In the inviscid case, the solution of themulti-fluid Riemann problem is an extension of the classical Riemann problemfor a single fluid. The jump of the initial states between different fluidsgenerates waves in both fluids and induces a movement of the interface, similarto a contact discontinuity. More subtle is the extension to viscous and heatconduction terms which is the main focus of this paper. We account for thediscontinuous coefficients of viscosity and heat conduction at the multi-fluidinterface and derive solutions of the Riemann problem for these parabolicterms, from which we can derive parabolic, interfacial fluxes.

A Viscous and Heat Conducting Ghost Fluid Method for Multi-Fluid Simulations