On Equations of State for Simulations of Multiphase Flows

An efficient Eulerian numerical method is considered for simulating multiphase flows governed by general equation of state (EOS). The method allows interfaces between phases to diffuse in a transitional region over a small number of computational cells. The seven-equation model of Saurel and Abgrall [Saurel, R. and Abgrall, R., A multiphase Godunov method for compressible multifluid and multiphase flows, J. Comput. Phys. 150 (1999), 425 467] is employed to describe the compressible multiphase flows. For one dimensional flow the model which is strictly hyperbolic consists of seven equations. These equations are the volume fraction evolution equation and the conservation equations (mass, momentum and energy) for each phase. The solution of the hyperbolic equations is obtained using HLL Riemann solver. In the present work various equations of state (EOSs) have been discussed. Error analysis, number of time steps and CPU time comparisons between EOSs have been presented. Well known test cases are examined to simulate compressible as well as incompressible multiphase flows.

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