In this work a numerical method for the solution of the two-dimensional Euler equations describing unsteady compressible two-fluid flow is presented. The method is based on the combination of a Runge-Kutta discontinuous Galerkin discretization of the Euler equations and a level-set method for the treatment of the two-fluid interface. The corresponding level-set equation is used in its advective form which, as opposed to the frequently used conservative form, does not generate an erroneous off-set in the interface location. A simple fix is applied to prevent the solution from becoming oscillatory near the two-fluid interface. Application of this fix requires the development of a special two-fluid slope limiter for the discontinuous Galerkin method. Numerical results show the competence of the developed method.

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Modelling, Analysis and Simulation [MAS]
Scientific Computing

Naber, J, & Koren, B. (2007). A Runge-Kutta discontinuous-Galerkin level-set method for unsteady compressible two-fluid flow. Modelling, Analysis and Simulation [MAS]. CWI.