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.

Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (msc 65M60), Liquid-gas two-phase flows, bubbly flows (msc 76T10), Dusty-gas two-phase flows (msc 76T15)
Life Sciences (theme 5), Energy (theme 4)
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.