An Extended Discontinuous Galerkin Framework for Multiphase Flows

We present a framework for handling cut cells in a high order discontinuous Galerkin (DG) context. To describe the boundary between fluid phases, we use a level-set formulation. When the interface cuts a computational cell, we discretize the resulting sub-cells with the same DG method as used on standard cells. This requires a suitable quadrature procedure. Within this framework, we present a solver for the two-phase Navier-Stokes equation, a reinitialization procedure for the level-set and a solver for transport-processes on the surface.

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