A discontinuous Galerkin front tracking method for two-phase flows with surface tension

Abstract

A discontinuous Galerkin method for solving hyperbolic systems of conservation laws involving interfaces is presented. The interfaces are represented by a collection of element boundaries and their position is updated using an arbitrary Lagrangian-Eulerian method. The motion of the interfaces and the numerical fluxes are obtained by solving a Riemann problem. As the interface is propagated, a simple and effective remeshing technique based on distance functions regenerates the grid to preserve its quality. Compared to other interface capturing techniques, the proposed approach avoids smearing of the jumps across the interface which leads to an improvement in accuracy. Numerical results are presented for several typical two-dimensional interface problems, including flows with surface tension. © 2009 Elsevier Ltd. All rights reserved.