Improvement of the Level-Set Ghost-Fluid Method for the Compressible Euler Equations

Abstract

This paper describes improvements of a level-set ghost-fluid algorithm in the scope of sharp interface multi-phase flow simulations. The method is used to simulate drop-drop and shock-drop interactions. Both, the level-set and the bulk phases are discretized by a high order discontinuous Galerkin spectral element method. The multi-phase interface and shocks are captured with a finite volume sub-cell method. The first improvement, is the use of the finite-volume sub-cells to capture discontinuities in the level-set equation. This allows the simulation of merging droplets. The second improvement is the introduction of an increased polynomial degree for the level-set equation in comparison to the Euler equations. The goal of this modification is to reduce parasitic currents. Additionally, the whole method is validated against experimental results.