A Discontinuous Galerkin Method for Droplet Dynamics in Weakly Compressible Flows

Considering weakly compressible droplet dynamic phenomena, large discrepancies in the magnitude of the occurring characteristic waves are present. This poses problems to numerical methods. In this work a novel numerical scheme to tackle these challenges, based on the high order discontinuous Galerkin method is introduced. Implicit-explicit flux splitting techniques are investigated towards their usability for the simulation of low Mach number flows. They then serve as a building block to extend the applicability of the compressible level-set ghost fluid method to flow situations at low Mach numbers. The novel scheme is validated and applied to typical problems of weakly compressible droplet dynamics such as free drop oscillation and drop collisions.