Jayesh Badwaik: Moving Mesh Methods for Compressible Flows
Speaker: Jayesh Badwaik (University of Würzburg)
Title: Moving Mesh Methods for Compressible Flows
Abstract: Fixed mesh methods impact the accuracy of astrophysical simulations due to their lack of Galilean invariance. In particular, the artificial dissipation introduced by such methods can lead to a significant loss of accuracy during simulations of fast moving fluids. Moving mesh methods are a class of methods which can reduce artificial dissipation by moving the mesh with velocity close to the local fluid velocity.
In this talk, we present one such method, in form of a single step, explicit in time discontinuous Galerkin scheme on moving meshes using the arbitrary Lagrangian-Eulerian approach for one and two dimensional compressible flows. A localized mesh repair algorithm allows us to maintain a high mesh quality while still keeping the mesh motion to an almost Lagrangian state. These methods are primarily designed to run on large scale simulation clusters, which come with their own performance characteristics and bottlenecks. We discuss the influence of those on the design of our algorithms. We finally show results for linear advection and Euler equations in one and two dimensions.