Kelvin-Helmholtz instability - Discontinuous Galerkin hydrodynamics

2D Simulation of a Kelvin-Helmholtz instability with 4th order discontinuous Galerkin (DG) and adaptive mesh refinement. The simulation starts with 64^2 cells and is refined down to an effective resolution of 4096^2 cells. Shown is the surface density of the fluid. DG offers several advantages over traditional finite volume (FV) directly solves also for the higher-order moments of the solution, no reconstruction is needed, resulting in an inherent conservation of angular momentum and less advection and diffusion errors compared to a FV method. Furthermore, DG is a higher-order method with a small stencil and many local computations, which renders it highly suitable for high performance computing on massively parallel systems. You may find the corresponding publication on arXiv: