Split Form Discontinuous Galerkin Methods and Trixi.jl

presentation Aachen

Fri, 9 Dec 2022 12:00
TUM AER journal club via Zoom

Prof. Gregor Gassner (University of Cologne) and Dr. Michael Schlottke-Lakemper (RWTH Aachen)

Split Form Discontinuous Galerkin Methods and Trixi.jl

The talk is organized in two parts. First, we will focus on the split form discontinuous Galerkin frame- work. The idea is to combine concepts from the finite difference community with ideas from finite vol- umes to construct a (provably) robust discontinuous Galerkin approximation for nonlinear hyperbolic partial differential equations (PDE), such as the compressible Euler equations, or the magnetohydro- dynamics equations. The basic idea is to use a combination of different product rules and chain rules to re-write the non-linearity in the PDE, such that their discretization gives better properties, such as improved robustness. An important question is how to retain full discrete conservation for such split formulations. Furthermore, we will show that this methodology enables shock capturing, via convex blending of a suitable compatible sub-cell low order discretization. In the second part of the talk, we focus on our novel simulation tool, Trixi.jl, where these methods are implemented and available. Trixi.jl is generally a numerical simulation framework for adaptive, high-order discretizations of conservation laws. It has a modular architecture that allows users to easily extend its functionality and was designed to be useful to experienced researchers and new users alike. We will give an overview of Trixi’s current features, present a typical workflow for creating and running a simulation, and show how to add new capabilities for your own research projects. We further evaluate the performance of Trixi.jl for serial and parallel workloads.

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