SC²S Colloquium - November 04, 2016
|Date:||November 04, 2016|
|Time:||3:00 pm, s.t.|
Leonhard Rannabauer: Developing an ADER Discontinuous Galerkin Method, with Finite Volume limiting approach for the sam(oa)2 framework
In my Thesis I developed a Discontinuous Galerkin Method within the sam(oa)^2 framework, for the simulation of Shallow Water Equations. The key element of this scheme is a newly proposed predictor step, replacing the common methods for time integration. To stabilize the DG Method a new limiter approach using a Finite Volume scheme was implemented. This limiter converts the solution for instabilities, e.g., through Gibbs Phenomenon, between DG approximation and the representation on a Finite Volume Patch. As criterion to detect these instabilities two admissibility conditions, Physical and Numerical, where introduced. Additionally I used an uncommon set of basis functions for the polynomial approximation of the solution, the Bernstein polynomials. These have properties simplifying the calculation of lower boundaries and obtaining their representation along element faces. In my first presentation I will introduce the methods used in my Master’s Thesis and share my difficulties and experiences with them.