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SC²S Colloquium - June 11, 2013

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Date: June 11, 2013
Room: 02.07.023
Time: 2:30 pm, s.t.

Michael Müller: Application of Shallow Water Equations on Spherical-Distorted Triangular Grids

The open source framework Sierpinski ( currently developed at the chair of SCCS plays an important role in the scope of solving dynamically refined hyperbolic problems on edge based communication. Therefore, the Sierpinski project provides key features for 2D and semi 3D hyperbolic simulation on dynamically adaptive regular triangular grids. Such are advanced flux solvers, Runge-Kutta time-stepping, bathymetry and benchmarks. Thus, the Sierpinski framework allows highly efficient near field tsunami simulations, where the influence of the spherical shape of the earth is negligible.

The goal of this interdisciplinary project is to develop and implement an extension of the Sierpinski framework allowing to simulate long-range tsunamis. Therefore, it is necessary to apply appropriate routines to project the existing solvers, which are applicable to plain two dimensional surfaces, onto spherical surfaces. Since the “Sierpinski” framework is supposed to compute a large number of momentum updates per simulation time step when using high refinement depths on global domains, it is of uttermost importance to provide efficient projection methods.

Philipp Müller and Stjepan Bakrac: Discontinous Galerkin Methods for Shallow Water Equations

For simulations based on the Shallow Water equations (SWE) as they are used for tsunami simulations, the use of Discontinuous Galerkin schemes with higher-order basis functions received growing attention during the last years. This project aims to examine differences between integrals computed analytically and by numerical quadrature. The SWE include three interesting terms: Mass term, flux term and stiffness term. Our last presentation dealt with the approximation of the Lax-Friedrichs flux (i.e. the flux term). Now we consider another error that is introduced by the stiffness term and empirically analyze its accuracy with a custom-built tool.