Prof. Dr. Christiane Helzel (Universität Düsseldorf)
Wednesday, November 29, 2017 - 14:15
FU Berlin, Pi-Gebäude
Arnimallee 6, 14195 Berlin, SR 025/026
The wave propagation algorithm of LeVeque and its implementation in the software package Clawpack are widely used for the approximation of hyperbolic problems. The method belongs to the class of truly multidimensional, high-resolution finite volume methods. Furthermore, it can be characterised as a one-step Lax-Wendroff type method, i.e. the PDE is solved simultaneously in space and time. Approximations obtained with this method are second order accurate for smooth solutions and avoid unphysical oscillations near discontinuities or steep gradients. Second order accurate methods are often a good choice in terms of balance between computational cost and desired resolution, especially for solutions dominated by shock waves or contact discontinuities and relatively simple structures between these discontinuities. However, for problems containing complicated smooth solution structures, where the accurate resolution of small scales is require, schemes with a higher order of accuracy are more efficient and computationally affordable. I will present my recent work towards the construction of a third order accurate wave propagation algorithm for hyperbolic pdes. Furthermore, I will compare this new method with other recently proposed third order accurate methods.
submitted by Stephan Gerber (stephan.gerber@fu-berlin.de, 030 83859322)