Colloquium April 28
Date: Friday April 28
Time: 16:00 to 17:00
Place: 455 McBryde (Commons Room)
Speaker: Wai Sun Don of Brown Univ
Title: High Order Methods for Discontinuous Hyperbolic PDEs
Abstract
In this talk, an overview of the hybridization of spectral
methods and
WENO (Weighted Essentially Non-Oscillatory) methods for discontinuous
hyperbolic conservation laws will be given. The domain is broken into
sub-domains of smoothness and sub-domains of discontinuous or steep
gradients. In the sub-domain containing discontinuities or steep
gradients, a WENO method is implemented, whereas in smooth regions, a
spectral method is used. Implementing this hybridization allows for
maintaining spectral accuracy in smooth regions while capturing
discontinuities without the use of post-processing techniques to
overcome the Gibbs phenomenon produced by spectral methods. To locate
regions of smoothness, a high order version of the multi-resolution
algorithm developed by Harten is used. A discussion of the numerical
treatment of the interfaces between the sub-domains and the sub-domain
switching algorithm will also be given. Numerical experiments with
compressible flow in the presence of shock waves are illustrated for
both one-dimensional (Shock-Density interaction) and two-dimensional
Euler equations (Shock-Vortex interaction and Richtmyer-Meshkov
instabilities).
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