Non-oscillatory Numerical Schemes for Conservation Laws on the Cubed Sphere

07/28/2011 - 1:45pm to 2:05pm
Main Seminar Room - ML
Yifan Zhang

Yifan Zhang, Brown University

Abstract:  The Discontinuous Galerkin (DG) method is high order, conservative and suitable to be extended to parallel environment.
However when there is discontinuity in the solution, the high order scheme will generate some oscillations, which deteriorates the quality of the numerical solution.
To suppress the oscillation and keep the initial bound of the numerical solution, we implement an HWENO (Hermite-Weighted Essentially None Oscillatory) limiter and a Bound-Preserving (BP) filter on the DG scheme, which will not degenerate the accuracy of the numerical solution in the smooth region, but will also effectively eliminate the overshoot and undershoot in the oscillatory region. Moreover, both the limiter and filter can be extended to arbitrary high order and has a local compact computational stencil.
In this talk, several numerical examples in 2D and on the cubed sphere will be presented.

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Presented on July 28, 2011 at NCAR