Year: 2009
Author: Michael Yang, Z.J. Wang
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 4 : pp. 451–480
Abstract
A parameter-free limiting technique is developed for high-order unstruc- tured-grid methods to capture discontinuities when solving hyperbolic conservation laws. The technique is based on a "troubled-cell" approach, in which cells requiring limiting are first marked, and then a limiter is applied to these marked cells. A parameter-free accuracy-preserving TVD marker based on the cell-averaged solutions and solution derivatives in a local stencil is compared to several other markers in the literature in identifying "troubled cells". This marker is shown to be reliable and efficient to consistently mark the discontinuities. Then a compact high-order hierarchical moment limiter is developed for arbitrary unstructured grids. The limiter preserves a degree $p$ polynomial on an arbitrary mesh. As a result, the solution accuracy near smooth local extrema is preserved. Numerical results for the high-order spectral difference methods are provided to illustrate the accuracy, effectiveness, and robustness of the present limiting technique.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.09-m0913
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 4 : pp. 451–480
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Limiter shock-capturing high-order unstructured grids.