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A Parameter-Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids

A Parameter-Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids
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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.

Author Details

Michael Yang

Z.J. Wang

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