Volume 1, Issue 4
A Parameter-Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids

Adv. Appl. Math. Mech., 1 (2009), pp. 451-480.

Published online: 2009-01

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• 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.

• Keywords

Limiter, shock-capturing, high-order, unstructured grids.

65M70, 76M20, 76M22

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@Article{AAMM-1-451, author = {Michael and Yang and and 20568 and and Michael Yang and Z.J. and Wang and and 20569 and and Z.J. Wang}, title = {A Parameter-Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0913}, url = {http://global-sci.org/intro/article_detail/aamm/8381.html} }
TY - JOUR T1 - A Parameter-Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids AU - Yang , Michael AU - Wang , Z.J. JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 451 EP - 480 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/10.4208/aamm.09-m0913 UR - https://global-sci.org/intro/article_detail/aamm/8381.html KW - Limiter, shock-capturing, high-order, unstructured grids. AB -

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.

Michael Yang & Z.J. Wang. (1970). A Parameter-Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids. Advances in Applied Mathematics and Mechanics. 1 (4). 451-480. doi:10.4208/aamm.09-m0913
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