@Article{AAMM-1-451,
author = {Yang , Michael and Wang , Z.J.},
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 = {<p style="text-align: justify;">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
&quot;troubled-cell&quot; 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 &quot;troubled cells&quot;. 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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.09-m0913},
url = {http://global-sci.org/intro/article_detail/aamm/8381.html}
}