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 - <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>