@Article{CiCP-21-623,
author = {Jun Zhu, Xinghui Zhong, Chi-Wang Shu and Jianxian Qiu},
title = {Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes},
journal = {Communications in Computational Physics},
year = {2018},
volume = {21},
number = {3},
pages = {623--649},
abstract = {<p style="text-align: justify;">In this paper we generalize a new type of compact Hermite weighted essentially
non-oscillatory (HWENO) limiter for the Runge-Kutta discontinuous Galerkin
(RKDG) method, which was recently developed in [38] for structured meshes, to two
dimensional unstructured meshes. The main idea of this HWENO limiter is to reconstruct
the new polynomial by the usage of the entire polynomials of the DG solution
from the target cell and its neighboring cells in a least squares fashion [11] while maintaining
the conservative property, then use the classical WENO methodology to form
a convex combination of these reconstructed polynomials based on the smoothness indicators
and associated nonlinear weights. The main advantage of this new HWENO
limiter is the robustness for very strong shocks and simplicity in implementation especially
for the unstructured meshes considered in this paper, since only information
from the target cell and its immediate neighbors is needed. Numerical results for both
scalar and system equations are provided to test and verify the good performance of
this new limiter.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.221015.160816a},
url = {http://global-sci.org/intro/article_detail/cicp/11253.html}
}