@Article{CiCP-33-5,
author = {Yizhou, Lu and Zhu, Jun and Shengzhu, Cui and Zhenming, Wang and Tian, Linlin and Zhao, Ning},
title = {High-Order Local Discontinuous Galerkin Method with Multi-Resolution WENO Limiter for Navier-Stokes Equations on Triangular Meshes},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {5},
pages = {1217--1239},
abstract = {<p style="text-align: justify;">In this paper, a new multi-resolution weighted essentially non-oscillatory
(MR-WENO) limiter for high-order local discontinuous Galerkin (LDG) method is designed for solving Navier-Stokes equations on triangular meshes. This MR-WENO
limiter is a new extension of the finite volume MR-WENO schemes. Such new limiter
uses information of the LDG solution essentially only within the troubled cell itself, to
build a sequence of hierarchical $L^2$ projection polynomials from zeroth degree to the
highest degree of the LDG method. As an example, a third-order LDG method with associated same order MR-WENO limiter has been developed in this paper, which could
maintain the original order of accuracy in smooth regions and could simultaneously
suppress spurious oscillations near strong shocks or contact discontinuities. The linear weights of such new MR-WENO limiter can be any positive numbers on condition
that their summation is one. This is the first time that a series of different degree polynomials within the troubled cell are applied in a WENO-type fashion to modify the
freedom of degrees of the LDG solutions in the troubled cell. This MR-WENO limiter
is very simple to construct, and can be easily implemented to arbitrary high-order accuracy and in higher dimensions on unstructured meshes. Such spatial reconstruction
methodology improves the robustness in the numerical simulation on the same compact spatial stencil of the original LDG methods on triangular meshes. Some classical&nbsp;viscous examples are given to show the good performance of this third-order LDG
method with associated MR-WENO limiter.</p>},
issn = {1991-7120},
doi = {https://doi.org/ 10.4208/cicp.OA-2022-0096},
url = {https://global-sci.com/article/79448/high-order-local-discontinuous-galerkin-method-with-multi-resolution-weno-limiter-for-navier-stokes-equations-on-triangular-meshes}
}