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Title: Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes

Abstract

Abstract 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.

Authors:
; ; ;
Publication Date:
Research Org.:
Brown Univ., Providence, RI (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1537202
DOE Contract Number:  
FG02-08ER25863
Resource Type:
Journal Article
Journal Name:
Communications in Computational Physics
Additional Journal Information:
Journal Volume: 21; Journal Issue: 3; Journal ID: ISSN 1815-2406
Publisher:
Global Science Press
Country of Publication:
United States
Language:
English
Subject:
Physics

Citation Formats

Zhu, Jun, Zhong, Xinghui, Shu, Chi-Wang, and Qiu, Jianxian. Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes. United States: N. p., 2017. Web. doi:10.4208/cicp.221015.160816a.
Zhu, Jun, Zhong, Xinghui, Shu, Chi-Wang, & Qiu, Jianxian. Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes. United States. doi:10.4208/cicp.221015.160816a.
Zhu, Jun, Zhong, Xinghui, Shu, Chi-Wang, and Qiu, Jianxian. Tue . "Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes". United States. doi:10.4208/cicp.221015.160816a.
@article{osti_1537202,
title = {Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes},
author = {Zhu, Jun and Zhong, Xinghui and Shu, Chi-Wang and Qiu, Jianxian},
abstractNote = {Abstract 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.},
doi = {10.4208/cicp.221015.160816a},
journal = {Communications in Computational Physics},
issn = {1815-2406},
number = 3,
volume = 21,
place = {United States},
year = {2017},
month = {2}
}