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Title: Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method

Abstract

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stability property is important for the robustness of the method, in particular when applied to problems with discontinuous solutions or when the mesh is under-resolved. This line-based method is significantly less computationally expensive than a standard DG method. Numerical results are shown demonstrating the effectiveness of the method on a variety of test cases, including Burgers’ equation and the Euler equations, in one, two, and three spatial dimensions.

Authors:
ORCiD logo [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1548369
Report Number(s):
LLNL-JRNL-767379
Journal ID: ISSN 0885-7474; 957725
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Scientific Computing
Additional Journal Information:
Journal Volume: 80; Journal Issue: 1; Journal ID: ISSN 0885-7474
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Entropy stability; Discontinuous Galerkin; Line-DG; Spectral element method

Citation Formats

Pazner, Will, and Persson, Per-Olof. Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method. United States: N. p., 2019. Web. doi:10.1007/s10915-019-00942-1.
Pazner, Will, & Persson, Per-Olof. Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method. United States. doi:10.1007/s10915-019-00942-1.
Pazner, Will, and Persson, Per-Olof. Wed . "Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method". United States. doi:10.1007/s10915-019-00942-1.
@article{osti_1548369,
title = {Analysis and Entropy Stability of the Line-Based Discontinuous Galerkin Method},
author = {Pazner, Will and Persson, Per-Olof},
abstractNote = {We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stability property is important for the robustness of the method, in particular when applied to problems with discontinuous solutions or when the mesh is under-resolved. This line-based method is significantly less computationally expensive than a standard DG method. Numerical results are shown demonstrating the effectiveness of the method on a variety of test cases, including Burgers’ equation and the Euler equations, in one, two, and three spatial dimensions.},
doi = {10.1007/s10915-019-00942-1},
journal = {Journal of Scientific Computing},
number = 1,
volume = 80,
place = {United States},
year = {2019},
month = {3}
}

Journal Article:
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This content will become publicly available on March 20, 2020
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