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Title: A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation

Abstract

In this work, a high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for solving two-dimensional hydrodynamic problems in cell-centered updated Lagrangian formulation. This method is the Lagrangian limit of the unsplit rDG-ALE formulation, and is obtained by assuming the equality of the grid velocity to the fluid velocity only at cell boundaries. The conservative variables and the Taylor basis defined on the time-dependent moving mesh, provide the piece-wise polynomial expansion in the updated Lagrangian formulation. A multi-directional nodal Riemann solver is implemented for computing the grid velocity at the vertices and the numerical flux at the cell boundaries. A characteristic limiting procedure is extended from the primitive variable version to the conservative variable version, and its performance is compared with the limiter on physical variables. A number of benchmark test cases are conducted to assess the accuracy, robustness, and non-oscillatory property of the DG(P0), DG(P1) and rDG(P1P2) methods. The numerical experiments demonstrate that the developed rDG method is able to attain the designed order of accuracy and the characteristic limiting procedure outperforms the limiter on physical variables in terms of the monotonicity and symmetry preservation for shock problems.

Authors:
 [1]; ORCiD logo [1]; ORCiD logo [2]
+ Show Author Affiliations
  1. North Carolina State Univ., Raleigh, NC (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
OSTI Identifier:
1607918
Report Number(s):
LA-UR-18-23023
Journal ID: ISSN 0045-7930
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 202; Journal Issue: C; Related Information: This paper is dedicated to the memory of Dr. Douglas Nelson Woods ( ∗January 11 th 1985 - † September 11 th 2019), promising young scientist and post-doctoral research fellow at Los Alamos National Laboratory.; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; Lagrangian; Reconstructed discontinuous Galerkin; High-order; Hydrodynamics; Conservative variables; Compressible flows

Citation Formats

Wang, Chuanjin, Luo, Hong, and Shashkov, Mikhail Jurievich. A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation. United States: N. p., 2020. Web. doi:10.1016/j.compfluid.2020.104522.
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Wang, Chuanjin, Luo, Hong, & Shashkov, Mikhail Jurievich. A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation. United States. https://doi.org/10.1016/j.compfluid.2020.104522
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Wang, Chuanjin, Luo, Hong, and Shashkov, Mikhail Jurievich. Thu . "A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation". United States. https://doi.org/10.1016/j.compfluid.2020.104522. https://www.osti.gov/servlets/purl/1607918.
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@article{osti_1607918,
title = {A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation},
author = {Wang, Chuanjin and Luo, Hong and Shashkov, Mikhail Jurievich},
abstractNote = {In this work, a high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for solving two-dimensional hydrodynamic problems in cell-centered updated Lagrangian formulation. This method is the Lagrangian limit of the unsplit rDG-ALE formulation, and is obtained by assuming the equality of the grid velocity to the fluid velocity only at cell boundaries. The conservative variables and the Taylor basis defined on the time-dependent moving mesh, provide the piece-wise polynomial expansion in the updated Lagrangian formulation. A multi-directional nodal Riemann solver is implemented for computing the grid velocity at the vertices and the numerical flux at the cell boundaries. A characteristic limiting procedure is extended from the primitive variable version to the conservative variable version, and its performance is compared with the limiter on physical variables. A number of benchmark test cases are conducted to assess the accuracy, robustness, and non-oscillatory property of the DG(P0), DG(P1) and rDG(P1P2) methods. The numerical experiments demonstrate that the developed rDG method is able to attain the designed order of accuracy and the characteristic limiting procedure outperforms the limiter on physical variables in terms of the monotonicity and symmetry preservation for shock problems.},
doi = {10.1016/j.compfluid.2020.104522},
journal = {Computers and Fluids},
number = C,
volume = 202,
place = {United States},
year = {Thu Mar 19 00:00:00 EDT 2020},
month = {Thu Mar 19 00:00:00 EDT 2020}
}
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https://doi.org/10.1016/j.compfluid.2020.104522
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