A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation

Wang, Chuanjin; Luo, Hong; Shashkov, Mikhail Jurievich

doi:10.1016/j.compfluid.2020.104522

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

Journal Article · Thu Mar 19 00:00:00 EDT 2020 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2020.104522· OSTI ID:1607918

Wang, Chuanjin ^[1];

^[1];

^[2]

North Carolina State Univ., Raleigh, NC (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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.

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Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1607918

Report Number(s):: LA-UR-18-23023

Journal Information:: Computers and Fluids, Vol. 202, 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.; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 7 works

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

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