An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics
Abstract
Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas dynamics. The new method evolves conserved unknowns in the current configuration, which obviates the Jacobi matrix that maps the element in a reference coordinate system or the initial coordinate system to the current configuration. The density, momentum, and total energy (ρ, ρu, E) are approximated with conservative higherorder Taylor expansions over the element and are limited toward a piecewise constant field near discontinuities using a limiter. Two new limiting methods are presented for enforcing the bounds on the primitive variables of density, velocity, and specific internal energy (ρ, u, e). The nodal velocity, and the corresponding forces, are calculated by solving an approximate Riemann problem at the element nodes. An explicit secondorder method is used to temporally advance the solution. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. 1D Cartesian coordinates test problem results are presented to demonstrate the accuracy and convergence order of the new DG method with the new limiters.
 Authors:

 North Carolina State Univ., Raleigh, NC (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Dortmund Univ. of Technology, Dortmund (Germany)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1434431
 Report Number(s):
 LAUR1729217
Journal ID: ISSN 08981221
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computers and Mathematics with Applications (Oxford)
 Additional Journal Information:
 Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 78; Journal Issue: 2; Journal ID: ISSN 08981221
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Lagrangian; Hydrodynamics; Discontinuous Galerkin; Limiters
Citation Formats
Wu, Tong, Shashkov, Mikhail Jurievich, Morgan, Nathaniel Ray, Kuzmin, Dimtry, and Luo, Hong. An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics. United States: N. p., 2018.
Web. doi:10.1016/j.camwa.2018.03.040.
Wu, Tong, Shashkov, Mikhail Jurievich, Morgan, Nathaniel Ray, Kuzmin, Dimtry, & Luo, Hong. An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics. United States. doi:10.1016/j.camwa.2018.03.040.
Wu, Tong, Shashkov, Mikhail Jurievich, Morgan, Nathaniel Ray, Kuzmin, Dimtry, and Luo, Hong. Mon .
"An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics". United States. doi:10.1016/j.camwa.2018.03.040. https://www.osti.gov/servlets/purl/1434431.
@article{osti_1434431,
title = {An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics},
author = {Wu, Tong and Shashkov, Mikhail Jurievich and Morgan, Nathaniel Ray and Kuzmin, Dimtry and Luo, Hong},
abstractNote = {Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas dynamics. The new method evolves conserved unknowns in the current configuration, which obviates the Jacobi matrix that maps the element in a reference coordinate system or the initial coordinate system to the current configuration. The density, momentum, and total energy (ρ, ρu, E) are approximated with conservative higherorder Taylor expansions over the element and are limited toward a piecewise constant field near discontinuities using a limiter. Two new limiting methods are presented for enforcing the bounds on the primitive variables of density, velocity, and specific internal energy (ρ, u, e). The nodal velocity, and the corresponding forces, are calculated by solving an approximate Riemann problem at the element nodes. An explicit secondorder method is used to temporally advance the solution. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. 1D Cartesian coordinates test problem results are presented to demonstrate the accuracy and convergence order of the new DG method with the new limiters.},
doi = {10.1016/j.camwa.2018.03.040},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 2,
volume = 78,
place = {United States},
year = {2018},
month = {4}
}