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This content will become publicly available on April 9, 2019

Title: An updated Lagrangian discontinuous Galerkin hydrodynamic method for gas dynamics

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 higher-order 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 second-order 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:
 [1] ; ORCiD logo [2] ; ORCiD logo [2] ;  [3] ;  [1]
  1. North Carolina State Univ., Raleigh, NC (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Dortmund Univ. of Technology, Dortmund (Germany)
Publication Date:
Report Number(s):
LA-UR-17-29217
Journal ID: ISSN 0898-1221
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford); Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE Laboratory Directed Research and Development (LDRD) Program
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Lagrangian; Hydrodynamics; Discontinuous Galerkin; Limiters
OSTI Identifier:
1434431