A Lagrangian discontinuous Galerkin hydrodynamic method
Abstract
Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the twodimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The third approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected secondorder accuracy of this new method.
 Authors:

 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 Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1414156
 Alternate Identifier(s):
 OSTI ID: 1548969
 Report Number(s):
 LAUR1724361
Journal ID: ISSN 00457930
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computers and Fluids
 Additional Journal Information:
 Journal Volume: 163; Journal ID: ISSN 00457930
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Lagrangian; Hydrodynamics; Discontinuous Galerkin; Taylor basis; cellcentered; compressible flows; shocks
Citation Formats
Liu, Xiaodong, Morgan, Nathaniel Ray, and Burton, Donald E. A Lagrangian discontinuous Galerkin hydrodynamic method. United States: N. p., 2017.
Web. doi:10.1016/j.compfluid.2017.12.007.
Liu, Xiaodong, Morgan, Nathaniel Ray, & Burton, Donald E. A Lagrangian discontinuous Galerkin hydrodynamic method. United States. doi:10.1016/j.compfluid.2017.12.007.
Liu, Xiaodong, Morgan, Nathaniel Ray, and Burton, Donald E. Mon .
"A Lagrangian discontinuous Galerkin hydrodynamic method". United States. doi:10.1016/j.compfluid.2017.12.007. https://www.osti.gov/servlets/purl/1414156.
@article{osti_1414156,
title = {A Lagrangian discontinuous Galerkin hydrodynamic method},
author = {Liu, Xiaodong and Morgan, Nathaniel Ray and Burton, Donald E.},
abstractNote = {Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the twodimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the element. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain finite element methods and uses the strong mass conservation to calculate the density field at a location inside the element or on the element surface. The third approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new Lagrangian DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected secondorder accuracy of this new method.},
doi = {10.1016/j.compfluid.2017.12.007},
journal = {Computers and Fluids},
number = ,
volume = 163,
place = {United States},
year = {2017},
month = {12}
}
Web of Science