A Lagrangian discontinuous Galerkin hydrodynamic method

Journal Article · Mon Dec 11 00:00:00 EST 2017 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2017.12.007· OSTI ID:1414156

Liu, Xiaodong ^[1]; Morgan, Nathaniel Ray ^[1]; Burton, Donald E. ^[1]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Here, we present a new Lagrangian discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional 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 second-order accuracy of this new method.

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: LDRD; USDOE; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1414156
• Alternate ID(s): OSTI ID: 1548969
• Report Number(s): LA-UR-17-24361
• Journal Information: Computers and Fluids, Journal Name: Computers and Fluids Vol. 163; ISSN 0045-7930
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Discontinuous Galerkin
Hydrodynamics
Lagrangian
Taylor basis
cell-centered
compressible flows
shocks