Stabilized shock hydrodynamics: I. A Lagrangian method

A new SUPG-stabilized formulation for Lagrangian hydrodynamics of materials satisfying Mie-Grüneisen equation of state is proposed. It allows the use of simplex-type (triangular/tetrahedral) meshes as well as the more commonly used brick-type (quadrilateral/hexahedral) meshes. The proposed method yields a globally conservative formulation, in which equal-order interpolation (P1 or Q1 isoparametric finite elements) is applied to velocities, displacements, and pressure. As a direct consequence, and in contrast to traditional cell-centered multidimensional hydrocode implementations, the proposed formulation allows a natural representation of the pressure gradient on element interiors. The SUPG stabilization involves additional design requirements, specific to the Lagrangian formulation. A discontinuity capturing operator in the form of a Noh-type viscosity with artificial heat flux is used to preserve stability and smoothness of the solution in shock regions. A set of challenging shock hydrodynamics benchmark tests for the Euler equations of gas dynamics in one and two space dimensions is presented. In the two-dimensional case, computations performed on quadrilateral and triangular grids are analyzed and compared. These results indicate that the new formulation is a promising technology for hydrocode applications. © 2006 Elsevier B.V. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Scovazzi, G; Christon, MA; Hughes, TJR; Shadid, JN

Published Date

  • 2007

Published In

Volume / Issue

  • 196 / 4-6

Start / End Page

  • 923 - 966

International Standard Serial Number (ISSN)

  • 0045-7825

Digital Object Identifier (DOI)

  • 10.1016/j.cma.2006.08.008

Citation Source

  • SciVal