- Scovazzi, G. and Christon, M. A. and Hughes, T. J. R. and Shadid, J. N., Stabilized shock hydrodynamics: I. A Lagrangian method,
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, vol. 196 no. 4-6
pp. 923--966 [doi] .
(last updated on 2012/08/21)
A new SUPG-stabilized formulation for Lagrangian hydrodynamics of materials satisfying Mie-Gruneisen 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 Enter 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. (c) 2006 Elsevier B.V. All rights reserved.