Second-order extension in space and time for a 3D cell-centered Lagrangian scheme

High Energy Density Physics (HEDP) flows are multi-material flows characterized by strong shock waves and large changes in the domain shape due to rarefaction waves. Numerical schemes based on the Lagrangian formalism are good candidates to model this kind of flows since the computational grid follows the fluid motion. This provides accurate results around the shocks as well as a natural tracking of multi-material interfaces and free-surfaces. The work proposed here is in continuity with the work of Maire and Nkonga (2009). More precisely, the aim of this article is to develop robust and accurate methods for the 3D extension of the EUCCLHYD scheme with a second-order extension based on MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) and GRP (Generalized Riemann Problem) procedures. Particular care is taken to preserve the symmetries and the monotonicity of the solutions. The scheme robustness and accuracy are assessed on numerous Lagrangian test cases for which the 3D extensions are very challenging. (C) 2018 Elsevier Ltd. All rights reserved.