High-Order Multi-Material ALE Hydrodynamics

We present a new approach for multi-material Arbitrary Lagrangian-Eulerian (ALE) hydrodynamics simulations based on high-order finite elements posed on high-order curvilinear meshes. The method builds on and extends our previous work in the Lagrangian [1] and remap [2] phases of ALE, and depends critically on a functional perspective that enables sub-zonal physics and material modeling [3]. Curvilinear mesh relaxation is based on node movement, which is defined through the solution of an elliptic equation. The remap phase is posed in terms of advecting state variables between two meshes over a fictitious time interval. The resulting advection equation is solved by a Discontinuous Galerkin (DG) formulation, combined with a customized Flux Corrected Transport (FCT) type algorithm. Because conservative fields are remapped, additional synchronization steps are introduced to preserve bounds with respect to primal fields. These steps include modification of the low-order FCT solutions, definition of conservative FCT fluxes based on primal field bounds, and monotone transitions between primal and conservative fields. This paper describes the mathematical formulation and properties of our approach and reports a number of numerical results from its implementation in the BLAST code [4].