Multi-material pressure relaxation methods for Lagrangian hydrodynamics

In Arbitrary Lagrangian–Eulerian (ALE) methods for hydrodynamics with several materials, multiple-material Lagrangian cells invariably arise when the flow field is remapped onto a new mesh. One must close the system of equations for multi-material cells; this, in effect, constitutes a model—either explicit or implicit—for the sub-scale dynamics. We discuss several different multi-material closure model algorithms for Lagrangian hydrodynamics under the assumption of a single velocity for 1D, multiple-material cells. Russian researchers at the All-Russian Research Institute of Experimental Physics (VNIIEF) have developed several models, which we describe in some detail; recent work by US researchers was developed independent of the details of these models. This work contains a comparison of these different approaches, which we believe is unique in the literature. We compare these methods on two standard test problems and discuss the results.