Development of a sub-scale dynamics model for pressure relaxation of multi-material cells in Lagrangian hydrodynamics

We have extended the Sub-Scale Dynamics (SSD) closure model for multi-fluid computational cells. Volume exchange between two materials is based on the interface area and a notional interface translation velocity, which is derived from a linearized Riemann solution. We have extended the model to cells with any number of materials, computing pressure-difference-driven volume and energy exchange as the algebraic sum of pairwise interactions. In multiple dimensions, we rely on interface reconstruction to provide interface areas and orientations, and centroids of material polygons. In order to prevent unphysically large or unmanageably small material volumes, we have used a flux-corrected transport (FCT) approach to limit the pressure-driven part of the volume exchange. We describe the implementation of this model in two dimensions in the FLAG hydrodynamics code. We also report on Lagrangian test calculations, comparing them with others made using a mixed-zone closure model due to Tipton, and with corresponding calculations made with only single-material cells. We find that in some cases, the SSD model more accurately predicts the state of material in mixed cells. By comparing the algebraic forms of both models, we identify similar dependencies on state and dynamical variables, and propose explanations for the apparent higher fidelity of the SSD model.