Interface-unaware sub-scale dynamics closure model for multimaterial cells in cell-centered arbitrary Lagrangian-Eulerian hydrodynamics

Abstract

We develop new interface-unaware sub-scale dynamics (IU-SSD) multimaterial cell closure models for the Lagrangian stage of cell-centered arbitrary Lagrangian-Eulerian method. The IU-SSD closure models do not require information about the interface in the multimaterial cell and consist of two stages. The first stage makes use of a constant volume fraction model, wherein the main ingredient is the construction of a nodal Riemann solver that is capable of handling multimaterial cells. This model provides the numerical flux at cell face and introduces the mechanism of velocity relaxation. The sub-scale interactions of the materials in a multimaterial cell are taken into account by incorporating the pressure relaxation model in the second stage. Two types of pressure relaxation models are designed utilizing the linear relation between viscous pressure and volume strain rate. The pressure relaxation models are implemented via a multi-step time marching procedure such that they satisfy the physically justified constraints: positivity of volume, positivity of internal energy and smooth relaxation of pressure. The performances of new IU-SSD models are demonstrated via a series of numerical tests involving both Lagrangian and arbitrary Lagrangian-Eulerian hydrodynamics calculations.