Compatible and energy conserving multi-material arbitrary Lagrangian Eulerian scheme for multi-group radiation hydrodynamics simulations

Abstract

A compatible, bounds preserving and energy conserving multi-material arbitrary Lagrangian Eulerian (ALE) scheme suitable for an unstructured mesh is developed for multi-group radiation hydrodynamics (RHD) simulation of various high energy density physics (HEDP) phenomena involving large material deformations, such as intense thermal radiation or high-power laser driven systems. In order to study very short time scale HEDP phenomena, the electron and ion energy equations (with the effect of electron-ion energy relaxation) are solved separately with an assumption of single macroscopic fluid velocity for each species (two-temperature hydrodynamics model). The governing multi-material hydrodynamics equations are solved by using a higher-order cell-centered hydrodynamics (CCH) scheme. In multi-material flows, the remapping step introduces mixed computational cells in which multiple materials exist in a single cell. Therefore, material interfaces in mixed cells are required to be reconstructed and tracked. In our implementation, this is achieved by using moment-of-fluid (MOF) method. The information of these interfaces is further used to formulate an interface aware sub-scale dynamics (IASSD) scheme for multi-material closure in mixed computational cells. The IASSD scheme is generalized for the two-temperature hydrodynamics model in which separate equations are used to update the electron and ion energies. The multi-group radiation transport on an unstructured mesh is computed using a cell-centered, monotonic, nonlinear finite volume (NLFV) scheme. The flux-limited diffusion (FLD) approximation is used to recover the free-streaming limit of the radiation propagation in optically thin regions. In the ALE step, the electron, ion and radiation energies due to MG-RHD model are conservatively remapped using a center-of-mass (CM) reconstruction of the fields and a compatible and energy conserving remapping scheme. An exact integration based on the intersection between the new (rezoned) and old meshes is used in the remap step. Similar procedure is followed for the remap of cell mass and cell-centered momentum components. In this paper, the details of a compatible, bounds preserving and conservative ALE scheme developed for MG-RHD are described. The remapping of relevant physical quantities due to multi-physics models implemented in the code such as non-local electron energy transport are also discussed. Several validation test problems including laser driven shock propagation in multi-material geometries are provided to demonstrate the accuracy and performance of the ALE scheme implemented.