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SUMMARYThe main ideas of compatible Lagrangian hydrodynamics were originally developed in the form of a finite volume scheme by Caramana et al. at LANL. A new compatible finite element Lagrangian hydrodynamics method has been developed and implemented in a 2D arbitrary Lagrangian Eulerian (ALE) code CORVUS. The new finite element method was developed in preference to the published finite volume schemes in order to see if the fundamental principles of compatible hydro could be translated across to other numerical methods in use in hydrocodes and to facilitate a more direct comparison of the performance of the compatible hydro scheme with the existing finite element scheme in CORVUS. The new finite element scheme provides total energy conservation to round off for the Lagrangian step. The edge artificial viscosities and sub-zonal pressures that have been introduced through the framework of the compatible hydro scheme provide further improvements in terms of accuracy and robustness for Lagrangian calculations. The details of the compatible finite element Lagrangian scheme and the extensions required to the scheme to allow it to be applied as the Lagrangian step of a multi-material ALE code are discussed. Test problems will be presented to demonstrate some of the benefits and the performance of the new method for hydrocode applications. q British Crown

A systematic description of the new interface-aware sub-scale-dynamics (IA-SSD) closure model for the Lagrangian stage of multimaterial arbitrary Lagrangian-Eulerian methods is presented. The IA-SSD closure model consists of two stages. During the first, bulk, stage, the well known equal compressibility model is used. During the second stage, sub-scale interactions of the materials inside the multimaterial cell are taken into account. At this stage, information about the topology of the materials inside the multimaterial cell is utilized, allowing the orientations of internal interfaces to be included in the model. Each material interacts in a pair-wise fashion with the materials with which it has a common boundary. The interactions are based on the solution of the acoustic Riemann problem between each pair of materials and is limited using physically justified constraints: positivity of volume, positivity of internal energy and controlled rate of pressure relaxation. To determine the values of the limiter coefficients, a constrained-optimization framework is employed using a quadratic objective function with linear constraints. The algorithm guarantees the positivity of the material volume and internal energy as well as the smooth relaxation of the pressure-this allows a significant increase in the robustness of the overall algorithm. The results of comprehensive testing of the new model have been presented for one-and two-dimensional multimaterial Lagrangian hydrodynamics along with representative results for 2D multimaterial arbitrary Lagrangian-Eulerian (ALE) calculations. The numerical tests have shown that in most cases the new IA-SSD closure model produces better results compared to the well known Tipton's closure model.

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