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Numerical Methods for PDEs: In Occasion of Raytcho Lazarov's 70th Birthday

Veselin Dobrev, Lawrence Livermore National Laboratory
High-Order Curvilinear ALE Hydrodynamics

Abstract

The Arbitrary Lagrangian-Eulerian (ALE) framework forms the basis of many large-scale multi-material shock hydrodynamics codes. Current ALE discretization approaches consist of a Lagrange phase, where the hydrodynamics equations are solved on a moving mesh, followed by a three-part "advection phase" involving mesh optimization, field remap and multi-material zone treatment. While current ALE methods have been successful at extending the capability of pure Lagrangian methods, they also introduce numerical problems of their own including a lack of total energy conservation and artificial breakup of material interfaces. In this talk, we will discuss the application of the curvilinear technology to the "advection phase" in order to develop new and more robust high-order ALE algorithms, while preserving the accuracy of the high-order Lagrange step. We will present some approaches for high-order extensions to classical mesh optimization algorithms, such as harmonic and equipotential smoothing, as well as the use of global mesh optimization methods. We will also discuss possible approaches to define conservative and monotonic high-order field remap and conclude the talk with some preliminary numerical results.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.