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Arbitrary-Lagrangian-Eulerian (ALE) methods for hydrodynamics equations in 2D and 3D

In this talk we will present in the context of Inertial Confinement Fusion (ICF) the developement of ALE numerical methods in 2D and 3D. After a brief review of the physics of ICF involved we will present a generic ALE code for hydrodynamics that can be decomposed into three successive phases:
1. Lagrangian phase. A numerical scheme (Lagrangian on moving mesh) computes the evolution in time and space of a mixture of materials described in a Lagrangian formalism. As the mesh deforms with the materials, it can be arbitrarily stretched, compressed and consequently of very bad geometrical quality; non-convex, tangled or long and thin cells may appear.
2. Mesh regularization or smoothing phase. Given the Lagrangian mesh a regularization technique provides a new regularized mesh that one chooses to proceed which.
3. Conservative remapping phase. The remapping phase transfers the physical variables from the Lagrangian mesh onto the regularized grid. This remapping must be conservative in mass, momentum and total energy and the remapping must be at least as accurate as the numerical scheme is.
After a description of each phase (methods and numerical implementation) we will present numerical results for classical and demanding test cases (Sod, Sedov, Noh, Rayleigh-Taylor). Results from the 2D ALE code with reconnection and the 3D code will be provided as to show the efficency of such an approach.
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