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. |