High order scheme for the non-local transport in ICF plasmas

A high order practical scheme for a model of nonlocal transport is here proposed to be used in multidimensional radiation hydrodynamic codes. The various investigations on electron heat transport in the Inertial Confinement Fusion (ICF) context, have shown the limits of the classical local SpitzerHarm heat flow model [1]. Monodimensionnal accurate models lying on convolution formulations have been proposed by Luciani and Mora [2] and improved by many other authors [3]. Schurtz, Nicolai and Busquet [4] purposed a practical multidimensional extension of the original convolution formula. The numerical implementation of non local models can be usually very delicate since an implicit resolution is considered. It is of use to force a diffusive formulation by introducing an ill-posed artificial nonlocal conductivity [3]. This choice can lead to mathematical and physical prejudicial anomalies (negative conductivity). An stability analysis leads us to consider an alternative for the implicit discretization of the non local operator. These remarks then led us to naturally set up a high order scheme [5] to solve the nonlocal problems on strongly deformed meshes. The use of such scheme is indeed essential to give a good description of the ablation front and of the hot spot induced by the implosion of the target during a nuclear fusion experience.