A new exceptional points method with application to cell-centered Lagrangian schemes and curved meshes

The aim of this paper is the numerical simulation of compressible hydrodynamic strong implosions, which take place for instance in Inertial Confinement Fusion. It focuses in particular on two crucial issues, for such calculations: very low CFL number at the implosion center and approximation error on the initial geometry. Thus, we propose an exceptional points method, which is translation invariant and suitable to curved meshes. This method is designed for cell-centered Lagrangian schemes (GLACE [8], [13] and [14], EUCCLHYD [25], [26], [27], [28] and [29]). Several numerical examples on significant test cases are presented to show the relevance of our approach.