(Institute of Applied Physics and Computational Mathematics, Beijing 100094, China)

The LARED-Integration code is used for the numerical simulation of the indirect-drive Inertial Confined Fusion. In order to meet with the physics analysis on the whole ignition implosion process, a robust grid relaxation algorithm adaptive to the flow variation is developed for the multi-material arbitrary Lagrangian Eulerian method used in the LARED-Integration code. Compared with the experiment phenomena, the shape of the bubble in the RM instability numerical results is considerable，and the relaxation factor used in the grid relaxation algorithm shows the variation of the density variable. The 2-D implosion process of the multi-layer ignition capsule driven by radiation source is simulated. The whole physical process can be finished and the numerical results are satisfactory according to the physical analysis.