We perform 2D ignition capsule implosion simulation by a 2D multi-group radiation diffusion hydrodynamic code LARED-S which simultaneously simulates radiation drive asymmetry and outer surface roughness. Implosion flow field shows large-amplitude spikes and bubbles as well as a significant low-mode shell areal density asymmetry. Amplitudes of modes generated by mode coupling are in good agreement with analytic mode coupling equation until perturbation amplitude of fundamental mode L24 is greater than nonlinear saturation amplitude. In deceleration phase, perturbation growth is in strong nonlinear phase, and strong mode coupling effects broaden mode distribution. High-density spikes are bent by vortex flow. Mode coupling degrades greatly implosion performance, leading to ignition failure. Further simulations of mode coupling between low-mode drive asymmetry and capsule surface roughness is critical for understanding influences of hydrodynamic instabilities on ignition capsule implosion.

High-foot high-adiabat implosion simulations of ICF ignition capsules are performed with one-dimensional multi-group radiation transport hydrodynamic code RDMG and two-dimensional few-group radiation diffusion hydrodynamic code LARED-S. Compared with low-adiabat implosion, high-foot implosions improve significantly stability of ablation front and ablator-fuel interface by increasing radiation drive temperature of the foot, leading to great reduction of hydrodynamic instability growth and hot-spot mix. Meanwhile, high-foot implosion decrease DT fuel compression. Final compression density and areal density of the main fuel at stagnation are decreased, causing lower neutron yield. A better stability of high-foot high-adiabat implosion is obtained at cost of reducing DT fuel compression.

Kelvin-Helmholtz instability is carried out with local Steger-Warming flux splitting method and NND scheme for hydrodynamic equations. Linear growth rates agree well with linear stability analysis. The method provides clear interface deformation images.

High order weighted essentially non-oscillatory finite difference schemes (FD-WENO) are applied successfully to numerical simulation of gravity-driven high density ratio Rayleigh-Taylor instability problems and laser ablative Rayleigh-Taylor instability problems in two dimensions. It provides important references to numerical study of inertial confinement fusion (ICF) as well as to other high-tech fields. High order FD-WENO schemes are applicable to numerical simulation of ICF inplosion.

The low phase error FCT numerical algorithm is introduced,and used to simulate Rayleigh-Taylor(RT) and Richtmyer-Meshkov(RM) instabilities.Simulation results agree well with the linear theories of RT and RM instabilities and the calculation of the shock tube experiment of Russia.It shows that the FCT method is fit to simulations of instabilities of ICF problems.