From mass conservation and energy conservation of hotspot, dynamics of hotspot combustion involving shell-mix are constructed by recalculating special internal energy and heat capacity, in which bremsstrahlung radiation loss and other energy transfer are considered. With power balance in hotspot, relations between fractions of shell-mixing in hotspot and ignition threshold and self-sustainable combustion are investigated. Theoretical analysis and numerical simulation show that enhancement of radiation loss induced by shell-mixing plays dominated role in failure of ignition. By adjusting materials and mixing fraction, effects to combustion paths are studied. Finally, two methods for degrading impact of shell-mixing are proposed.

By using kinetic BGK scheme with new Maxiwellian distribution function and block-structured adaptive mesh refinement (AMR) algorithm, we construct a second-order BGK-AMR scheme for radiation hydrodynamics equation (RHE) in zero diffusion limit. Merits of the scheme are that we can reduce computational meshes and put more refinement meshes on location where should be concerned mostly, at the same time computational time is reduced greatly comparing with uniform finer meshes. And comparing with old Maxiwellian distribution for kinetic scheme of radiation hydrodynamics, parameters in new Maxwellian function are deeoupled, so construction of the scheme is simplified greatly. One- and two-dimensional numerical examples demonstrate performance of the scheme.

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.

Steady state flow field around ablation front is solved and taken as a basic flow in the simulation of ablative Rayleigh-Taylor instability with a high-order WENO scheme. Linear growth rate simulated agrees with Lindl formula and linear stability analysis. It indicates validity and accuracy of the method. The method shows good ability in capturing interface deformation.