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.

A class of meshless methods for heat conduction equations are constructed.They can be performed on structured or unstructured meshes.The methods are conservative and consistent.They have at least the first order accuracy when performed on irregular quadrilateral or triangular meshes,and have the second order accuracy when performed on rectangular or uniform parallelogram meshes. These meshless methods are suitable and efficient in solving linear or nonlinear parabolic problems on irregular quadrilateral meshes or mixed meshes, especially in solving two-dimensional three-temperature radiation heat conduction equations on irregular and mixed meshes.