A nine point difference scheme and iteration solving method is presented for two dimensional energy equations with three temperatures, in numerical simulation of driven implosion by laser. Some results are given as well.

Main processes involved in the laser-target coupling are described,including the absorption of laser light,heat conduction of electron,plasma motion,nonequilibrium ionization,laser X-ray conversion and the radiation transport.It outlines the numerical simulation,presenting the partial differential equations,constructing the finite difference schemes and describing the solving methods.Finally,some calculated results are given.

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.

A fully conservative implicit difference scheme for Lagrangean form of the fluid dynamic equations is presented. This new scheme not only guarantees the laws of conservation of mass, momentum and total energy, but also satisfies the balance properties of inner energy and kinetic energy. Two numerical tests are calculated by this scheme as comparied with other difference schemes.

In order to study physical laws related to laser X-ray conversion, two kinds of difference schemes, i.e.implicit method and splitting scheme, for solving electronic、ionic and photonic temperature equations are presented. The splitting scheme separating the energy exchange term from other terms is introduced and its influence on temperature is also investigated.

The paper presents the main processes of physics and the outline of the computational program related laser X-ray conversion, gives the typical pictures and numerical results. Based on numerical simulations, the laws of some important properies of physics are obtained, the results estimated by the scaling lasw are in comparison with the measurement values, they are coincident each other on quantitative tendency and quantitative results.