Numerical simulation for three dimensional diffusion equation is studied.Using variation principle,the difference discrete scheme with diffusion flux form on the irregular hexahedral grid is constructed.The flux of diffusion as an unknown function is obtained by minimizing the functional and solved with the equation of temperature function simultaneously.Computational formulas are deduced and numerical test is given.

Numerical simulation for three-dimensional diffusion equation is studied. Using integral interpolation method, the difference scheme on the irregular hexahedral grid is constructed which consists of 27 neighboring grids and is available for solving quasi-linear diffusion equation with discontinuous coefficients on distortion mesh. Flow flux through interfaces and temperature on the nodes are deduced and numerical test is given.

Numerical simulations of two-dimensional laser driven implosion with spherical coordinates and the relative computational methods are mainly summarized.Features of solving the hydrodynamic equations by the fully conservative implicit difference scheme and solving the thermal conductive equations by the variational method are discussed.Eexamples of relative physical models are presented and effects of the non-symmetry on the laser driven implosive processes are examined.

Difference numerical simulation for two dimensional thermal conduction equation is studied.Using the variational principle,the difference scheme with thermal-flux form in the irregular structured mesh is presented.The thermal flux as an unknown function is obtained by minimizing the functional and solved with the equation of temperature function simultaneously.This scheme overcomes the defects of general nine-point schemes,which have to calculate the thermal conduction coefficients on the cell boundaries and the temperatures located in the cell vertices by interpolation.

Two numerical schemes of discontinuous finite element methods are presented for Hamilton Jacobi equations which are obtained by using the different basic functions. The numerical solutions of these schemes converge to weak solutions of the Hamilton Jacobi equation under some conditions. Numerical tests given illustrate the accuracy and resolution of discontinuity for the two different schemes.

This paper presents the numerical method for solving the rate equations of electron's average occupation probabilities by using multiple-time-scale perturbation theory.It is especially suitable for lower levels of elements, Since in that case the transition between neighbouring bound energy levels could be considered as fast, the others as slow. Under some reasonable physical assumptions the method leads to the analytic expressions for P_n as functions of the number of free electron, n_s.As a result, in stead of solvingstrong stitff ordinary ditferential equations of (dp_n)/(dt), we just need solving thedifferential equation for n_e and the algebraical equations for P_n. Therefore the problem is much simplified with avoiding the computation of Jacobi iaverse matrix which generally appears is the implicit schemes.