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.

Two-dimensional compressible flow field for the interaction of shocks with cylinder interface is directly simulated by using Ghost Fluid method (Ghost) and γ-model method, respectively, with the same discrete order in space and time. Numerical results are compared with the experimental results. They are almost alike in the beginning time and show the right position of interface, right strength and velocity of shocks. With the time developing, the effect of large numerical dissipation of γ-model method becomes greater and greater while the low numerical dissipation of Ghost method makes it efficient to simulate the moving interface well. Comparison with experiments proves that Ghost method is better than γ-model method in simulating the problem of interface instability.

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.