Abstract: Numerical simulation in oil-field exploration and exploitation with computational mathematics and dynamics of fluids in porous media is discussed. The numerical method of nuclear waste disposal contamination, prediction and prevention of sea-water intrusion and the numerical simulation of transient behavior of semi-conductor devices are also studied. The mathematical model is the nonlinear convection-dominated diffusion coupled systems with initial-boundary value problem. Characteristic finite difference method, characteristic finite element method, fractional step numerical method and its theoretical analysis are mainly dealed with.

Key words: petroleum geology, characteristic finite difference, characteristic finite element, fractional step method