Finite proximate method for two-dimensional diffusion equation

The finite proximate solution for two-dimensional diffusion equation in the local unit of curvilinear grid is hypothesized, and the computational region is discrete to deduce the relational expression between center function value and eight points function value around. A finite approximate method with 9 points scheme of the curvilinear grid is proposed to solve the two-dimensional diffusion equation thereby. The comparison of the computational and exact values for both the steady diffusion equation with the irregular region and the unsteady diffusion equation with regular region indicates that the method has the properties of simple process, high precision and strong adaptability. Compared with FPM (5 points scheme), the method is improved in precision. Then the typical seepage flow field of the bottom for spillway dam is obtained, the computational results are in good agreement with the measured results by electrical analogue method.