A numerical scheme for solving special class of nonlinear diffusion-convection equation

The nonlinear diffusion-convection equations arising from the theory of transport in porous media is analyzed. The problem under analysis has the form∂c∂t=∂∂zD(c)∂c∂z-K(c),where D(c) = D0cm/(1 − vc)m+2 and K(c) = K0cm+2/(1 − vc)m+1. The behavior of solutions when m > 1 and 0 < m < 1, is stated. A numerical method, based on extrapolation, is derived, for solving this problem for m > 0. Numerical and analytical results compared for the cases m = 0, 1 and numerical results for m = 2 and m = 0.5 are stated.