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

摘要

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.