William Scott

A finite difference technique for numerical analysis of the partial differential equation for advection and dispersion with sorption is presented in detail. The sorption term is non-linear and it is difficult to simulate the breakthrough curves when the rate of change of concentration is large. A general technique is used which expands the derivatives in terms of increasing orders of finite differences. This has become possible with the advent of symbolic manipulation. It is possible to expand to any order and, importantly, separate out the terms for each order. Details are presented, together with methods for exploring the convergence and stability as well as adjusting the time and spatial differencing to lower or minimise· the error.