In order to surmount the difficulty of numerical dispersion and numerical oscillation an improved characteristic finite element method is presented to solve the highly nonlinear sea water intrusion problem.The solved three-dimensional mathematical model,which regards exchanging cations Na⁺ and Ca²⁺ as simulation factor,takes account of cation exchange reaction between water and rock.The simulated results are satisfactory by comparison with the field data,and show that this model can be applied to predict the movement and evolution of exchanging cations during sea water intrusion.

A new method is presented to solve the three-dimensional advection dominant advection-dispersion equation, in which not only the advective-dispersive actions, but also the adsorption,radioactive decay and sources(sinks) are considered. Operator-splitting(OS) technique is used to split the equation over a time step into three parts, which are respectively solved by the method of constant variation (CV), the matched artificial dispersivity (MAD) method and the alternating direction implicit (ADI) method. Finally, the new method is applied to a synthetic three-dimensional contaminant transport problem. The simulated results are satisfactory by comparison with the analytical and the improved characteristic (IC) method solutions.