Iterative Solutions of Salinity Intrusion Problems in Confined Coastal Groundwater

Abstract

The problem studied is associated with the iterative techniques employed in simulating the steady state salinity intrusion in a coastal groundwater. Two widely used iterative methods for simulation, the Picard method (PCM) and the Partial Newton method (PNM), are considered. Properties of both methods are investigated and contrasted in terms of rapidity and stability of solution convergency. It is mathematically elucidated that the solution performance of PCM is identical with that of PNM when properly underrelaxed in its iterative process. With respect to the manner of relaxation in application of PCM, many numerical experiments imply that such relaxation should be done only to the solutions of salinity, but not to those of velocity, and at the same time the value of the relaxation parameter should be iteration by iteration varied in an appropriate manner. As a useful methodology for reasonably varying the parameter value, incorporation of the fuzzy reasoning in the method is proposed. The results show that the variable relaxation induced from the fuzzy reasoning is indeed capable of making iterative process paramount in comparison with PNM and the other conventional relaxed PCM.