Application of a moving grid method to a class of 1D brine transport problems in porous media

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Abstract
The background of this paper is the study of transport of pollutants by groundwater flow when released from a repository in a rock salt formation. Flow in regions surrounding such formations may be strongly influenced by variations in salt concentrations, a factor requiring special attention in the development of realistic mathematical models for predicting transport of pollutants. Indispensable for this development are advanced numerical methods. The aim of this paper is to illustrate the application of such a method to a class of non‐linear brine transport problems in one space dimension. Our method is based on the method of lines for solving time‐dependent partial differential equations. The method is of the finite difference type, implicit and thus applicable to wide classes of (one‐space‐dimensional) partial differential equation systems. The main feature of the method, however, is that it can automatically move the spatial grid for evolving time and thus is able to refine the grid in regions with large, special transitions. The grid refinement has provea to be a very valuable facility in the numerical modelling of brine transport problems involving low and high salt concentrations. From the user's point of view an additional advantage of the moving grid method is that it can be implemented in advanced, user‐oriented method‐of‐lines software packages based on implicit stiff ODE solvers. In the brine transport application discussed here we have used the package SPRINT.