We consider axisymmetric flow towards a point sink from a stratified fluid in a vertically confined aquifer. We present two approaches to solve the equations of flow for the linear density gradient case. Firstly, a series method results in an eigenfunction expansion in Whittaker functions. The second method is a simple finite difference method. Comparison of the two methods verifies the finite difference method is accurate, so that more complicated nonlinear, density stratification can be considered. Such nonlinear profiles cannot be considered with the eigenfunction approach. Interesting results for the case where the density stratification changes from linear to almost two-layer are presented, showing that in the nonlinear case there are certain values of flow rate for which a steady solution does not occur.
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An integrated finite difference method for analyzing fluid flow in porous media
