Groundwater flow in a medium with periodic inclusions

A study is made of the problem of two-dimensional confined steady flow through a porous reservoir whose percolation coefficient is a step function, while the homogeneity zones are rectangular inclusions (blocks) and a matrix (fractures). The velocity distributions, streamlines, isochrones of the motion of marked particles, and their time of passage through the elementary cell are found for this doubly periodic structure under conditions of continuity of the fluid head and the normal component of the flow on the phase contact boundary. Conclusions concerning the "convective component" of the longitudinal and transverse dispersion are drawn on the basis of these essentially two-dimensional hydrodynamic characteristics. The exact solutions obtained are compared with the results of numerical calculations carried out by the finite-difference method.