Resurgence flows in three-dimensional periodic porous media

Abstract

Three-dimensional flows are addressed in porous media with resurgences. These media are characterized by a double structure, i.e., a continuous porous medium and capillaries with impermeable walls which relate distant points of the continuous medium. Spatially periodic harmonic functions with singularities at given points are constructed by means of the Berdichevskij functions; these functions extend to three dimensions the classical Weierstrass functions. The solution of the same medium with two vertices is obtained in two and three dimensions and thoroughly compared and discussed.