Mathematical simulation of the evolution of a liquid-liquid interface in piecewise inhomogeneous layers of complex geological structure

A mathematical model describing two incompressible liquids displacing one another in piecewise inhomogeneous porous ground layers is constructed. The ground layers are assumed to contain impermeable and semipermeable inclusions and free-liquid cavities. The square root of the conductivity of a layer is modeled by a metaharmonic (harmonic) function of coordinates.