Consideration of osmosis phenomena in modeling processes by the type of filtration-convection in multiply connected areas using perturbation theory methods

Abstract

In this paper considers the synthesis of methods of complex analysis and perturbation theory. A new approach has been developed to take into account osmosis when predicting filtration-convection processes in quasi-ideal porous media (multiply connected areas) bounded by flow lines and equipotential lines. The solution of the corresponding degenerate problem is obtained on the basis of the developed method of non-linear mapping of solutions of boundary value problems onto conformal reflections. An algorithm for calculating a uniform dynamic grid, flow dividing lines (finite points on the internal contour-filler of the flow) and the speed of an ideal filtration field in a three-connected area limited by equipotential lines is built. Taking into account the above and the developed method of characteristics, formulas for the approximate solution of problems of convective mass transfer on the filtration field perturbed by osmosis are obtained.