Investigation of “Fingers” Instability in Filtration Flows.
The classical problem, the problem of displacement stability in the filtration flow, is considered in the article. The governing system consists of the hyperbolic equations, describing the saturation evolution, and elliptic one for the pore pressure evolution. The TVD difference schemes are used for the hyperbolic equations and Peaceman - Douglas iteration method for boundary elliptic problem. The theoretical investigation results of the instability increments dependence on the spatial frequency of the perturbation were proved. It is established there is no frequency discrimination: the perturbation of the maximal spatial frequency has the maximal increment of the instability.
Mathematical modelling in actual problems of science and technics