Numerical Solution of a Two-Dimensional Problem of Fluid Filtration in a Deformable Porous Medium

The paper considers a two-dimensional mathematical model of filtration viscous incompressible fluid in deformable porous medium. is based on the equations conservation mass for liquid and solid phases, Darcy’s law, rheological relationship medium, law balance forces. In this article, equation forces taken full form, i.e. elastic properties medium are into account. aim work numerical study initial-boundary value problem. Section 1 gives statement problem brief review literature works related to topic. item 2, original system transformed. case slow flows, when convective term can be neglected, arises that consists second-order parabolic effective pressure first-order porosity. 3 proposes an algorithm solution resulting For implementation, variable direction scheme heat with coefficients used, as well Runge — Kutta fourth order approximation.