AXISIMMETRIC FLUID MOTION IN A POROUS MEDIUM IN THE PRESENCE OF A NON-STATIONARY EXTERNAL SOURCE OR ABSORPTION
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Abstract
The generalized axisymmetric model of fluid motion in a porous medium in the presence of a non-stationary external source or absorption is studied by methods of group (symmetry) analysis of differential equations. All its invariant submodels of rank 1 are studied. They are specified by invariant solutions of rank 1 of the equation of the original model. These solutions are obtained either explicitly, or their search is reduced to solving systems of ordinary differential equations of the first order. For explicit solutions at specific values of the parameters included in their expressions, graphs of the pressure distribution in the porous medium are constructed. The remaining solutions are used to study physically meaningful boundary value problems for which, at the initial moment of time, the pressure and either the rate of its change along the axis of symmetry or the radial rate of its change are specified at a fixed point of the medium. These boundary value problems are solved numerically for some specific values of the parameters included in them. Graphs of the functions determining these solutions are obtained. The conducted research is relevant in many areas of applied science and technology: filtration, soil mechanics, rock mechanics, oil field engineering, construction engineering, petroleum geology, biology and biophysics, materials science.
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