SOLUTION OF NON-STATIONARY THREE-DIMENSIONAL FILTRATION PROBLEMS IN A HETEROGENEOUS ANISOTROPIC MEDIUM USING SERIES
Keywords:
filtration, anisotropic medium, unsteady flow, mathematical modeling, differential equations, series solution, landslide phenomena, self-similarityAbstract
This paper examines the solution of transient three-dimensional seepage problems in a homogeneously anisotropic medium using series. Particular attention is paid to the role of hydrogeological factors in the formation of landslide processes and methods for their quantitative description. The study utilized a mathematical modeling method, where the original problem is described by a second-order partial differential equation. By introducing self-similar transformations, the original equation is reduced to an ordinary differential equation, the solution of which is represented as a power series with coefficients determined by a recurrence formula. The resulting analytical solutions can serve as a benchmark for testing and verifying numerical methods for calculating seepage flows.
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