Чисельний метод дослідження фільтраційних течій в областях під каскадом гідроспоруд з прямокутною основою на базі R-функцій

Abstract

This work addresses the problem of stationary fluid filtration in soil beneath a cascade of hydraulic structures, assuming Darcy's law holds. The mathematical model is formulated as an elliptic equation for the stream function, involving mixed boundary conditions. To determine the unknown flow rates under each structure, additional integral relations are formulated. The study employs a structural-variational approach (the R-function method), which incorporates full geometric and analytical data into the computational algorithm. By applying the superposition principle, the original problem is decomposed into a set of boundary value problems with predefined conditions. Solution structures that exactly satisfy all boundary conditions are constructed, with the Ritz variational method used to approximate the unknown components