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Construction and investigation of a filtration model for a suspension in a porous soil
Gorbunova Tatiana Nikolaevna

PhD in Technical Science

associate professor of the Department of Applied Mathematics, Moscow State University of Civil Engineering, Department of Information Systems and Technolologies, Moscow Polytechnic University

107023, Russia, g. Moscow, ul. B.semenovskaya, 38, of. 4603





The subject of the study is the filtration problem, which describes the distribution of suspended solids in a loose porous soil. The urgency of constructing a model is determined by the need to strengthen loose soil by pumping under pressure a solution in the form of a suspension that, when hardened, forms a waterproof layer. The author's main goal is to construct a model for the motion of suspended particles of a suspension and colloids and to form a sediment in a porous ground for various filtration regimes. The distributions of solid particles of various sizes carried by the carrier liquid and settled on the framework of the porous medium are studied at different rates of precipitate growth.The one-dimensional filtration model with the particle retention mechanism includes a hyperbolic system of first-order equations with inconsistent initial and boundary conditions that generate discontinuous solutions. For polydisperse media, a modified mathematical model describing the competition of particles of different sizes for small pores is considered. The computer circuit for finding the numerical solution is constructed by the method of finite differences. The optimization of the method is used to improve convergence and reduce computation time. The main results of the study are a multi-particle model of solution filtration in a porous soil, taking into account the variety of sizes of suspended particles. A numerical calculation of the problem is performed for various blocking filter coefficients. Solutions are obtained with a discontinuity at the concentration front. Approbation of the found numerical solutions is carried out. Plots of the dependence of the concentrations of suspended and sedimented particles on time and coordinates are constructed.

Keywords: finite-difference methods, numerical solution, mathematical model, suspended particles, porous medium, deep bed filtration, grout, discontinuous solutions, retained particles, Euler's method



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