Numerical Solution of One-Dimensional Problem of Filtration with Suffosion Processes
Abstract
In this paper, a mathematical model of isothermal internal erosion without deformation of a porous medium is studied. Removal of soil particles from a flow occurs at a certain value of filtration velocity. Mass conservation equation for water, moving solids and stationary porous skeleton along with Darcy's law for water and moving solid particles, and an equation for the suffosion intensity are utilized for a mathematical model of the problem. Problem formulation and development of the equation system are shown in section 1. There are the degenerate parabolic equation for water phase saturation, the elliptical equation for pressure, and the first order equation for porosity. The analogy with the classical Musket-Leverette model is also revealed. The numerical solution algorithm for a one-dimensional initial boundary value problem for internal soil erosion is proposed in section 2, and numerical solution results for the problem are presented in section 3. Values of speed and pressure of ground water, porosity and density of moving soil particles are obtained. Also, a brief overview of internal suffusion models is provided.Downloads
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