Calculation of the filtration problem by finite differences methods

The filtration problem of a suspension in a porous medium is relevant for the construction industry. In the design of hydraulic structures, construction of waterproof walls in the ground, grouting the loose soil, it is necessary to calculate the transfer and deposition of solid particles by the fluid flow. A one-dimensional filtration problem of a monodisperse suspension in a porous medium with a size-exclusion capture mechanism is considered. It is assumed that as the deposit grows, the porosity and admissible flow of particles through the porous medium change. The solution of the initial filtration model and the equivalent equations are calculated. For the numerical calculation of the problem, both standard first-order finite difference formulas and more accurate second-order schemes were used. The obtained solutions are compared with the results given by the TVD-scheme