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September 11, 2026
How to Assess Students Knowledge in the Age of AI
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CHARACTERISTIC METHOD FOR SOLVING FILTRATION PROBLEM

International Journal for Computational Civil and Structural Engineering. 2023. Vol. 19. No. 3. P. 39–48.
Liudmila I. Kuzmina, Osipov, Y., Pesterev, A.

During construction, a liquid solution of a grout or waterproof filler is pumped into porous rock to improve its properties. The filtration of a suspension moving at a variable speed in a porous medium is simulated. A one-dimensional problem of filtration in a homogeneous porous medium with a curvilinear concentration front of suspended and retained particles is considered. For the numerical solution of the problem by the method of finite differences, the method of characteristics is used. The transition to characteristic variables allows one to straighten the front and construct a discrete grid with a constant step. When calculating the solution using an explicit difference scheme, additional points are used that do not coincide with the grid nodes. A detailed description of the algorithm for calculating a solution at the grid nodes and an example of a numerical solution of the problem are given.

Research target: Mathematics
Language: English
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Keywords: numerical solutionfinite difference methodsuspended and retained particlesmethod of characteristics porous medium deep bed filtration
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