Sakyi, Adu and Amoako-Yirenkyi, Peter and Dontwi, Isaac Kwame (2020) A Rigorous Homogenization for a Two-Scale Convergence Approach to Piping Flow Erosion with Deposition in a Spatially Heterogeneous Soil. Journal of Advances in Mathematics and Computer Science, 35 (3). pp. 9-25. ISSN 2456-9968
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Abstract
We present a rigorous homogenization approach to modelling piping flow erosion in a spatially heterogeneous soil. The aim is to provide a justication to a formal homogenization approach to piping flow erosion with deposition in a spatially heterogeneous soil. Under the assumption that the soil domain is perforated periodically with cylindrical repeating microstructure, we begin by proving that a solution to the proposed set of microscopic equations exist. Two-scale convergence is then used to study the asymptotic behaviour of solutions to the microscopic problem as the microscopic length scale approaches zero(0). We thus derive rigorously a homogenized model or macro problem as well as explicit formula for the eective coecients. A strong observation from the numerical simulation was that, soil particle concentration in the water/soil mixture decreases but at a decreasing rate whereas soil particle deposition increases at regions with increasing amount of particle concentration in the flow causing a reduction in bare pore spaces across the soil domain.
Item Type: | Article |
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Subjects: | Librbary Digital > Mathematical Science |
Depositing User: | Unnamed user with email support@librbarydigit.com |
Date Deposited: | 24 Feb 2023 12:48 |
Last Modified: | 25 May 2024 09:32 |
URI: | http://info.openarchivelibrary.com/id/eprint/306 |