A Rigorous Homogenization for a Two-Scale Convergence Approach to Piping Flow Erosion with Deposition in a Spatially Heterogeneous Soil
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Published:2020-05-27
Issue:
Volume:
Page:9-25
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ISSN:2456-9968
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Container-title:Journal of Advances in Mathematics and Computer Science
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language:
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Short-container-title:JAMCS
Author:
Sakyi Adu,Amoako-Yirenkyi Peter,Dontwi Isaac Kwame
Abstract
We present a rigorous homogenization approach to modelling piping ow erosion in a spatially heterogeneous soil. The aim is to provide a justication to a formal homogenization approach to piping ow 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 ow causing a reduction in bare pore spaces across the soil domain.
Publisher
Sciencedomain International
Subject
Geology,Ocean Engineering,Water Science and Technology
Cited by
1 articles.
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