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Dimension reduction for models of pollutant transport with sedimentation
Author(s) -
Limić N.,
Starčević M.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200144
Subject(s) - sedimentation , reduction (mathematics) , dimension (graph theory) , dimensional reduction , structural basin , flow (mathematics) , mass transport , infinity , conservation of mass , mathematics , conservation law , hydrology (agriculture) , geology , mathematical analysis , pure mathematics , geometry , mathematical physics , sediment , physics , mechanics , geotechnical engineering , geomorphology , engineering physics
In this paper we present a model for transport of substance with sedimentation governed by a water flow in a shallow basin. The model is developed by using a dimension reduction technique in an infinite layer. The concentration of substance is modeled by a 2D‐approximation, corrected in the vertical direction. In applications 2D‐models are often used in shallow basins as it was illustrated for instance in [Legović T., Limić N., Valković V., Estuar. Coast. Shelf Sci. 30 , 619–654, (1990)]. Here we establish the acceptability criterion for the reduction, based on the mass conservation law. Thus we discuss the existence of solutions to the original 3D‐model and the deduced 2D‐model with L 1 source terms. For the conclusion we prove that the relative error of sedimentation rates for the original and deduced model tends to zero as the distance from the source of substance tends to infinity.