Reduced 3D Model of a Passive Admixture Transport in Shallow, Elongated and Weakly Curved Natural Water-Stream

  • Konstantin NadolinEmail author
  • Igor Zhilyaev
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


The main goal of the study is a validation of a simplified 3D mathematical model for passive admixture spreading in shallow flows. The tested model is oriented to the hydrological and ecological problems, and it can be applied to natural streams like rivers and channels. The earlier proposed model of the ‘elongated, shallow and weakly curved stream’ (Nadolin, Mat Model 21(2):4–28, 2009) takes into account the structure of a stream-bed for evaluation of flow velocity in every point of domain. This is a model advantage, which allows calculation of the admixture spreading in a channel with varying width and depth more accurately than by using in-depth averaged models. For example, we can observe the opposite flow in a near-surface zone, which may be caused e.g. by the wind. The results of numerical experiments show that this reduced 3D model adequately describes the admixture spreading processes in natural streams with acceptable accuracy.



The research is partly supported by a grant from the Vladimir Potanin Charity Fund (project GPK-96/17). The results of the study will be used in the Master Program “Computational Mechanics and Information Technologies”.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute for Mathematics, Mechanics and Computer ScienceSouthern Federal UniversityRostov-on-DonRussia
  2. 2.Institute of Polymer EngineeringFHNW University of Applied Sciences and Arts Northwestern SwitzerlandWindischSwitzerland

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