Model for Laminar and Turbulent Flows of Viscous and Nonlinear Viscous non-Newtonian Fluids

  • We develop a model that describes laminar and turbulent flows of viscous and nonlinear viscous fluids. A basis for the model is a characteristic, which we call a local Reynolds number, and which is calculated at each point of the domain of flow. In the subdomain wherein the local Reynolds number does not exceed some value, the flow is laminar; otherwise it is turbulent, i.e. the model identifies the areas of laminar and turbulent flows. The model predicts the existence of a laminar boundary layer at turbulent flows. It enables us to describe special features of turbulent flows such as a drastic increase in the resistance to flow and the variation of the velocity profile with the increase of the Reynolds number, and so on. The model is mathematically grounded. We prove the existence of global solutions to stationary and nonstationary flow problems with the nonhomogeneous Dirichlet and mixed boundary conditions, where velocities and surface forces are given on different parts of theWe develop a model that describes laminar and turbulent flows of viscous and nonlinear viscous fluids. A basis for the model is a characteristic, which we call a local Reynolds number, and which is calculated at each point of the domain of flow. In the subdomain wherein the local Reynolds number does not exceed some value, the flow is laminar; otherwise it is turbulent, i.e. the model identifies the areas of laminar and turbulent flows. The model predicts the existence of a laminar boundary layer at turbulent flows. It enables us to describe special features of turbulent flows such as a drastic increase in the resistance to flow and the variation of the velocity profile with the increase of the Reynolds number, and so on. The model is mathematically grounded. We prove the existence of global solutions to stationary and nonstationary flow problems with the nonhomogeneous Dirichlet and mixed boundary conditions, where velocities and surface forces are given on different parts of the boundary. Numerical methods for solving stationary and nonstationary flow problems are investigated.show moreshow less

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Metadaten
Author:William G. LitvinovGND
URN:urn:nbn:de:bvb:384-opus4-11929
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1470
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2010-20)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Release Date:2010/12/13
Tag:laminar flow; turbulent flow; local Reynolds number; existence theorem; approximate solution
GND-Keyword:Numerische Strömungssimulation; Viskose Flüssigkeit; Laminare Strömung; Turbulente Strömung; Grenzschicht; Reynolds-Zahl
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand