Abstract
The flow of incompressible and viscous fluid is considered in this chapter. The continuity condition and the equations of motion, the Navier-Stokes equations for the Newtonian fluid, are derived. The Stokes equation for the low Reynolds number flow is discussed and its associated functional expression is presented. The governing equations are then made dimensionless and employing the Galerkin method, the finite element equation is derived, using two different shape functions for the velocity components and pressure. The general finite element equations are then reduced to the case of two-dimensional fluid flow and the elements of mass, stiffness, and force matrices are calculated. The general form of boundary conditions are discussed and the selection/limitation of the shape functions for the velocity components and pressure is explained. As another method of fluid flow problems, the vorticity transport technique is presented and the finite element modeling of the fluid flow in terms of the vorticity and stream function is presented and the element matrices are derived. Since the governing finite element equations are nonlinear, the method of linearization technique is discussed. The finite element matrices for two-dimensional flow of an incompressible viscous fluid employing two-dimensional simplex elements are derived.
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Brodkey RR (1967) The phenomena of fluid motions. Addison-Wesley, Reading
Yuan SW (1969) Foundations of fluid mechanics. Prentice-Hall, New Delhi
Soheili A (1988) Finite element analysis of two-dimensional incompressible viscous fluid flow, BS final project, submitted to ME department. Amirkabir University of Technology, Tehran
Eftekhari K (1988) A galerkin finite element analysis of free surface fluid flow, MS thesis submitted to ME department. Amirkabir University of Technology, Tehran
Teman R (2001) Navier-stokes equations. AMS Chelsea Publishing, New York
Saffar-Avval M, Damangir E, Eslami MR, and Sorooshe AA (1994) Finite element formulation of blood flow in bifurcation of femoral artery to predict atherosclerosis plaque formation. In:proccedings of ASME-ESDA94 conference London
Damangir E, Mehdinejad V, Marivani M, Eslami MR, and Saffar-Avval M (1996) Numerical solution of pulsatile blood flow in a bifurcation with elastic wall. In:proccedings of ASME-ESDA96 conference France, July 1–4
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© 2014 Springer International Publishing Switzerland
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Eslami, M.R. (2014). Incompressible Viscous Fluid Flow. In: Finite Elements Methods in Mechanics. Solid Mechanics and Its Applications, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-08037-6_13
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DOI: https://doi.org/10.1007/978-3-319-08037-6_13
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08036-9
Online ISBN: 978-3-319-08037-6
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