A Numerical Study Of Incompressible Navier Stokes Equations In Three Dimensional Cylindrical Coordinates
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A Numerical Study Of Incompressible Navier Stokes Equations In Three Dimensional Cylindrical Coordinates
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Author : Douglas Xuedong Zhu
language : en
Publisher:
Release Date : 2005
A Numerical Study Of Incompressible Navier Stokes Equations In Three Dimensional Cylindrical Coordinates written by Douglas Xuedong Zhu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Heat categories.
Abstract: This dissertation is on a numerical study in primitive variables of three-dimensional Navier-Stokes equations and energy equation in an annular geometry. A fast direct method is developed to solve the Poisson equation for pressure with Neumann boundary conditions in radial and axial directions, and periodic boundary conditions in azimuthal direction. The velocities and temperature are solved using Douglas-Gunn ADI method, which makes use of an implicit Crank-Nicholson scheme to discretize the governing equations. The numerical method developed in this study, after being validated by comparing the numerical solutions to analytical known solutions and results published in the literature, is then used to study thermocapillary convection, Reyleigh-Benard convection, and Taylor-Couette flow. In the thermocapillary convection in an annulus with heated inner cylinder, the free surface was assumed to be flat. The resulting flow is two-dimensional and axisymmetric. The flow becomes three-dimensional when angular dependent temperature boundary condition is applied on the inner cylinder. Numerical solution of Rayleigh-Benard convection in a shallow annular disk results in two-dimensional axisymmetric flow when the Rayleigh number is above a critical value. A layer of concentric rolls are formed encircling the inner cylinder. The axisymmetricity and concentricity are destroyed by an initial temperature disturbance at a single grid point, or a non-uniform boundary condition on the bottom. Numerical solution of Taylor-Couette flow results in a series of axisymmetric toroidal rolls which encircle the inner cylinder between the cylinders and are stacked in the axial direction when Taylor number exceeds a critical value. As Taylor number further increases, the flow becomes non-axisymmetric and azimuthal waves are formed on the resulting wavy vortex flow.
Numerical Solution Of The Incompressible Navier Stokes Equations In Three Dimensional Generalized Curvilinear Coordinates
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Author : Stuart Eames Rogers
language : en
Publisher:
Release Date : 1986
Numerical Solution Of The Incompressible Navier Stokes Equations In Three Dimensional Generalized Curvilinear Coordinates written by Stuart Eames Rogers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Navier-Stokes equations categories.
A Numerical Study Of The Two And Three Dimensional Unsteady Navier Stokes Equations In Velocity Vorticity Variables Using Compact Difference Schemes
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Author : Institute for Computer Applications in Science and Engineering
language : en
Publisher:
Release Date : 1984
A Numerical Study Of The Two And Three Dimensional Unsteady Navier Stokes Equations In Velocity Vorticity Variables Using Compact Difference Schemes written by Institute for Computer Applications in Science and Engineering and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Fluid dynamics (Space environment) categories.
A Numerical Method For The Incompressible Navier Stokes Equations In Three Dimensional Cylindrical Geometry
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Author : John C. Strikwerda
language : en
Publisher:
Release Date : 1986
A Numerical Method For The Incompressible Navier Stokes Equations In Three Dimensional Cylindrical Geometry written by John C. Strikwerda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
The authors finite difference describe a method for solving the steady, three-dimensional, incompressible Navier-Stokes equations in cylindrical geometry. Also, they present results of computations in which this method is used determine the flow in fluid-filled cylinders undergoing spinning and coning motion. Second-order accurate central finite difference formulas are used to approximate derivatives in the radial and axial directions and a Fourier method is used to approximate the angular derivatives. Nonuniform grids are used to improve the resolution of the velocity and pressure near the cylinder walls. The system of difference equations are solved using an iterative method based on successive-over-relaxation. The method has been found to be very efficient in terms of both computer time and storage. Results of the numerical method applied to the flow in spinning and coning cylinders are presented for several cases for which experimental data are available. In addition, perturbation methods are used to study the data a t small coning speeds and small coning angles. Numerical results of this no-coning limit are compared with both the numerical data and experimental data at low coning conditions.
The Navier Stokes Equations Theory And Numerical Methods
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Author : John G. Heywood
language : en
Publisher: Springer
Release Date : 2006-11-14
The Navier Stokes Equations Theory And Numerical Methods written by John G. Heywood and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.
Behavior Of Solutions Of The Navier Stokes Equations For A Complete Class Of Three Dimensional Viscous Vortices
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Author : Coleman duP. Donaldson
language : en
Publisher:
Release Date : 1960
Behavior Of Solutions Of The Navier Stokes Equations For A Complete Class Of Three Dimensional Viscous Vortices written by Coleman duP. Donaldson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Navier-Stokes equations categories.
Numerical Study On The Regularity Of The Navier Stokes Equations
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Author :
language : en
Publisher:
Release Date : 2012
Numerical Study On The Regularity Of The Navier Stokes Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Fluid Flow Phenomena
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Author : Paolo Orlandi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fluid Flow Phenomena written by Paolo Orlandi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This book deals with the simulation of the incompressible Navier-Stokes equations for laminar and turbulent flows. The book is limited to explaining and employing the finite difference method. It furnishes a large number of source codes which permit to play with the Navier-Stokes equations and to understand the complex physics related to fluid mechanics. Numerical simulations are useful tools to understand the complexity of the flows, which often is difficult to derive from laboratory experiments. This book, then, can be very useful to scholars doing laboratory experiments, since they often do not have extra time to study the large variety of numerical methods; furthermore they cannot spend more time in transferring one of the methods into a computer language. By means of numerical simulations, for example, insights into the vorticity field can be obtained which are difficult to obtain by measurements. This book can be used by graduate as well as undergraduate students while reading books on theoretical fluid mechanics; it teaches how to simulate the dynamics of flow fields on personal computers. This will provide a better way of understanding the theory. Two chapters on Large Eddy Simulations have been included, since this is a methodology that in the near future will allow more universal turbulence models for practical applications. The direct simulation of the Navier-Stokes equations (DNS) is simple by finite-differences, that are satisfactory to reproduce the dynamics of turbulent flows. A large part of the book is devoted to the study of homogeneous and wall turbulent flows. In the second chapter the elementary concept of finite difference is given to solve parabolic and elliptical partial differential equations. In successive chapters the 1D, 2D, and 3D Navier-Stokes equations are solved in Cartesian and cylindrical coordinates. Finally, Large Eddy Simulations are performed to check the importance of the subgrid scale models. Results for turbulent and laminar flows are discussed, with particular emphasis on vortex dynamics. This volume will be of interest to graduate students and researchers wanting to compare experiments and numerical simulations, and to workers in the mechanical and aeronautic industries.
Numerical Solution Of The Incompressible Navier Stokes Equations About A Three Dimensional Body Using Boundary Fitted Coordinates
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Author : Tien Hua Fu
language : en
Publisher:
Release Date : 1979
Numerical Solution Of The Incompressible Navier Stokes Equations About A Three Dimensional Body Using Boundary Fitted Coordinates written by Tien Hua Fu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Laminar flow categories.
A Solution Procedure For Three Dimensional Incompressible Navier Stokes Equation And Its Application
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Author : Dochan Kwak
language : en
Publisher:
Release Date : 1984
A Solution Procedure For Three Dimensional Incompressible Navier Stokes Equation And Its Application written by Dochan Kwak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.