A Numerical Study of the Two-dimensional Navier-Stokes Equations in Vorticity-velocity Variables
Author: T. B. Gatski
Publisher:
Published: 1981
Total Pages: 24
ISBN-13:
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Author: T. B. Gatski
Publisher:
Published: 1981
Total Pages: 24
ISBN-13:
DOWNLOAD EBOOKAuthor: Institute for Computer Applications in Science and Engineering
Publisher:
Published: 1984
Total Pages: 28
ISBN-13:
DOWNLOAD EBOOKAuthor: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
Published: 2018-07-25
Total Pages: 28
ISBN-13: 9781724216175
DOWNLOAD EBOOKA compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented. Gatski, T. B. and Grosch, C. E. Langley Research Center NASA-CR-172353, ICASE-84-15, NAS 1.26:172353 NAS1-17070
Author: Paul G. Hershall
Publisher:
Published: 1974
Total Pages: 69
ISBN-13:
DOWNLOAD EBOOKThe two-dimensional, viscous, incompressible, steady flow in a semi-infinite rectangular channel is investigated numerically. A given jet with asymmetrical velocity profile is assumed at the inlet and fully developed flow is assumed at an infinite distance downstream. Using the split Navier-Stokes equation, with stream function and vorticity as dependent variables, central differences are used to set up difference equations. These are relaxed in the Gauss-Seidel mode with the aid of two relaxation factors for each equation and a maximum-number-of-iterations parameter for each equation. The optimum convergence rate is investigated empirically as a function of these six parameters. Convergence is obtained in this way up to Reynolds number 200 and optimum sets of values are given for (R sub e) = 1, 10, 50, and 200.
Author: Joe F Thompson (Jr)
Publisher:
Published: 1968
Total Pages: 257
ISBN-13:
DOWNLOAD EBOOKA numerical solution of the incompressible, two-dimensional, time-dependent Navier-Stokes equations, which is implicit in time as well as space, has been developed for the case of a uniform flow past a body with rectangular boundaries undergoing pitch oscillations. The Navier-Stokes equations are written in the form of the vorticity equation and the Poisson equation for the stream function, thus using the vorticity and stream function as dependent variables, rather than the velocity components and the pressure. The equations are written in a moving coordinate system fixed with respect to the oscillating body, which undergoes pitch oscillations about an arbitrary axis. (Author).
Author: North Atlantic Treaty Organization. Advisory Group for Aerospace Research and Development
Publisher:
Published: 1972
Total Pages: 356
ISBN-13:
DOWNLOAD EBOOK;Contents: On the numerical approximation of some equations arising in hydrodynamics; Approximation of Navier-Stokes equations; Sur l'approximation des equations de Navier-Stokes des fluides visqueux incompressibles; Numerical solution of steady state Navier-Stokes equations; Numerical solution of the Navier-Stokes equations at high reynolds numbers and the problem of discretization of convective derivatives; Numerical analysis of viscous one-dimensional flows; A critical analysis of numerical techniques: the piston-driven inviscid flow; Transient and asymptotically steady flow of an inviscid compressible gas past a circular cylinder; The blunt body problem for a viscous rarefied gas; The choice of a time-dependent technique in gas dynamics; Application of finite elements methods in fluid dynamics; Computational methods for inviscid transonic flows with inbedded shock waves; Numerical treatment of time-dependent three-dimensional flows; Un example de modele mathematique complexe en mecanique des fluides.
Author: J.T. Beale
Publisher: Springer Science & Business Media
Published: 2013-04-18
Total Pages: 385
ISBN-13: 9401581371
DOWNLOAD EBOOKMany important phenomena in fluid motion are evident in vortex flow, i.e., flows in which vortical structures are significant in determining the whole flow. This book, which consists of lectures given at a NATO ARW held in Grenoble (France) in June 1992, provides an up-to-date account of current research in the study of these phenomena by means of numerical methods and mathematical modelling. Such methods include Eulerian methods (finite difference, spectral and wavelet methods) as well as Lagrangian methods (contour dynamics, vortex methods) and are used to study such topics as 2- or 3-dimensional turbulence, vorticity generation by solid bodies, shear layers and vortex sheets, and vortex reconnection. For researchers and graduate students in computational fluid dynamics, numerical analysis, and applied mathematics.
Author: Mohamed M Hafez
Publisher: World Scientific
Published: 2003-01-23
Total Pages: 708
ISBN-13: 9814486396
DOWNLOAD EBOOKThis book consists of 37 articles dealing with simulation of incompressible flows and applications in many areas. It covers numerical methods and algorithm developments as well as applications in aeronautics and other areas. It represents the state of the art in the field.
Author: L. Quartapelle
Publisher: Birkhäuser
Published: 2013-03-07
Total Pages: 296
ISBN-13: 3034885792
DOWNLOAD EBOOKThis book presents different formulations of the equations governing incompressible viscous flows, in the form needed for developing numerical solution procedures. The conditions required to satisfy the no-slip boundary conditions in the various formulations are discussed in detail. Rather than focussing on a particular spatial discretization method, the text provides a unitary view of several methods currently in use for the numerical solution of incompressible Navier-Stokes equations, using either finite differences, finite elements or spectral approximations. For each formulation, a complete statement of the mathematical problem is provided, comprising the various boundary, possibly integral, and initial conditions, suitable for any theoretical and/or computational development of the governing equations. The text is suitable for courses in fluid mechanics and computational fluid dynamics. It covers that part of the subject matter dealing with the equations for incompressible viscous flows and their determination by means of numerical methods. A substantial portion of the book contains new results and unpublished material.
Author: Douglas Xuedong Zhu
Publisher:
Published: 2005
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAbstract: 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.