Numerical Solution of Incompressible Navier-Stokes Equations Using a Velocity-vorticity Formulation
Author: Jennifer Samson Dacles
Publisher:
Published: 1991
Total Pages: 266
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Jennifer Samson Dacles
Publisher:
Published: 1991
Total Pages: 266
ISBN-13:
DOWNLOAD EBOOKAuthor: L. Quartapelle
Publisher: Springer Science & Business Media
Published: 1993-09-01
Total Pages: 312
ISBN-13: 9783764329358
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 A substantial portion of the book contains new results and unpublished material.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: 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: Yong Huang
Publisher:
Published: 1997
Total Pages: 366
ISBN-13:
DOWNLOAD EBOOKAuthor: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
Published: 2018-07-11
Total Pages: 28
ISBN-13: 9781722421847
DOWNLOAD EBOOKThe numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows. Hafez, Mohammed and Dacles, Jennifer Unspecified Center NCA2-210...
Author: Murli M. Gupta
Publisher:
Published: 1990
Total Pages: 30
ISBN-13:
DOWNLOAD EBOOKAuthor: S. N. Kempka
Publisher:
Published: 1995
Total Pages: 57
ISBN-13:
DOWNLOAD EBOOKA formulation to satisfy velocity boundary conditions for the vorticity form of the incompressible, viscous fluid momentum equations is presented. The tangential and normal components of the velocity boundary condition are satisfied simultaneously by creating vorticity adjacent to boundaries. The newly created vorticity is determined using a kinematical formulation which is a generalization of Helmholtz, decomposition of a vector field. Related forms of the decomposition were developed by Bykhovskiy and Smirnov in 1983, and Wu and Thompson in 1973. Though it has not been generally recognized, these formulations resolve the over-specification issue associated with creating vorticity to satisfy velocity boundary conditions. The generalized decomposition has not been widely used, apparently due to a lack of a useful physical interpretation. An analysis is presented which shows that the generalized decomposition has a relatively simple physical interpretation which facilitates its numerical implementation.
Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
Published: 2019
Total Pages: 32
ISBN-13: 9781792834691
DOWNLOAD EBOOKA p-version of the least squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady state incompressible viscous flow problems. The resulting system of symmetric and positive definite linear equations can be solved satisfactorily with the conjugate gradient method. In conjunction with the use of rapid operator application which avoids the formation of either element of global matrices, it is possible to achieve a highly compact and efficient solution scheme for the incompressible Navier-Stokes equations. Numerical results are presented for two-dimensional flow over a backward facing step. The effectiveness of simple outflow boundary conditions is also demonstrated. Jiang, Bo-Nan and Sonnad, Vijay Glenn Research Center NASA-TM-105203, ICOMP-91-14, E-6506, NAS 1.15:105203 NASA ORDER C-99066-G...
Author: Alexander Shatalov
Publisher:
Published: 2001
Total Pages: 178
ISBN-13:
DOWNLOAD EBOOKAuthor: Michel Deville
Publisher: Vieweg+Teubner Verlag
Published: 2013-03-09
Total Pages: 234
ISBN-13: 3663002217
DOWNLOAD EBOOKThe GAMM-Commi ttee for Numerical Methods in Fluid Mechanics (GAMM-Fachausschuss für Numerische Methoden in der Strömungsmechanik) has sponsored the organization of a GAMM Workshop dedicated to the numerical simulation of three dimensional incompressible unsteady viscous laminar flows to test Navier-Stokes solvers. The Workshop was held in Paris from June 12th to June 14th, 1991 at the Ecole Nationale Superieure des Arts et Metiers. Two test problems were set up. The first one is the flow in a driven-lid parallelepipedic cavity at Re = 3200 . The second problem is a flow around a prolate spheroid at incidence. These problems are challenging as fully transient solutions are expected to show up. The difficulties for meaningful calculations come from both space and temporal discretizations which have to be sufficiently accurate to resol ve detailed structures like Taylor-Görtler-like vortices and the appropriate time development. Several research teams from academia and industry tackled the tests using different formulations (veloci ty-pressure, vortici ty velocity), different numerical methods (finite differences, finite volumes, finite elements), various solution algorithms (splitting, coupled ...), various solvers (direct, iterative, semi-iterative) with preconditioners or other numerical speed-up procedures. The results show some scatter and achieve different levels of efficiency. The Workshop was attended by about 25 scientists and drove much interaction between the participants. The contributions in these proceedings are presented in alphabetical order according to the first author, first for the cavi ty problem and then for the prolate spheroid problem. No definite conclusions about benchmark solutions can be drawn.