Download or read book On Numerical Solutions of the General Navier Stokes Equations for Two layered Stratified Flows written by John Dzen Hwang and published by . This book was released on 1968 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this paper is to seek the general solution of the complete Navier-Stokes equations governing heterogeneous, time-dependent, incompressible, viscous, laminar fluid dynamics through digital simulation. In particular, two-layered stratified flows are treated by using a numerical algorithm called the Marker-and-Cell extended method (MACE), which is an extension of the MAC code originated by the Los Alamos Scientific Laboratory. To provide the necessary background, the paper begins with a mathematical description of stratified flows. The controlling equations are the Navier-Stokes equations, the continuity relation, and the incompressible condition. These equations and various alternative formulations are presented in axiomatic form; care has been taken in this exposition so as to exhibit the hypotheses involved in analytical hydrodynamics. Necessary boundary conditions characterizing the physical states of the stratified fluids are also stated. The finite difference scheme of MACE algorithm is discussed in detail, and specific boundary conditions are derived for the MACE code allowing inflow and outflow capabilities, no-slip and free-slip boundary-layer considerations, and free-surface formulation. In order to place the MACE method on a solid mathematical foundation, a discussion of numerous aspects of stability and error are derived for the Navier-Stokes equations. The stability of the MACE numerical scheme and the convergence of the numerical solution to the theoretical solution are proven. An example involving two-layered stratified fluid flow with inflow and outflow is presented to show how the previously non-realizable solutions of the general Navier-Stokes equations can be computed systematically through this algorithm. The example was simulated digitally to obtain movie-frames illustrating various stages of the transient state of stratified flow patterns. A complete set of flow diagrams demonstrating the logical sequence of calculations by the MACE method is provided; a FORTRAN IV program listing is appended. Natural extensions of the MACE method are proposed to handle general heterogeneous fluids of both the continuum and the discrete layered stratification. The MACE method has great potential, for continuations of this method may lead to discover whether or not viscous, laminar fluid flow can be fully described by the fundamental Navier-Stokes equations.
Download or read book The Navier Stokes Equations written by P. G. Drazin and published by Cambridge University Press. This book was released on 2006-05-25 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 book details exact solutions to the Navier-Stokes equations for senior undergraduates and graduates or research reference.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solution of the Incompressible Navier Stokes Equations written by L. Quartapelle and published by Birkhäuser. This book was released on 2013-03-07 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Download or read book Numerical Solutions of the Incompressible Navier Stokes Equations in Two and Three Dimensional Coordinates written by Alexander Victor and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important applications of finite difference lies in the field of computational fluid dynamics (CFD). In particular, the solution to the Navier-Stokes equation grants us insight into the behavior of many physical systems. The 2-D and 3-D incompressible Navier-Stokes equation has been studied extensively due to its analogous nature to many practical applications, and several numerical schemes have been developed to provide solutions dedicated to different environmental conditions (such as different Reynolds numbers). This research also covers the assignment of boundary conditions, starting with the simple case of driven cavity flow problem. In addition, several parts of the equations are given implicitly, which requires efficient ways of solving large systems of equations.We also considered numerical solution methods for the incompressible Navier-Stokes equations discretized on staggered grids in general coordinates. Numerical experiments are carried out on a vector computer. Robustness and efficiency of these methods are studied. It appears that good methods result from suitable combinations of multigrid methods.Numerically solving the incompressible Navier-Stokes equations is known to be time-consuming and expensive; hence this research presents some MATLAB codes for obtaining numerical solution of the Navier-Stokes equations for incompressible flow through flow cavities, using method of lines, in three-dimensional space (3-D). The code treats the laminar flow over a two-dimensional backward-facing step, and the results of the computations over the backward-facing step are in excellent agreement with experimental results.
Download or read book College of Engineering written by University of Michigan. College of Engineering and published by UM Libraries. This book was released on 1995 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Thermal Plume Model for Vertical Outfalls in Shallow Water written by Donald S. Trent and published by . This book was released on 1973 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Analysis of the Navier Stokes Equations written by Charles R. Doering and published by Cambridge University Press. This book was released on 1995 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory physical and mathematical presentation of the Navier-Stokes equations focuses on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion.
Download or read book Theory Of The Navier stokes Equations written by John G Heywood and published by World Scientific. This book was released on 1998-05-30 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the articles presented at the Third International Conference on “The Navier-Stokes Equations: Theory and Numerical Methods”, held in Oberwolfach, Germany. The articles are important contributions to a wide variety of topics in the Navier-Stokes theory: general boundary conditions, flow exterior to an obstacle, conical boundary points, the controllability of solutions, compressible flow, non-Newtonian flow, magneto-hydrodynamics, thermal convection, the interaction of fluids with elastic solids, the regularity of solutions, and Rothe's method of approximation.
Download or read book Numerical Solution of the Unsteady Navier Stokes Equations and Application to Flow in a Rectangular Cavity with a Moving Wall written by Leo F. Donovan and published by . This book was released on 1971 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Solutions of the Navier Stokes Equations for the Flow of Two Incompressible Nonmiscible Viscous Fluids written by Vasilios Tsikkinis and published by . This book was released on 1989 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Navier Stokes Equations written by Rodolfo Salvi and published by CRC Press. This book was released on 2001-09-27 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Contains proceedings of Varenna 2000, the international conference on theory and numerical methods of the navier-Stokes equations, held in Villa Monastero in Varenna, Lecco, Italy, surveying a wide range of topics in fluid mechanics, including compressible, incompressible, and non-newtonian fluids, the free boundary problem, and hydrodynamic potential theory."
Download or read book NBS Special Publication written by and published by . This book was released on 1976 with total page 838 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hydraulic Research in the United States and Canada written by and published by . This book was released on 1972 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hydraulic Research in the United States and Canada 1974 written by Pauline H. Gurewitz and published by . This book was released on 1976 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Research Reporting Series written by and published by . This book was released on 1973 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt:
