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Numerical Solutions To The Navier Stokes Equations In Two And Three Dimensions
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Book Synopsis Numerical Solutions to the Navier-Stokes Equations in Two and Three Dimensions by : Badr Alkahtani
Download or read book Numerical Solutions to the Navier-Stokes Equations in Two and Three Dimensions written by Badr Alkahtani and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis the solutions of the two-dimensional (2D) and three-dimensional (3D) lid-driven cavity problem are obtained by solving the steady Navier-Stokes equations at high Reynolds numbers. In 2D, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to $Re=25000$ on a fine grid of 131 * 131. The same method is also used to obtain the numerical solutions for the steady separated corner flow at high Reynolds numbers are generated using a for various domain sizes, at various Reynolds number which are much higher than those obtained by other researchers. Finally, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200.
Book Synopsis Numerical Solutions of the Incompressible Navier-Stokes Equations in Two and Three-Dimensional Coordinates by : Alexander Victor
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.
Book Synopsis The Three-Dimensional Navier-Stokes Equations by : James C. Robinson
Download or read book The Three-Dimensional Navier-Stokes Equations written by James C. Robinson and published by Cambridge University Press. This book was released on 2016-09-07 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students.
Book Synopsis The Navier-Stokes Equations Theory and Numerical Methods by : John G. Heywood
Download or read book The Navier-Stokes Equations Theory and Numerical Methods written by John G. Heywood and published by Springer. This book was released on 2006-11-14 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Study of the Navier Stokes Equations in Three Dimensions by : Padam Jain
Download or read book Numerical Study of the Navier Stokes Equations in Three Dimensions written by Padam Jain and published by . This book was released on 1967 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: To investigate the process of energy transfer from large eddies to smaller ones at high Reynolds Numbers, a finite difference method is used to obtain the periodic solutions of the Navier-Stokes equations in three dimensions when the initial motion is assumed to be v sub 1 = cos x sin y sin z, v sub 2 = -sin x cos y sin z, v sub 3 = 0. A numerical technique for the solution of Poisson's equation for the three dimensional problem is described and used for the solution of the problem. Mean kinetic energy and mean square vorticity are calculated and it is found that the numerical method provides estimates of these quantities up to a time of the order of 2. The structure of the turbulent flow is investigated by a study of the velocity correlation function R sub ij. (Author).
Book Synopsis A Numerical Study of the Two- and Three-dimensional Unsteady Navier-Stokes Equations in Velocity-vorticity Variables Using Compact Difference Schemes by : Institute for Computer Applications in Science and Engineering
Download or read book 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 published by . This book was released on 1984 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Volume Methods for the Incompressible Navier–Stokes Equations by : Jian Li
Download or read book Finite Volume Methods for the Incompressible Navier–Stokes Equations written by Jian Li and published by Springer Nature. This book was released on 2022-01-20 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to provide a comprehensive understanding of the most recent developments in finite volume methods. Its focus is on the development and analysis of these methods for the two- and three-dimensional Navier-Stokes equations, supported by extensive numerical results. It covers the most used lower-order finite element pairs, with well-posedness and optimal analysis for these finite volume methods.The authors have attempted to make this book self-contained by offering complete proofs and theoretical results. While most of the material presented has been taught by the authors in a number of institutions over the past several years, they also include several updated theoretical results for the finite volume methods for the incompressible Navier-Stokes equations. This book is primarily developed to address research needs for students and academic and industrial researchers. It is particularly valuable as a research reference in the fields of engineering, mathematics, physics, and computer sciences.
Book Synopsis Numerical Solution of the Incompressible Navier-Stokes Equations by : L. Quartapelle
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.
Book Synopsis Numerical Solutions of the Navier-Stokes Equations in Three Dimensions by : Robert Neal Cook
Download or read book Numerical Solutions of the Navier-Stokes Equations in Three Dimensions written by Robert Neal Cook and published by c1976.. This book was released on 1976 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Time-dependent FEM Solution of the Incompressible Navier--Stokes Equations in Two- and Three-dimensions by :
Download or read book Time-dependent FEM Solution of the Incompressible Navier--Stokes Equations in Two- and Three-dimensions written by and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Future prospects regarding the numerical solution of the Navier-Stokes equations using the finite element method are discussed. Since the ultimate goal is to solve these equations in three-dimensions, only the primitive variable (u, P) formulation is considered. A novel feature of the two-dimensional solution technique relates to the methodology developed and employed for solving the semi-discretized system of ordinary differential equations, which are outlined in the section describing the development of the two-dimensional code. Following the discussion of numerical results from two-dimensional calculations, three-dimensional flows are discussed, where several potentially viable options are considered. (TFD).
Book Synopsis Navier-Stokes Equations and Nonlinear Functional Analysis by : Roger Temam
Download or read book Navier-Stokes Equations and Nonlinear Functional Analysis written by Roger Temam and published by SIAM. This book was released on 1995-01-01 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition, like the first, attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations in the following areas: existence, uniqueness, and regularity of solutions in space dimensions two and three; large time behavior of solutions and attractors; and numerical analysis of the Navier-Stokes equations. Since publication of the first edition of these lectures in 1983, there has been extensive research in the area of inertial manifolds for Navier-Stokes equations. These developments are addressed in a new section devoted entirely to inertial manifolds. Inertial manifolds were first introduced under this name in 1985 and, since then, have been systematically studied for partial differential equations of the Navier-Stokes type. Inertial manifolds are a global version of central manifolds. When they exist they encompass the complete dynamics of a system, reducing the dynamics of an infinite system to that of a smooth, finite-dimensional one called the inertial system. Although the theory of inertial manifolds for Navier-Stokes equations is not complete at this time, there is already a very interesting and significant set of results which deserves to be known, in the hope that it will stimulate further research in this area. These results are reported in this edition.
Book Synopsis Numerical Solutions of Navier-Stokes Equations for Compressible Turbulent Two/three Dimensional Flows in the Terminal Shock Region of an Inlet/diffuser by : N.-S. Liu
Download or read book Numerical Solutions of Navier-Stokes Equations for Compressible Turbulent Two/three Dimensional Flows in the Terminal Shock Region of an Inlet/diffuser written by N.-S. Liu and published by . This book was released on 1983 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of the Incompressible Navier-Stokes Equations in Three-dimensional Generalized Curvilinear Coordinates by : Stuart Eames Rogers
Download or read book Numerical Solution of the Incompressible Navier-Stokes Equations in Three-dimensional Generalized Curvilinear Coordinates written by Stuart Eames Rogers and published by . This book was released on 1986 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Experiments with the Two- and Three-Dimensional Unsteady Navier-Stokes Equations by : Gustave Hokenson
Download or read book Numerical Experiments with the Two- and Three-Dimensional Unsteady Navier-Stokes Equations written by Gustave Hokenson and published by . This book was released on 1973 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two- and three-dimensional unsteady Navier-Stokes equations are solved numerically for the flow field about an impulsively started flat plate. In attempting to obtain an exact time dependent solution, several significant results were observed. First, with regard to the formulation of the differential equations themselves, it appears that Poisson's equation for the pressure field is a fundamental equation in as much as it allows us to solve for pressure moat exactly at any given time. Secondly, the difference equations must be carefully and consistently formulated. In this research, a non-uniform lateral grid, a unique interpretation of the continuity equation, and leap frog integration in time proved to be valuable techniques in obtaining an exact solution. (Author).
Book Synopsis Numerical Solution of the Navier-Stokes and Energy Equations in Two and Three Dimensional Flow Problems by : Yaya Aremu 'Sesan Aregbesola
Download or read book Numerical Solution of the Navier-Stokes and Energy Equations in Two and Three Dimensional Flow Problems written by Yaya Aremu 'Sesan Aregbesola and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solutions for the Navier-Stokes Equations in Two-dimensional Space by : Rebecca Eileen Smith
Download or read book Numerical Solutions for the Navier-Stokes Equations in Two-dimensional Space written by Rebecca Eileen Smith and published by . This book was released on 2013 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: In this thesis, we will study the numerical solutions for fluid dynamic systems such as the study of air flow, water flow, etc. We use the finite difference method and partial differential equations via matrices to obtain the numerical solutions. We will study partial differential equations in the one and two dimensional space. The study in one dimensional space will examine the finite difference method on the second derivative. The two dimensional space will analyze the nonlinear Navier-Stokes equations. Error analysis and relative residual will play a key role in the solution and will be a main focus in this study. Numerical analysis utilizing MATLAB software will be performed.
Book Synopsis Numerical Experiments with the Two- and Three-dimensional Unsteady Navier-Stokes Equation by : Gustave John Hokenson
Download or read book Numerical Experiments with the Two- and Three-dimensional Unsteady Navier-Stokes Equation written by Gustave John Hokenson and published by . This book was released on 1973 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two- and three-dimensional unsteady Navier-Stokes equations are solved numerically for the flow field about an impulsively started flat plate. In attempting to obtain an exact time dependent solution, several significant results were observed. First, with regard to the formulation of the differential equations themselves, it appears that Poisson's equation for the pressure field is a fundamental equation in as much as it allows us to solve for pressure moat exactly at any given time. Secondly, the difference equations must be carefully and consistently formulated. In this research, a non-uniform lateral grid, a unique interpretation of the continuity equation, and leap frog integration in time proved to be valuable techniques in obtaining an exact solution. (Author).
