Accuracy of Projection Methods for the Incompressible Navier-Stokes Equations
Title | Accuracy of Projection Methods for the Incompressible Navier-Stokes Equations PDF eBook |
Author | |
Publisher | |
Pages | |
Release | 2001 |
Genre | |
ISBN |
Numerous papers have appeared in the literature over the past thirty years discussing projection-type methods for solving the incompressible Navier-Stokes equations. A recurring difficulty encountered is the choice of boundary conditions for the intermediate or predicted velocity in order to obtain at least second order convergence. A further issue is the formula for the pressure correction at each timestep. A simple overview is presented here based on recently published results by Brown, Cortez and Minion [2].
Accurate Projection Method for Incompressible Navier-stokes Equation by Numerical Methods
Title | Accurate Projection Method for Incompressible Navier-stokes Equation by Numerical Methods PDF eBook |
Author | Mohd Azad Mohd Kamil |
Publisher | |
Pages | 228 |
Release | 2006 |
Genre | Mathematical models |
ISBN |
The Immersed Interface Method
Title | The Immersed Interface Method PDF eBook |
Author | Zhilin Li |
Publisher | SIAM |
Pages | 348 |
Release | 2006-01-01 |
Genre | Mathematics |
ISBN | 9780898717464 |
This book provides an introduction to the immersed interface method (IIM), a powerful numerical method for solving interface problems and problems defined on irregular domains for which analytic solutions are rarely available. This book gives a complete description of the IIM, discusses recent progress in the area, and describes numerical methods for a number of classic interface problems. It also contains many numerical examples that can be used as benchmark problems for numerical methods designed for interface problems on irregular domains.
Higher-Order Semi-Implicit Projection Methods
Title | Higher-Order Semi-Implicit Projection Methods PDF eBook |
Author | |
Publisher | |
Pages | |
Release | 2001 |
Genre | |
ISBN |
A semi-implicit form of the method of spectral deferred corrections is applied to the solution of the incompressible Navier-Stokes equations. A methodology for constructing semi-implicit projection methods with arbitrarily high order of temporal accuracy in both the velocity and pressure is presented. Three variations of projection methods are discussed which differ in the manner in which the auxiliary velocity and the pressure are calculated. The presentation will make clear that project methods in general need not be viewed as fractional step methods as is often the practice. Two simple numerical examples re used to demonstrate fourth-order accuracy in time for an implementation of each variation of projection method.
Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations
Title | Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations PDF eBook |
Author | |
Publisher | Springer Science & Business Media |
Pages | 302 |
Release | 2013-11-11 |
Genre | Technology & Engineering |
ISBN | 3663111717 |
Projection methods had been introduced in the late sixties by A. Chorin and R. Teman to decouple the computation of velocity and pressure within the time-stepping for solving the nonstationary Navier-Stokes equations. Despite the good performance of projection methods in practical computations, their success remained somewhat mysterious as the operator splitting implicitly introduces a nonphysical boundary condition for the pressure. The objectives of this monograph are twofold. First, a rigorous error analysis is presented for existing projection methods by means of relating them to so-called quasi-compressibility methods (e.g. penalty method, pressure stabilzation method, etc.). This approach highlights the intrinsic error mechanisms of these schemes and explains the reasons for their limitations. Then, in the second part, more sophisticated new schemes are constructed and analyzed which are exempted from most of the deficiencies of the classical projection and quasi-compressibility methods. '... this book should be mandatory reading for applied mathematicians specializing in computational fluid dynamics.' J.-L.Guermond. Mathematical Reviews, Ann Arbor
Accuracy of Least-squares Methods for the Navier-Stokes Equations
Title | Accuracy of Least-squares Methods for the Navier-Stokes Equations PDF eBook |
Author | Pavel B. Bochev |
Publisher | |
Pages | 24 |
Release | 1993 |
Genre | Least squares |
ISBN |
Numerical Simulations of Incompressible Flows
Title | Numerical Simulations of Incompressible Flows PDF eBook |
Author | M. M. Hafez |
Publisher | World Scientific |
Pages | 712 |
Release | 2003 |
Genre | Mathematics |
ISBN | 9789812796837 |
This 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. Contents: NavierOCoStokes Solvers; Projection Methods; Finite Element Methods; Higher-Order Methods; Innovative Methods; Applications in Aeronautics; Applications Beyond Aeronautics; Multiphase and Cavitating Flows; Special Topics. Readership: Researchers and graduate students in computational science and engineering."