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Book Accuracy of Least squares Methods for the Navier Stokes Equations

Download or read book Accuracy of Least squares Methods for the Navier Stokes Equations written by Pavel B. Bochev and published by . This book was released on 1993 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Accuracy of Projection Methods for the Incompressible Navier Stokes Equations

Download or read book Accuracy of Projection Methods for the Incompressible Navier Stokes Equations written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].

Book The Immersed Interface Method

Download or read book The Immersed Interface Method written by Zhilin Li and published by SIAM. This book was released on 2006-01-01 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Accuracy of Least Squares Methods for the Navier Stokes Equations

Download or read book Accuracy of Least Squares Methods for the Navier Stokes Equations written by National Aeronautics and Space Administration NASA and published by . This book was released on 2018-10-23 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations. Bochev, Pavel B. and Gunzburger, Max D. Glenn Research Center NCC3-233; RTOP 505-90-5K...

Book Numerical Solution of the Incompressible Navier Stokes Equations

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 Numerical Solution of the Incompressible Navier Stokes Equations in Three dimensional Generalized Curvilinear Coordinates

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 A New Method for the Solution of the Incompressible Navier Stokes Equations

Download or read book A New Method for the Solution of the Incompressible Navier Stokes Equations written by Hazem Said and published by . This book was released on 2001 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solution of the incompressible Navier-Stokes (INS) equations in primitive variables requires special care to ensure that the resulting flow field will satisfy the discrete governing equations (DGE). However, these equations are not satisfied by the existing solution methods, thus requiring the need to develop a new method. A new method is developed in this work to solve the INS equations in primitive variables. The method uses the velocity and pressure gradients as dependent variables compared to velocity and pressure that are used by all other primitive variables methods. These new dependent variables require additional constraint to be determined. The condition of irrotationality of the gradient of the pressure is employed to give the necessary equations to close the problem. Thus the flow field is represented by a new set of equations that when solved together produces a solution that satisfies the DGE. of the present method are summarized as follows: (1) it eliminates the compatability condition of the pressure equation typical of all pressure-based techniques, (2) it satisfies the discrete continuity and momentum equations. (3) Boundary conditions are physically known for all the dependent variables. (4) It eliminates the inversion of the implicit operator typical of the implicit primitive variables formulation, (5) Robust, stable and more accurate computational codes can be developed. Numerical results are obtained for the driven cavity problem, using both the explicit and the implicit forms of the method. Results are obtained for Reynolds numbers of 100, 400 and 1000. These results show that the present method produces a stable solution and that the resulting flow field does satisfy the DGE to machine zero.

Book Numerical Approximation of Partial Differential Equations

Download or read book Numerical Approximation of Partial Differential Equations written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

Book New Developments in the Method of Space time Conservation Element and Solution Element Applications to the Euler and Navier Stokes Equations

Download or read book New Developments in the Method of Space time Conservation Element and Solution Element Applications to the Euler and Navier Stokes Equations written by Sin-Chung Chang and published by . This book was released on 1993 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Numerical Solution of Two dimensional Incompressible Navier Stokes Equations

Download or read book Numerical Solution of Two dimensional Incompressible Navier Stokes Equations written by S. M. H. Karimian and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: