Solution of the Steady and Unsteady Incompressible Navier-Stokes Equations Using the Finite Element Method PDF Download
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Author: O. R. Sørensen
Publisher:
ISBN:
Category :
Languages : en
Pages : 172
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Book Description
Author: O. R. Sørensen
Publisher:
ISBN:
Category :
Languages : en
Pages : 172
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Book Description
Author: Shrinivas G. Apte
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
A primitive variable mixed order formulation of finite element method for solving three dimensional incompressible Navier-Stokes equations is presented. The method of weighted residuals is used for obtaining the approximate solutions of linear and nonlinear partial differential equations. The Physical domain is discretized by using unstructured tetrahedral elements. Unequal order interpolation functions are used for pressure & velocity variables while the temporal discretization is carried out by using an implicit time marching scheme based on finite differencing. One of the major diffculties arising during the finite element solution of an incompressible Navier-Stokes equations is the efficient factorization/preconditioning of the resulting indefinite stiffness matrix. In this work, the formation of an indefinite matrix is avoided by using a pseudo compressibility technique in which an artificial term is introduced into the mass matrix. The artificial term is time dependent and disposed at a later stage once the steady state is reached. Using this approach, the resulting system of equations can then be solved iteratively with standard preconditioners. The non-linear convective term in the Navier-Stokes equations is linearized in time. To diffuse the numerical oscillations which may occur in convection dominated flows, second-orderTaylor-Galerkinstabilization technique is used. The entire solution procedure is encoded in C++ using object oriented programming. One of the special features of this FEM code is that it uses the exact integrals of the shape functions in order to improve the accuracy of the solution, as supposed to any numerical integration schemes. The solution procedure is validated using the benchmark computations for 3D steady incompressible flows.
Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
ISBN: 9781792834691
Category :
Languages : en
Pages : 32
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Book Description
A 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: Pavel B. Bochev
Publisher: Springer Science & Business Media
ISBN: 0387689222
Category : Mathematics
Languages : en
Pages : 669
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Book Description
Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.
Author: Bo-nan Jiang
Publisher:
ISBN:
Category : Navier-Stokes equations
Languages : en
Pages : 18
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Book Description
Author: Pavel B. Bochev
Publisher:
ISBN:
Category : Least squares
Languages : en
Pages : 24
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Book Description
Author: Jean Donea
Publisher: John Wiley & Sons
ISBN: 9780471496663
Category : Science
Languages : en
Pages : 366
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Book Description
Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden.
Author: R. Rautmann
Publisher: Springer
ISBN: 3540385509
Category : Mathematics
Languages : en
Pages : 602
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Book Description
Author: Guang Ren
Publisher:
ISBN:
Category : Finite element method
Languages : en
Pages : 16
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Book Description
Author: Amar Khennane
Publisher: CRC Press
ISBN: 1466580208
Category : Technology & Engineering
Languages : en
Pages : 490
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Book Description
There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB® and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MATLAB is a high-level language specially designed for dealing with matrices, making it particularly suited for programming the finite element method, while Abaqus is a suite of commercial finite element software. Includes more than 100 tables, photographs, and figures Provides MATLAB codes to generate contour plots for sample results Introduction to Finite Element Analysis Using MATLAB and Abaqus introduces and explains theory in each chapter, and provides corresponding examples. It offers introductory notes and provides matrix structural analysis for trusses, beams, and frames. The book examines the theories of stress and strain and the relationships between them. The author then covers weighted residual methods and finite element approximation and numerical integration. He presents the finite element formulation for plane stress/strain problems, introduces axisymmetric problems, and highlights the theory of plates. The text supplies step-by-step procedures for solving problems with Abaqus interactive and keyword editions. The described procedures are implemented as MATLAB codes and Abaqus files can be found on the CRC Press website.
