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Development Of Versatile Mixed Finite Element Methods For The Non Isothermal Incompressible And Compressible Navier Stokes Equations
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Book Synopsis Development of Versatile Mixed Finite Element Methods for the Non-Isothermal Incompressible and Compressible Navier-Stokes Equations by : Edward Miller
Download or read book Development of Versatile Mixed Finite Element Methods for the Non-Isothermal Incompressible and Compressible Navier-Stokes Equations written by Edward Miller and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ever increasing demand for accurate numerical methods has led to the development of more and more sophisticated methods for simulating fluid flow. These methods are often designed to handle a specific flow regime or be valid under specific circumstances. What is needed in the field is a method that is accurate and robust over a wide range of conditions. Here, we propose a finite element method designed to work over a broad range of flow regimes and remain consistent and accurate in each regime. This is accomplished utilizing a mixed finite element method whose properties are rigorously analyzed to demonstrate the method's effectiveness at handling these different flow regimes. We first use standard mathematical techniques to prove that the method is stable and obtains optimal error estimates for the non-isothermal incompressible Navier-Stokes equations. We then demonstrate on a series of test cases that the method accurately captures the physics of the non-isothermal incompressible Navier-Stokes equations. Next, we extend our method to the compressible Navier-Stokes equations where again the order of accuracy is demonstrated, this time using a series of numerical experiments. Finally, we present a series of compressible flow test cases to prove that the method can capture the physics of this regime.
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 Finite Element Solutions of Axisymmetric Navier-Stokes Equations for Non-isothermal Flows with Swirl by : ShuShi Huang
Download or read book Finite Element Solutions of Axisymmetric Navier-Stokes Equations for Non-isothermal Flows with Swirl written by ShuShi Huang and published by . This book was released on 1996 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robust Arbitrary Order Mixed Finite Element Methods for the Incompressible Stokes Equations by :
Download or read book Robust Arbitrary Order Mixed Finite Element Methods for the Incompressible Stokes Equations written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Standard mixed finite element methods for the incompressible Navier-Stokes equations that relax the divergence constraint are not robust against large irrotational forces in the momentum balance and the velocity error depends on the continuous pressure. This robustness issue can be completely cured by using divergence-free mixed finite elements which deliver pressure-independent velocity error estimates. However, the construction of H1-conforming, divergence-free mixed finite element methods is rather difficult. Instead, we present a novel approach for the construction of arbitrary order mixed finite element methods which deliver pressure-independent velocity errors. The approach does not change the trial functions but replaces discretely divergence-free test functions in some operators of the weak formulation by divergence-free ones. This modification is applied to inf-sup stable conforming and nonconforming mixed finite element methods of arbitrary order in two and three dimensions. Optimal estimates for the incompressible Stokes equations are proved for the H1 and L2 errors of the velocity and the L2 error of the pressure. Moreover, both velocity errors are pressure-independent, demonstrating the improved robustness. Several numerical examples illustrate the results.
Book Synopsis Implementation of Finite Element Methods for Navier-Stokes Equations by : F. Thomasset
Download or read book Implementation of Finite Element Methods for Navier-Stokes Equations written by F. Thomasset and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.
Book Synopsis The Least-Squares Finite Element Method by : Bo-nan Jiang
Download or read book The Least-Squares Finite Element Method written by Bo-nan Jiang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.
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 . This book was released on 2022 with total page 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 On Conforming Mixed Finite Element Methods for Incompressible Viscous Flow Problems by : Max D. Gunzburger
Download or read book On Conforming Mixed Finite Element Methods for Incompressible Viscous Flow Problems written by Max D. Gunzburger and published by . This book was released on 1981 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Methods for Navier-Stokes Equations by : Vivette Girault
Download or read book Finite Element Methods for Navier-Stokes Equations written by Vivette Girault and published by . This book was released on 1986-05-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows by : Volker John
Download or read book On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows written by Volker John and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The divergence constraint of the incompressible Navier-Stokes equations is revisited in the mixed finite element framework. While many stable and convergent mixed elements have been developed throughout the past four decades, most classical methods relax the divergence constraint and only enforce the condition discretely. As a result, these methods introduce a pressure-dependent consistency error which can potentially pollute the computed velocity. These methods are not robust in the sense that a contribution from the right-hand side, which in fluences only the pressure in the continuous equations, impacts both velocity and pressure in the discrete equations. This paper reviews the theory and practical implications of relaxing the divergence constraint. Several approaches for improving the discrete mass balance or even for computing divergence-free solutions will be discussed: grad-div stabilization, higher order mixed methods derived on the basis of an exact de Rham complex, H(div)-conforming finite elements, and mixed methods with an appropriate reconstruction of the test functions. Numerical examples illustrate both the potential effects of using non-robust discretizations and the improvements obtained by utilizing pressure-robust discretizations.
Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781722005139 Total Pages :24 pages Book Rating :4.0/5 (51 download)
Book Synopsis A Least-Squares Finite Element Method for Incompressible Navier-Stokes Problems by : National Aeronautics and Space Administration (NASA)
Download or read book A Least-Squares Finite Element Method for Incompressible Navier-Stokes Problems written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-28 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method, and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented. Jiang, Bo-Nan Glenn Research Center NASA ORDER C-99066-G; RTOP 505-62-21...
Book Synopsis Stabilized Finite Element Methods for Coupled Incompressible Flow Problems by : Daniel Arndt
Download or read book Stabilized Finite Element Methods for Coupled Incompressible Flow Problems written by Daniel Arndt and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, a finite element discretization of the incompressible Navier-Stokes equations for a non-isothermal and electrically conducting fluid in a possibly rotating frame of reference is considered. In particular, the Oberbeck-Boussinesq model is combined with resistive incompressible magnetohydrodynamics. In order to account for instabilities and to diminish unphysical oscillations a stabilization for the incompressibility constraint as well as a local projection approach for various terms is considered. For the spatial discretization inf-sub stable ansatz spaces for velocity and pr ...
Book Synopsis A Mixed Finite Element Projection Method for the Incompressible Navier-Stokes Equations by : Daniele Boffi
Download or read book A Mixed Finite Element Projection Method for the Incompressible Navier-Stokes Equations written by Daniele Boffi and published by . This book was released on 1998 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Methods and Navier-Stokes Equations by : C. Cuvelier
Download or read book Finite Element Methods and Navier-Stokes Equations written by C. Cuvelier and published by Springer Science & Business Media. This book was released on 1986-03-31 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On Conforming Mixed Finite Element Methods for the Inhomogeneous Stationary Navier-Stokes Equations by : Max D. Gunzburger
Download or read book On Conforming Mixed Finite Element Methods for the Inhomogeneous Stationary Navier-Stokes Equations written by Max D. Gunzburger and published by . This book was released on 1982 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We consider the stationary Navier-Stokes equations in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, we prove the existence and uniqueness of the solution of a weak formulation of the equations. Next, a conforming mixed finite element method is presented and optimal estimates for the error of the approximate solution are provided. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are analyzed. Numerical examples, using an efficient choice of finite element spaces, are also provided" -- abstract.
Book Synopsis Mixed Finite Elements, Compatibility Conditions, and Applications by : Daniele Boffi
Download or read book Mixed Finite Elements, Compatibility Conditions, and Applications written by Daniele Boffi and published by Springer. This book was released on 2008-04-01 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.
Book Synopsis A Mixed Finite Element Method for the Navier-Stokes Equations by : Pierre-Arnaud Raviart
Download or read book A Mixed Finite Element Method for the Navier-Stokes Equations written by Pierre-Arnaud Raviart and published by . This book was released on 1977 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
