Stabilized Finite Element Methods For Time Dependent Convection Diffusion Equations
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Stabilized Finite Element Methods For Time Dependent Convection Diffusion Equations
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Author : Onur Baysal
language : en
Publisher:
Release Date : 2012
Stabilized Finite Element Methods For Time Dependent Convection Diffusion Equations written by Onur Baysal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Finite element method categories.
In this thesis, enriched finite element methods are presented for both steady and unsteady convection diffusion equations. For the unsteady case, we follow the method of lines approach that consists of first discretizing in space and then use some time integrator to solve the resulting system of ordinary differential equation. Discretization in time is performed by the generalized Euler finite difference scheme, while for the space discretization the streamline upwind Petrov-Galerkin (SUPG), the Residual free bubble (RFB), the more recent multiscale (MS) and specific combination of RFB with MS (MIX) methods are considered. To apply the RFB and the MS methods, the steady local problem, which is as complicated as the original steady equation, should be solved in each element. That requirement makes these methods quite expensive especially for two dimensional problems. In order to overcome that drawback the pseudo approximation techniques, which employ only a few nodes in each element, are used. Next, for the unsteady problem a proper adaptation recipe, including these approximations combined with the generalized Euler time discretization, is described. For piecewise linear finite element discretization on triangular grid, the SUPG method is used. Then we derive an efficient stability parameter by examining the relation of the RFB and the SUPG methods. Stability and convergence analysis of the SUPG method applied to the unsteady problem is obtained by extending the Burman's analysis techniques for the pure convection problem. We also suggest a novel operator splitting strategy for the transport equations with nonlinear reaction term. As a result two subproblems are obtained. One of which we may apply using the SUPG stabilization while the other equation can be solved analytically. Lastly, numerical experiments are presented to illustrate the good performance of the method.
Finite Element Methods For Flow Problems
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Author : Jean Donea
language : en
Publisher: John Wiley & Sons
Release Date : 2003-06-02
Finite Element Methods For Flow Problems written by Jean Donea and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-02 with Science categories.
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.
Moving Mesh Finite Element Method For Time Dependent Convection Diffusion Problems
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Author : Matthew Maxwell McCoy
language : en
Publisher:
Release Date : 2021
Moving Mesh Finite Element Method For Time Dependent Convection Diffusion Problems written by Matthew Maxwell McCoy and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Electronic dissertations categories.
The moving mesh finite element method (MM-FEM) has been a significant force in numerically approximating solutions to differential equations that otherwise exhibit spurious, artificial oscillations. This is especially true for singularly perturbed convection-diffusion problems. In the presence of vanishing molecular diffusivity, MM- FEM may not suffice. The numerical method may exhibit under-diffusive properties and other methods need to be integrated into the classic Galerkin formulation. We implement the so-called streamline upwind Petrov-Galerkin method into the adaptive moving mesh method. In particular, we investigate the computation of so-called enhanced diffusivity for spatiotemporal periodic turbulent flows. We look at the case of Brownian tracer particles, i.e. negligible inertial effects. These types of passive advection-diffusion models are used in atmospheric models with turbulent diffusion, so-called Benard-advection cells, and porous materials, along with many other areas of science and engineering. As molecular diffusivity decreases, interior and boundary layers propagate along the streamlines. Once spurious oscillations are present, they too will propagate along the streamlines. Thus, specialized numerical methods are needed in order to resolve these areas of the domain where large gradients are present. The discrete maximum principle is also investigated for general anisotropic time dependent convection-diffusion equations. We obtain lower and upper bounds for time steps as well as obtain conditions on the mass and stiffness matrices resulting from the SUPG formulation. Our approach depends on two meshes and taking into consideration two diffusion matrices and applying metric intersection.
Finite Elements And Fast Iterative Solvers
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Author : Howard C. Elman
language : en
Publisher:
Release Date : 2014
Finite Elements And Fast Iterative Solvers written by Howard C. Elman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
This book describes why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory" provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.
Finite Elements And Fast Iterative Solvers
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Author : Howard Elman
language : en
Publisher: OUP Oxford
Release Date : 2014-06-19
Finite Elements And Fast Iterative Solvers written by Howard Elman and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-19 with Mathematics categories.
This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.
The Local Discontinuous Galerkin Method For Time Dependent Convection Diffusion Systems
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Author : Bernardo Cockburn
language : en
Publisher:
Release Date : 1997
The Local Discontinuous Galerkin Method For Time Dependent Convection Diffusion Systems written by Bernardo Cockburn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Stabilized Finite Element Methods Applied To Transient Convection Diffusion Reaction And Population Balance Equations
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Author : Naveed Ahmed
language : en
Publisher:
Release Date : 2011
Stabilized Finite Element Methods Applied To Transient Convection Diffusion Reaction And Population Balance Equations written by Naveed Ahmed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
An Assessment Of Solvers For Algebraically Stabilized Discretizations Of Convection Diffusion Reaction Equations
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Author : Abhinav Jha
language : en
Publisher:
Release Date : 2021
An Assessment Of Solvers For Algebraically Stabilized Discretizations Of Convection Diffusion Reaction Equations written by Abhinav Jha and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include flux-corrected transport schemes and monolithic limiters. We discretize in space using a continuous Galerkin method and P1 or Q1 finite elements. Time integration is performed using the Crank- Nicolson method or an explicit strong stability preserving Runge-Kutta method. Nonlinear systems are solved using a fixed-point iteration method, which requires solution of large linear systems at each iteration or time step. The great variety of options in the choice of discretization methods and solver components calls for a dedicated comparative study of existing approaches. To perform such a study, we define new 3D test problems for time dependent and stationary convection-diffusion-reaction equations. The results of our numerical experiments illustrate how the limiting technique, time discretization and solver impact on the overall performance.
Adaptive Streamline Diffusion Finite Element Methods For Time Dependent Convection Diffusion Problems
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Author : Kenneth Eriksson
language : en
Publisher:
Release Date : 1993
Adaptive Streamline Diffusion Finite Element Methods For Time Dependent Convection Diffusion Problems written by Kenneth Eriksson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Finite Element Methods For Convection Dominated Flows
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Author : Thomas J. R. Hughes
language : en
Publisher:
Release Date : 1979
Finite Element Methods For Convection Dominated Flows written by Thomas J. R. Hughes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.