On The Numerical Solution Of Convection Dominated Convection Diffusion Problems

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Analytical And Numerical Methods For Convection Dominated And Singularly Perturbed Problems

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Author : Lubin Vulkov
language : en
Publisher: Nova Publishers
Release Date : 2000

Analytical And Numerical Methods For Convection Dominated And Singularly Perturbed Problems written by Lubin Vulkov and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

This volume is the Proceedings of the Workshop on Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems, which took place in Lozenetz, Bulgaria, 27-31 August 1998. The workshop attracted about 50 participants from 12 countries. The volume includes 13 invited lectures and 19 contributed papers presented at the workshop and thus gives an overview of the latest developments in both the theory and applications of advanced numerical methods to problems having boundary and interior layers. There was an emphasis on experiences from the numerical analysis of such problems and on theoretical developments. The aim of the workshop was to provide an opportunity for scientists from the East and the West, who develop robust methods for singularly perturbed and related problems and also who apply these methods to real-life problems, to discuss recent achievements in this area and to exchange ideas with a view of possible research co-operation.

Convection Diffusion Problems

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Author : Martin Stynes
language : en
Publisher:
Release Date : 2018

Convection Diffusion Problems written by Martin Stynes and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.

Many physical problems involve diffusive and convective (transport) processes. When diffusion dominates convection, standard numerical methods work satisfactorily. But when convection dominates diffusion, the standard methods become unstable, and special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book. After discussing at length the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and design numerical methods that are particularly suited to this c.

On The Numerical Solution Of Convection Dominated Convection Diffusion Problems

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Author : Owe Axelsson
language : en
Publisher:
Release Date : 1983

On The Numerical Solution Of Convection Dominated Convection Diffusion Problems written by Owe Axelsson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.

Welsh H Devitt

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Author :
language : en
Publisher:
Release Date :

Welsh H Devitt written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

The folder may include clippings, announcements, small exhibition catalogs, and other ephemeral items.

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.

Adaptive Defect Correction Methods For Convection Dominated Convection Diffusion Problems

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Author : V. Ervin
language : en
Publisher:
Release Date : 1998

Adaptive Defect Correction Methods For Convection Dominated Convection Diffusion Problems written by V. Ervin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

On Slope Limiting And Deep Learning Techniques For The Numerical Solution To Convection Dominated Convection Diffusion Problems

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Author : Derk Frerichs-Mihov
language : en
Publisher:
Release Date : 2023

On Slope Limiting And Deep Learning Techniques For The Numerical Solution To Convection Dominated Convection Diffusion Problems written by Derk Frerichs-Mihov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

Numerical Implementation Of A Mixed Finite Element Formulation For Convection Diffusion Problems

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Author : Ivan Padilla Montero
language : en
Publisher:
Release Date : 2014

Numerical Implementation Of A Mixed Finite Element Formulation For Convection Diffusion Problems written by Ivan Padilla Montero and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.

This document aims to the numerical solution of convection-diffusion problems in a fluid dynamics context by means of the Finite Element Method (FEM). It describes the classical finite element solution of convection-diffusion problems and presents the implementation and validation of a new formulation for improving the accuracy of the standard approach. On first place, the importance and need of numerical convection-diffusion models for Computational Fluid Dynamics (CFD) is emphasized, highlighting the similarities between the convection-diffusion equation and the governing equations of fluid dynamics for incompressible flow. The basic aspects of the finite element method needed for the standard solution of general convection-diffusion problems are then explained and applied to the steady state case. These include the weak formulation of the initial boundary value problem for the convection-diffusion equation and the posterior finite element spatial discretization of the weak form based on the Galerkin method. After their application to the steady transport equation a simple numerical test is performed to show that the standard Galerkin formulation is not stable in convection-dominated situations, and the need for stabilization is justified. Attention is then focused on the analysis of the truncation error provided by the Galerkin formulation, leading to the derivation of a classical stabilization technique based on the addition of artificial diffusion along the flow direction, the so-called streamline-upwind (SU) schemes. Next, a more general and modern stabilization approach known as the Sub-Grid-Scale (SGS) method is described, showing that SU schemes are a particular case of it. Taking into account all the concepts explained, a new mixed finite element formulation for convection-diffusion problems is presented. It has been proposed by Dr. Riccardo Rossi, a researcher from the International Center for Numerical Methods in Engineering (CIMNE), and consists on extending the original convection-diffusion equation to a system in mixed form in which both the unknown variable and its gradient are computed simultaneously, leading to an increase in the convergence rate of the solution. The formulation, which had not been tested before, is then implemented and validated by means of a multiphysics finite element software called \texttt{Kratos}. Eventually, the obtained results are analyzed, showing the improved performance of the mixed formulation in pure diffusion problems.

Moving Space Time Finite Element Methods For Convection Diffusion Problems

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Author : Rafael Brigham Neves Ferreira Santos
language : en
Publisher:
Release Date : 1991

Moving Space Time Finite Element Methods For Convection Diffusion Problems written by Rafael Brigham Neves Ferreira Santos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.

Discontinuous Petrov Galerkin Methods With Optimal Test Spaces For Convection Dominated Convection Diffusion Equations

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Author : Dirk Broersen
language : en
Publisher:
Release Date : 2016

Discontinuous Petrov Galerkin Methods With Optimal Test Spaces For Convection Dominated Convection Diffusion Equations written by Dirk Broersen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.

"In this thesis, Discontinuous Petrov-Galerkin (DPG) finite element methods are developed for convection-diffusion equations. In particular, this thesis focuses on the use of optimal test spaces. A convection-diffusion equation is a singularly perturbed problem. That is, the nature of the problem changes when the diffusion term vanishes, which makes it challenging to solve numerically for small diffusion values, i.e. when convection dominates. Standard finite element methods give very unsatisfactory results, producing approximations that exhibit spurious oscillations and other nonphysical behavior. Recently, a class of finite element methods has been developed, in which optimal test spaces are used. These spaces guarantee that one gets the best approximation from the trial space in which the solution is sought. The methods are examples of least-squares methods, with the special property that one can choose the norm in which the residual is minimized. This freedom of choice allows us to control the norm in which the best approximation is obtained. The new approach in this thesis is that the variational formulation associated with the convection-diffusion problem also gives a well-posed variational formulation of the limit convection problem if the diffusion term vanishes. This is necessary in order to retain stability, and to make sure that the computational cost does not grow, when the diffusion term decreases. Special attention is paid to the transport problem which, besides being the limit problem for vanishing diffusion, also has other applications. A new method is introduced that outperforms existing methods in convergence rates, but also in reducing the smearing of discontinuities of solutions. The theory developed in this thesis is illustrated by various numerical results."--Samenvatting auteur.