An Implicit Numerical Method For Solving The Two Dimensional Heat Equation
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An Implicit Numerical Method For Solving The Two Dimensional Heat Equation
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Author : George A. Baker
language : en
Publisher:
Release Date : 1958
An Implicit Numerical Method For Solving The Two Dimensional Heat Equation written by George A. Baker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Heat equation categories.
Oscillatory Solutions Of The Peaceman Rachford Alternating Direction Implicit Method And A Comparison Of Methods For The Solution Of The Two Dimensional Heat Diffusion Equation
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Author : R. F. Kropf
language : en
Publisher:
Release Date : 1985
Oscillatory Solutions Of The Peaceman Rachford Alternating Direction Implicit Method And A Comparison Of Methods For The Solution Of The Two Dimensional Heat Diffusion Equation written by R. F. Kropf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
The two dimensional heat diffusion equation with Dirichlet boundary conditions was solved using the fully explicit, fully implicit, Crank-Nicolson implicit, and Peaceman-Rachford alternating direction implicit (ADI) methods. Comparisons of accuracy and time requirements were made. The possibility that the ADI method has stable oscillatory solutions with large time steps was investigated. Results of computations revealed that the ADI has stable oscillations for large time steps, in some cases producing large enough errors to render the solution unusable. Time steps greater than twice the square of the mesh spacing divided by the thermal diffusivity must be used with care. For small time steps, the Crank-Nicolson and ADI methods were the most accurate, and the ADI was the fastest method. The fully implicit method was the most accurate at large time steps, but the ADI, with a smaller time step to reduce the oscillatory error, was still the fastest method to reach a solution with the desired degree of accuracy. Additional keywords: theses; numerical analysis; finite difference theory; conduction (heat transfer); partial differential equations; stability.(Author).
A Comparison Of Implicit Numerical Methods For Solving The Transient Spherical Diffusion Equation
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Author :
language : en
Publisher:
Release Date : 1977
A Comparison Of Implicit Numerical Methods For Solving The Transient Spherical Diffusion Equation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.
Finite Difference Methods In Heat Transfer
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Author : M. Necati Özişik
language : en
Publisher: CRC Press
Release Date : 2017-07-12
Finite Difference Methods In Heat Transfer written by M. Necati Özişik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Science categories.
Finite Difference Methods in Heat Transfer presents a clear, step-by-step delineation of finite difference methods for solving engineering problems governed by ordinary and partial differential equations, with emphasis on heat transfer applications. The finite difference techniques presented apply to the numerical solution of problems governed by similar differential equations encountered in many other fields. Fundamental concepts are introduced in an easy-to-follow manner. Representative examples illustrate the application of a variety of powerful and widely used finite difference techniques. The physical situations considered include the steady state and transient heat conduction, phase-change involving melting and solidification, steady and transient forced convection inside ducts, free convection over a flat plate, hyperbolic heat conduction, nonlinear diffusion, numerical grid generation techniques, and hybrid numerical-analytic solutions.
Finite Difference Methods In Heat Transfer
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Author : M. Necati Özişik
language : en
Publisher: CRC Press
Release Date : 2017-07-20
Finite Difference Methods In Heat Transfer written by M. Necati Özişik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-20 with Science categories.
Finite Difference Methods in Heat Transfer, Second Edition focuses on finite difference methods and their application to the solution of heat transfer problems. Such methods are based on the discretization of governing equations, initial and boundary conditions, which then replace a continuous partial differential problem by a system of algebraic equations. Finite difference methods are a versatile tool for scientists and for engineers. This updated book serves university students taking graduate-level coursework in heat transfer, as well as being an important reference for researchers and engineering. Features Provides a self-contained approach in finite difference methods for students and professionals Covers the use of finite difference methods in convective, conductive, and radiative heat transfer Presents numerical solution techniques to elliptic, parabolic, and hyperbolic problems Includes hybrid analytical–numerical approaches
Application Of The Hughes Liu Algorithm To The Two Dimensional Heat Equation
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Author : David S. Malkus
language : en
Publisher:
Release Date : 1982
Application Of The Hughes Liu Algorithm To The Two Dimensional Heat Equation written by David S. Malkus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Heat categories.
Numerical Methods For Solving Linear Systems And Applications To Elliptic Difference Equations
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Author : Clarence Edgar Lee
language : en
Publisher:
Release Date : 1959
Numerical Methods For Solving Linear Systems And Applications To Elliptic Difference Equations written by Clarence Edgar Lee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Differential equations, Elliptic categories.
Iterative numerical methods for solving independent, simultaneous, inhomogeneous linear equations are surveyed. Application of the methods to elliptic difference equations as arise in neutron diffasion, heat conduction, and potential problems is discussed.
Solving Direct And Inverse Heat Conduction Problems
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Author : Jan Taler
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-16
Solving Direct And Inverse Heat Conduction Problems written by Jan Taler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-16 with Science categories.
This book presents a solution for direct and inverse heat conduction problems, discussing the theoretical basis for the heat transfer process and presenting selected theoretical and numerical problems in the form of exercises with solutions. The book covers one-, two- and three dimensional problems which are solved by using exact and approximate analytical methods and numerical methods. An accompanying CD-Rom includes computational solutions of the examples and extensive FORTRAN code.
Solution Of Two Dimensional Heat Problems Using The Alternating Direction Method
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Author : Frederick James Leipold
language : en
Publisher:
Release Date : 1967
Solution Of Two Dimensional Heat Problems Using The Alternating Direction Method written by Frederick James Leipold and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Finite difference approximations to the one-dimensional heat equation Ut = Uxx are used to introduce explicit and implicit difference equations. The convergence and stability of these equations is discussed and those concepts are used to show the restrictions imposed on explicit equations. The Implicit Alternating Direction (IAD) method is introduced as a means for solution of the two-dimensional heat equation. Although the IAD method in its basic form is applicable only to parabolic problems it is possible by slight modification to apply the method to elliptic problems. Two examples are used to illustrate the use of the IAD method for solution of parabolic and elliptic equations for a rectangular region. These examples include a work requirement comparision with other difference methods. A third example is given to show the applicability of the IAD method to non-rectangular regions, in this case a parabolic problem over a circular region. Results of these examples show that the IAD method is a convenient and accurate method when applied to both parabolic and elliptic partial differential equations and suggest applicability to a wide range of problems. (Author).
Solution Of Two Dimensional Heat Problems Using The Alternating Direction Method
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Author :
language : en
Publisher:
Release Date : 1967
Solution Of Two Dimensional Heat Problems Using The Alternating Direction Method written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Finite difference approximations to the one-dimensional heat equation Ut = Uxx are used to introduce explicit and implicit difference equations. The convergence and stability of these equations is discussed and those concepts are used to show the restrictions imposed on explicit equations. The Implicit Alternating Direction (IAD) method is introduced as a means for solution of the two-dimensional heat equation. Although the IAD method in its basic form is applicable only to parabolic problems it is possible by slight modification to apply the method to elliptic problems. Two examples are used to illustrate the use of the IAD method for solution of parabolic and elliptic equations for a rectangular region. These examples include a work requirement comparision with other difference methods. A third example is given to show the applicability of the IAD method to non-rectangular regions, in this case a parabolic problem over a circular region. Results of these examples show that the IAD method is a convenient and accurate method when applied to both parabolic and elliptic partial differential equations and suggest applicability to a wide range of problems. (Author).