Download or read book Oscillatory Behavior of Finite Difference Methods for the Solution of the Two Dimensional Transient Heat diffusion Equation written by Joseph E. Cuthrell (CAPT, USAF.) and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Oscillatory Behavior of Finite Difference Methods for the Solution of the Two Dimensional Transient Heat Diffusion Equation written by Joseph E. Cuthrell and published by . This book was released on 1986 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two dimensional transient heat (diffusion) equation with Dirichlet boundary conditions was solved using the Dufort-Frankel, Saul'ev, and, Exponential (Power-law) finite fidderence schemes. All methods were investigated for oscillatory behavior and comparisons of accuracy made. To predict the time step at which oscillatory behavior would occur, the coefficient, matrix, and probabilistic methods of stability analysis were utilized. At time steps greater than the square of the mesh divided by the thermal diffusivity, oscillatory solutions were apparent in both the Dufort-Frankel and Saul'ev schems. The exponential method, as predicted, did not oscillate for any size time step. Although the exponential scheme was the most accurate at large time steps, the solution still contained enough error to be unusable in many engineering applications. At small time steps, all methods were more accurate than the fully implicit formulation. The exponential method was found to be the slowest computationally. The Saul'ev scheme proved to be the fastest while still achieving the required degree of accuracy.
Download or read book Predicting Oscillatory Finite Difference Solutions to the Heat Equation A Comparative Study of the Coefficient and Matrix Methods written by Thomas M. Dipp and published by . This book was released on 1987 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis compared the coefficient method with the full matrix method for predicting stability and oscillatory behavior of Finite Difference Methods, FDMS, used in solving the one and two dimensional transient heat (diffusion) equation with Dirichlet boundary conditions. Five FDMs were used: the fully implicit, fully explicit, DuFort-Frankel, Crank-Nicolson, and Peaceman-Rachford ADI. Analytically, the Pade' method was found to be equivalent to the matrix method in predicting stability and oscillations. The matrix method was shown to be more severe than the coefficient method in predicting both stable and non-oscillatory step size constraints. Also, the matrix method, while mathematically more rigorous, proved to be more difficult to derive and analyze, possibly limiting its usefulness. Ultimately, it was found that the coefficient method's predictions could be derived from the matrix method for two-level FDMs. Numerically, all methods were solved repeatedly and the results investigated for oscillatory behavior and maximum errors in the h-k, or space and time step, domain.
Download or read book Accuracy of Finite Difference Methods for Solution of the Transient Heat Conduction Diffusion Equation written by Thomas Sidney Chivers (Jr) and published by . This book was released on 1983 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-dimensional transient heat conduction (diffusion) equation was solved using the fully explicit, fully implicit, Crank-Nicholson implicit, and Peaceman-Rachford alternating direction implicit (ADI) finite difference methods (FDMTHs). The general stability condition for the same FDMTHs was derived by the matrix, coefficient, and a probabilistic method. The matrix, coefficient, and probabilistic methods were found to be equivalent in that each lead to the same general stability condition. Oscillatory behavior of the fully explicit FDMTH was as predicted by the general stability condition. Though the Crank-Nicholson implicit and the Peaceman-Rachford ADI FDMTHs were expected to be unconditionally stable, unstable oscillations were observed for large sizes of time step. For large numbers of time steps and sizes of time steps for which all FDMTHs considered are stable, the Crank-Nicholson implicit FDMTH is the more accurate. (Author).
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Masters Theses in the Pure and Applied Sciences written by Wade H. Shafer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Masters Theses in the Pure and Applied Sciences was first conceived, published, and disseminated by the Center for Information and Numerical Data Analysis and Synthesis (CINDAS) * at Purdue University in 1957, starting its coverage of theses with the academic year 1955. Beginning with Volume 13, the printing and dissemination phases of the activity were transferred to University Microfilms/Xerox of Ann Arbor, Michigan, with the thougtit that such an arrangement would be more beneficial to the academic and general scientific and technical community. After five years of this joint undertaking we had concluded that it was in the interest of all con cerned if the printing and distribution of the volumes were handled by an interna tional publishing house to assure improved service and broader dissemination. Hence, starting with Volume 18, Masters Theses in the Pure and Applied Sciences has been disseminated on a worldwide basis by Plenum Publishing Cor poration of New York, and in the same year the coverage was broadened to include Canadian universities. All back issues can also be ordered from Plenum. We have reported in Volume 31 (thesis year 1986) a total of 11 ,480 theses titles trom 24 Canadian and 182 United States universities. We are sure that this broader base tor these titles reported will greatly enhance the value ot this important annual reterence work. While Volume 31 reports theses submitted in 1986, on occasion, certain univer sities do re port theses submitted in previousyears but not reported at the time.
Download or read book 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 published by . This book was released on 1985 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book A Comparison of Finite Difference Methods for the Solution of the Transient Heat Conduction Equation in Inhomogeneous Media written by Kenneth William Blevins and published by . This book was released on 1982 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The transient heat conduction equation is solved for inhomogeneous media using the Explicit, Pure-Implicit, Crank-Nicolson and Douglas finite-difference methods, and the numerical solutions are investigated with respect to accuracy and stability. The inherent discontinuity between the initial and boundary conditions is accounted for by mesh refinement. For the two versions of the problem for which the four numerical methods are investigated, all four methods are found to be of equivalent accuracy for small values of the Fourier Modulus. While the Pure-Implicit, Crank-Nicolson and Douglas methods are unconditionally stable, the Crank-Nicolson and Douglas methods are very inaccurate at large values of the Fourier Modulus due to oscillatory behavior. (Author).
Download or read book Government Reports Annual Index written by and published by . This book was released on 1987 with total page 1064 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sections 1-2. Keyword Index.--Section 3. Personal author index.--Section 4. Corporate author index.-- Section 5. Contract/grant number index, NTIS order/report number index 1-E.--Section 6. NTIS order/report number index F-Z.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1974 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Annual Index Keyword A L written by and published by . This book was released on 1987 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1975 with total page 1550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reviews in Numerical Analysis 1980 86 written by and published by . This book was released on 1987 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: These five volumes bring together a wealth of bibliographic information in the area of numerical analysis. Containing over 17,600 reviews of articles, books, and conference proceedings, these volumes represent all the numerical analysis entries that appeared in Mathematical Reviews between 1980 and 1986. Author and key indexes appear at the end of volume 5.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1982 with total page 1696 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Modelling in Science and Technology written by Xavier J.R. Avula and published by Elsevier. This book was released on 2014-05-09 with total page 1023 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling in Science and Technology: The Fourth International Conference covers the proceedings of the Fourth International Conference by the same title, held at the Swiss Federal Institute of Technology, Zurich, Switzerland on August 15-17, 1983. Mathematical modeling is a powerful tool to solve many complex problems presented by scientific and technological developments. This book is organized into 20 parts encompassing 180 chapters. The first parts present the basic principles, methodology, systems theory, parameter estimation, system identification, and optimization of mathematical modeling. The succeeding parts discuss the features of stochastic and numerical modeling and simulation languages. Considerable parts deal with the application areas of mathematical modeling, such as in chemical engineering, solid and fluid mechanics, water resources, medicine, economics, transportation, and industry. The last parts tackle the application of mathematical modeling in student management and other academic cases. This book will prove useful to researchers in various science and technology fields.
Download or read book Finite Difference Methods in Heat Transfer written by M. Necati Özişik and published by CRC Press. This book was released on 2017-07-20 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book ICCS19 19th International Conference on Composite Structures written by Antonio J.M. Ferreira and published by Società Editrice Esculapio. This book was released on 2016-08-01 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, it is quite easy to see various applications of fibrous composites, functionally graded materials, laminated composite, nano-structured reinforcement, morphing composites, in many engineering fields, such as aerospace, mechanical, naval and civil engineering. The increase in the use of composite structures in different engineering practices justify the present international meeting where researches from every part of the globe can share and discuss the recent advancements regarding the use of standard structural components within advanced applications such as buckling, vibrations, repair, reinforcements, concrete, composite laminated materials and more recent metamaterials. For this reason, the establishment of this 19th edition of International Conference on Composite Structures has appeared appropriate to continue what has been begun during the previous editions. ICCS wants to be an occasion for many researchers from each part of the globe to meet and discuss about the recent advancements regarding the use of composite structures, sandwich panels, nanotechnology, bio-composites, delamination and fracture, experimental methods, manufacturing and other countless topics that have filled many sessions during this conference. As a proof of this event, which has taken place in Porto (Portugal), selected plenary and keynote lectures have been collected in the present book.
