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Accession Number:
ADA056508
Title:
An Investigation of the Numerical Methods of Finite Differences and Finite Elements for Digital Computer Solution of the Transient Heat Conduction (Diffusion) Equation Using Optimum Implicit Formulations.
Descriptive Note:
Master's thesis,
Corporate Author:
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
Report Date:
1978-03-01
Pagination or Media Count:
328.0
Abstract:
The transient heat conduction equation, with Dirichlet and Neumann boundary conditions, is solved by the methods of finite-differences and finite-elements, and the numerical solutions are investigated with respect to accuracy and stability. A general six point finite-difference expression is used for which there exists a high order accurate modification. The finite-element method used is based on a stationary variational principle. Several methods for treating accuracy and convergence problems which result from a discontinuity in the initial condition are investigated. The Crank-Nicolson method is a special case of both the finite-difference and finite-element methods. The finite-difference version of the Crank-Nicolson method is shown to be more accurate than the finite-element version, especially when a discontinuity exists between the initial condition and the boundary conditions. The high order accurate schemes for both finite-differences and finite-elements are shown to be equivalent for the case of linear elements. Some of the results suggest the possibility of finding a finite-element scheme which is highly accurate in a mean square sensr over the entire solution domain. Author
Distribution Statement:
APPROVED FOR PUBLIC RELEASE
