Local Green's Function Techniques for the Solution of Heat Conduction and Incompressible Fluid Flow Problems
Horak, William Charles
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https://hdl.handle.net/2142/67795
Description
Title
Local Green's Function Techniques for the Solution of Heat Conduction and Incompressible Fluid Flow Problems
Author(s)
Horak, William Charles
Issue Date
1980
Department of Study
Nuclear Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Nuclear
Energy
Language
eng
Abstract
Coarse mesh numerical methods, based on the use of a local Green's function, are developed and applied to the numerical solution of heat conduction and incompressible fluid flow problems. In the solution of heat conduction problems, a local Green's function is used to develop a local integral equation for the pointwise temperature distribution within a computational volume element. These local integral equations are naturally coupled to those defined on adjacent elements through surface quantities, and thus retain the desirable property of nearest neighbor coupling. In the solution of incompressible fluid flow problems, a transverse integration technique is used to convert the partial differential equations governing fluid flow to a set of ordinary differential equations. This set of ordinary differential equations is then converted to a set of local integral equations through the use of a locally defined Green's tensor. This method yields directionally integrated velocities and pressures as opposed to the pointwise distributions which are obtained in the method for heat conduction.
Both techniques are applied to a series of test problems. Comparisons are then made between these techniques and the finite element method and the finite difference method. These comparisons show that the local Green's function techniques have substantial computational advantages in both accuracy and computing time as compared to these more standard methods.
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