Local Green's Function Techniques for the Solution of Heat Conduction and Incompressible Fluid Flow Problems

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Nuclear Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Horak, William Charles

• Engineering, Nuclear
• Energy

Language dc:language

eng

Identifier

(UMI)AAI8108544

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/67795