Numerical solutions to the Poisson equation in media surrounding multiple arbitrarily shaped bodies

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] The dissertation describes a general, efficient, and parallelized approach to solving the Poisson equation in the volume surrounding multiple, arbitrarily shaped bodies. Green's function method is applied and a quadrature technique approximates the resulting integrals from which singularities are subtracted-yielding a large set of equations. The solution is implemented with a general, parallelized, functional program; the input of which are parametric equations defining the surfaces of multiple, arbitrarily shaped bodies and a number of possible boundary conditions. Taking full advantage of available computational resources, the method can be very efficient. The utility, generality, and efficiency of the approach is demonstrated by application to various problems in electrostatics and diffusion; both to validate its accuracy, and in specific cases, to elucidate the phenomena of interest. As the motivation for this research stems from aerosol science and specifically, the critical need for accurate source term modeling for gas-cooled, graphite-moderated nuclear reactors, discussion of the results is done in light of these topics. However, the approach is applicable to any phenomena governed by the Poisson equation-these phenomena are numerous and have implications in nearly all areas of science and engineering.