A coarse-mesh nodal diffusion method based on response matrix considerations

Abstract

The overall objective of this thesis is to develop an economical computational method for multidimensional transient analysis of nuclear power reactors. Specifically, the application of nodal methods based on the multigroup diffusion theory approximation to reactors composed of regular arrays of large homogeneous (or homogenized) zones was investigated. A nodal scheme is formulated using the response matrix approach as a conceptual basis. Solutions of equivalent sets of coupled one dimensional problems are used to treat the local multidimensional response problems. Polynomial expansions in conjunction with weighted residual procedures are employed to obtain approximate solutions of the one-dimensional problems. A linear set of nodal equations expressed in terms of nodal average fluxes and interface average partial currents is obtained. Applications to two-dimensional few-group, static and transient problems demonstrate that the nodal scheme can be an order of magnitude more computationally efficient than conventional finite difference methods.