Boundary element method for neutron diffusion equation with chebyshev's equal weight integration formula

Abstract

To solve the neutron diffusion equation in two-dimensional rectangular geometry, the boundary element method (BEM) with Chebyshev`s equal weight integration formula is applied. Although BEM has been developed for mechanical analyses, it can be also used to solve the neutron diffusion equation. In this study, BEM is applied to solve neutron diffusion equation for the system with/without multiplying source. If there are multiplying sources in the system, the domain is divided into several subregions. In that case, appropriate weighting for the discrete internal fluxes in each subregion is necessary. Both Chebyshev`s equal weight integration formula and Gaussian non-equal weight integration formula are used to determine which method is more appropriate for the problems with source. A system of homogenious single region square with one energy group is chosen for test. The results of calculations show that Chebyshev`s equal weight integration formula is better than Gauss` non-equal weight integration formula for the integration of the discrete internal fluxes. Also, another test is performed to compare the currents on the boundary of core in the IAEA-2D problems with L-shaped/inverted L-shaped boundary and equivalent circular boundary. The comparison shows that there is not much difference in the currents of the two cases.