Nuclear Science and Engineering / Volume 155 / Number 2 / February 2007 / Pages 264-275
Technical Paper / Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications
This paper describes a new technique for determining the pin power in heterogeneous three-dimensional calculations. It is based on a domain decomposition with overlapping subdomains and a component mode synthesis (CMS) technique for the global flux determination. Local basis functions are used to span a discrete space that allows fundamental global mode approximation through a Galerkin technique. Two approaches are given to obtain these local basis functions. In the first one (the CMS method), the first few spatial eigenfunctions are computed on each subdomain, using periodic boundary conditions. In the second one (factorized CMS method), only the fundamental mode is computed, and we use a factorization principle for the flux in order to replace the higher-order eigenmodes. These different local spatial functions are extended to the global domain by defining them as zero outside the subdomain. These methods are well fitted for heterogeneous core calculations because the spatial interface modes are taken into account in the domain decomposition. Although these methods could be applied to higher-order angular approximations - particularly easily to an SPN approximation - the numerical results we provide are obtained using a diffusion model. We show the methods' accuracy for reactor cores loaded with uranium dioxide and mixed oxide assemblies, for which standard reconstruction techniques are known to perform poorly. Furthermore, we show that our methods are highly and easily parallelizable.