A spectral-galerkin coarse-mesh approach to solving the two-dimensional multigroup diffusion equations

Based on the spectral-Galer kin method and domain decomposition method, a novel coarse-mesh model (SGCM) has been developed for solving the two-dimensional multigroup neutron diffusion equations. In this study, the reactor domain is decomposed into subdomains (or coarse meshes). Within any individual subdomain, the neutron diffusion equations with the Robin boundary condition are first reformulated in a weak (variational) form, which is then solved by means of the Legendre-spectral method. As for interfacial coupling between subdomains, it is relaxed by an interfacial relation of discontinuity between incoming and outgoing partial currents if discontinuity factors are considered on subdomain interfaces. The resulting discretized system with block-sparsestructured matrix is solved by the block successive over-relaxation method (BSOR). The method was examined with two well-known PWR benchmark problems and a realistic reactor core. It turns out that the method can generate not only extremely accurate assemblywise average quantities, but also satisfactory smooth homogenized fluxes, and heterogeneous reconstructed pinwise fluxes, which results from the fact that all the formulations are derived in a variational form in which the admissible solution space consists of higher-order Legendre polynomials