A Nonlinear Space-Angle Multigrid Acceleration for the Method of Characteristics in Unstructured Meshes

A new space-angle multigrid technique has been developed to accelerate the free inner transport iterations based upon the method of characteristics (MOC). We present a two-level scheme that consists of a fine level on which the MOC transport calculation is performed and a more coarsely discretized phase-space in which a low-order problem is solved as an acceleration step. A flux-volume homogenization technique is employed to define the coarse-level cross sections. This entails the nonlinearity of the scheme. Restriction and prolongation operators are defined between the two levels. After each fine transport iteration, a low-order transport problem is iteratively solved on the homogenized grid. A coarser angular representation is used within an MOC-like framework. Discontinuity factors are employed to reconstruct the scalar incoming and outgoing currents on each region of the coarse discretization. The solution of the aforementioned low-order problem is used to correct the angular moments of the flux resulting from the previous free transport sweep. A complete description of the low-order operator and of the grid-to-grid transfer operators is given. A further application of the method to the acceleration of outer transport iterations is also presented. In order to test the effectiveness of this method, numerical tests for given benchmark geometries have been performed. Results are discussed.