A Non-Linear Space-Angle Multi-Grid Acceleration for the Method of Characteristics in Unstructured Meshes

Abstract : A new space-angle multi-grid technique has been developed to accelerate the free inner transport iterations based upon the Method of Characteristics (MOC). We present a two-level scheme it consists of a fine level on which the MOC transport calculation is performed and a more coarsely discretised phase space in which a low-order problem is solved as an acceleration step. A flux-volume homogenisation technique is employed to define the coarse-level cross sections. This entails the non-linearity 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 homogenised grid. A coarser angular representation is used within a MOC-like framework. We employ discontinuity factors to reconstruct the scalar incoming and outgoing currents on each region of the coarse discretisation. The solution of the above-mentioned 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 our method, numerical tests for given benchmarks geometries have been performed. Results are discussed.
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Gabriele Grassi. A Non-Linear Space-Angle Multi-Grid Acceleration for the Method of Characteristics in Unstructured Meshes. Nuclear Science and Engineering, Academic Press, 2006, 155 (2), pp.208-222. ⟨10.13182/NSE07-A2657⟩. ⟨cea-02356008⟩

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