Solution-dependent predictor-corrector flux mapping algorithm for discrete ordinates calculation on multilevel discontinuous grids

Abstract The block-based and cell-based discontinuous Cartesian grid techniques have been one effective method to increase the geometric description accuracy for neutronics calculation codes using the discrete ordinates method. The reliability of the transport calculation on multilevel discontinuous grids depends on the accuracy and robustness of the spatial mapping algorithm for passing angular flux between neighboring meshes. In this work, we present a predictor-corrector algorithm together with multiple mapping schemes for the zeroth-order spatial discretization methods. This algorithm uses the shape and balance factors to predict the applicability of different mapping schemes, and an optimal method can be selected from the non-negative linear and nonlinear mapping techniques. We test this algorithm on three simple problems, where the average mapping errors, region-averaged flux and local flux are compared against the references of fine standard grids. The numerical results show that our method can control the mapping errors in an acceptable range of approximately 10% for optically thick grids twice as large as the mean free path. The accuracy degradation of spatial discretization method caused by the mapping errors can be mitigated to a great extent in our algorithm.