A linear-discontinuous cut-cell discretization for the SN equations in R-Z geometry
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abstract
We have developed, implemented, and tested a new linear-discontinuous Galerkin cut-cell discretization for the Sn equations in R-Z geometry. This approach represents an alternative to homogenization in rectangular spatial cells containing a material discontinuity (referred to as mixed cells). A line is used to represent the boundary between the two materials in a mixed cell converting a rectangular mixed cell into two non-orthogonal, homogeneous sub-cells. The linear-discontinuous Galerkin spatial discretization is used on all of the rectangular cells as well as the non-orthogonal sub-cells. The method is described and computational results are presented that demonstrate second-order accuracy in multi-material problems with curved material interfaces. Additionally some evidence is provided that indicates that the cut-cell method is more computationally efficient than employing homogenization.
