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An Efficient Sweep-Based Solver for the SN Equations on High-Order Meshes

T. S. Haut, P. G. Maginot, V. Z. Tomov, B. S. Southworth, T. A. Brunner, T. S. Bailey

Nuclear Science and Engineering / Volume 193 / Number 7 / July 2019 / Pages 746-759

Technical Paper /

Received:October 24, 2018
Accepted:December 19, 2018
Published:June 18, 2019

We propose a graph-based sweep algorithm for solving the steady-state, monoenergetic discrete ordinates on meshes of high-order (HO) curved mesh elements. Our spatial discretization consists of arbitrarily HO discontinuous Galerkin finite elements using upwinding at mesh element faces. To determine mesh element sweep ordering, we define a directed, weighted graph whose vertices correspond to mesh elements and whose edges correspond to mesh element upwind dependencies. This graph is made acyclic by removing select edges in a way that approximately minimizes the sum of removed edge weights. Once the set of removed edges is determined, transport sweeps are performed by lagging the upwind dependency associated with the removed edges. The proposed algorithm is tested on several two-dimensional and three-dimensional meshes composed of HO curved mesh elements.