An Efficient Sweep-based Solver for the $S_{N}$ Equations on High-Order Meshes
This work addresses the need for efficient transport sweeps on high-order meshes, which is a bottleneck in neutron transport simulations.
The paper proposes a graph-based sweep algorithm for solving the S_N equations on high-order curved meshes, demonstrating its effectiveness on 2D and 3D meshes.
We propose a graph-based sweep algorithm for solving the steady state, mono-energetic discrete ordinates on meshes of high-order curved mesh elements. Our spatial discretization consists of arbitrarily high-order 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 2D and 3D meshes composed of high-order curved mesh elements.