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

Abstract

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.

Keywords:

• Transport
• discrete ordinates
• high order
• sweep, unstructured

Acknowledgments

The work of T. S. Haut, P. G. Maginot, V. Z. Tomov, T. A. Brunner, and T. S. Bailey was performed under the auspices of the U.S. Department of Energy (DOE) by Lawrence Livermore National Laboratory (LLNL) under contract number DE-AC52-07NA27344 and supported by the LLNL Laboratory Directed Research and Development Program under project number 18-ERD-002.

The work of B. S. Southworth was performed under the auspices of DOE by LLNL under contract number DE-AC52-07NA27344 and supported by subcontract numbers B614452 and B627942 of Lawrence Livermore National Security, LLC. Additional funding for B. S. Southworth was provided under grant number DE-NA0002376 (National Nuclear Security Administration).

This work has been reviewed for unlimited public release as LLNL-JRNL-759880-DRAFT.