Solving the Neutron Transport Equation for Microreactor Modeling Using Unstructured Meshes and Exascale Computing Architectures

Abstract

The Microreactor Exascale eZ CALculation (MEZCAL) tool has been developed to accurately and efficiently solve the neutron transport equation in general, unstructured meshes to support the design and modeling of microreactors. MEZCAL solves the self-adjoint angular flux form of the neutron transport equation using the finite element method. As the neutron transport equation is computationally expensive to solve, MEZCAL is designed to efficiently use exascale computing architectures, with an emphasis on graphics processing unit computing. To leverage existing tools, MEZCAL is built using the MFEM library and uses solvers from HYPRE, PETSc, and SLEPc. Verification of the neutron transport solver in MEZCAL is demonstrated with the solution to a one-dimensional cylindrical problem that has a semi-analytic solution. After verification, a realistic microreactor based on the MARVEL microreactor design is modeled using MEZCAL. Spatial and angular refinement results are presented for a two-dimensional model of the MARVEL microreactor, and the eigenvalue is converged to approximately 60 pcm. This convergence required a very fine mesh and more than 3.76 Billion Degrees Of Freedom (BDOF). Preliminary results are also presented for a three-dimensional model of the MARVEL microreactor. Finally, a weak scaling study is performed to investigate how the methods in MEZCAL will scale for larger problems with the next generation of exascale computing architectures.

Keywords:

• Neutron transport
• unstructured mesh
• finite element method
• Exascale Computing Project
• microreactor

Acknowledgments

The authors thank Michael Smith of Argonne National Laboratory for his helpful insight into second-order neutron transport methods on unstructured meshes, Tom Evans and Steven Hamilton of ORNL for their help investigating the solver methodologies in MEZCAL, and Jean-Sylvain Camier of LLNL for his help improving the performance of MFEM for solving the SAAF equations.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

^a See https://mfem.org.

Additional information

Funding

This research was supported by the ECP (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy’s Office of Science and the National Nuclear Security Administration.This research used resources of the Oak Ridge Leadership Computing Facility at ORNL, which is supported by the Office of Science of the U.S. Department of Energy under contract no. DE-AC05-00OR22725.