Scalable implicit solvers with dynamic mesh adaptation for a relativistic drift-kinetic Fokker–Planck–Boltzmann model

In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. We develop a new scalable fully implicit solver utilizing fin...

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Bibliographic Details
Published in:Journal of computational physics Vol. 507; p. 112954
Main Authors: Rudi, Johann, Heldman, Max, Constantinescu, Emil M., Tang, Qi, Tang, Xian-Zhu
Format: Journal Article
Language:English
Published: United States Elsevier Inc 15-06-2024
Elsevier
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Summary:In this work we consider a relativistic drift-kinetic model for runaway electrons along with a Fokker–Planck operator for small-angle Coulomb collisions, a radiation damping operator, and a secondary knock-on (Boltzmann) collision source. We develop a new scalable fully implicit solver utilizing finite volume and conservative finite difference schemes and dynamic mesh adaptivity. A new data management framework in the PETSc library based on the p4est library is developed to enable simulations with dynamic adaptive mesh refinement (AMR), distributed memory parallelization, and dynamic load balancing of computational work. This framework and the runaway electron solver building on the framework are able to dynamically capture both bulk Maxwellian at the low-energy region and a runaway tail at the high-energy region. To effectively capture features via the AMR algorithm, a new AMR indicator prediction strategy is proposed that is performed alongside the implicit time evolution of the solution. This strategy is complemented by the introduction of computationally cheap feature-based AMR indicators that are analyzed theoretically. Numerical results quantify the advantages of the prediction strategy in better capturing features compared with nonpredictive strategies; and we demonstrate trade-offs regarding computational costs. The robustness with respect to model parameters, algorithmic scalability, and parallel scalability are demonstrated through several benchmark problems including manufactured solutions and solutions of different physics models. We focus on demonstrating the advantages of using implicit time stepping and AMR for runaway electron simulations.
Bibliography:89233218CNA000001; AC02-05CH11231; FES-ERCAP0021219; AC02–06CH11357
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
LA-UR-23-22498
USDOE National Nuclear Security Administration (NNSA)
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2024.112954