Reduced Memory Space-Time Discretization Schemes for High-Energy-Density Physics

ORAL

Abstract

This talk presents implicit space-time discretization methods with reduced memory for approximation of the radiative transfer equation (RTE) and their application in thermal radiative transfer and radiation hydrodynamics simulations. The reduced-memory methods (RMMs) are formulated for the RTE discretized with the backward-Euler time integration scheme and the bilinear-discontinuous (BLD) finite element method in space. The BLD scheme requires a spatial degree of freedom at each corner of a cell. The RMMs store only the cell-average value of the specific intensity within each cell between timesteps, reducing the persistent memory allocation requirement to just one value per cell. At the new time step, the RMMs utilize spatial reconstruction schemes to approximate the numerical solution at each spatial degree of freedom of the BLD scheme. We developed the RMMs with different spatial reconstruction techniques: zero-slope approximation, linear and bilinear interpolation functions. We analyzed convergence in space and time of the developed RMMs using a set of tests with manufactured solutions. Numerical results for thermal radiative transfer and radiation hydrodynamics problems in 2D Cartesian and axisymmetric (r-z) geometries will be presented to demonstrate performance of the proposed RMMs.

*The work of the first author (RCP) was supported under an University Nuclear Leadership Program Graduate Fellowship. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the Department of Energy Office of Nuclear Energy. The work of the second and fourth authors (DYA and JEM) was funded by the Joint Center for Resilient National Security of Los Alamos National Laboratory and Texas A\&M University System. The work of the third and fifth authors (JSW and JMC) was supported by the U.S. Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001). LA-UR-25-27441

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Publication: R. Paye, D. Y. Anistratov, J. E. Morel, and J. S. Warsa. "Reduced-Memory Methods for Linear Discontinuous Discretization of the Time-Dependent Boltzmann Transport Equation." In Proceedings of The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M&C2023, p. 9. Niagara Falls, Ontario, Canada (August 13-17 2023).

R. C. Paye. Reduced Memory Discretization Methods for the Time-Dependent Boltzmann Transport Equation. M.S. thesis, North Carolina State University, Raleigh, NC (2024). Available at https://www.lib.ncsu.edu/resolver/1840.20/42079.

R. C. Paye, J. M. Coale, J. S. Warsa, D. Y. Anistratov, C. A. Woodsford, and J. E. Morel. "Reduced Memory Discretization Scheme for Time-Dependent Thermal Radiative Transfer Problems." In Proceedings of The International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M&C2025, p. 9. Denver, Colorado, USA (April 27-30, 2025)

Presenters

  • Rylan C Paye

    • North Carolina State University

Authors

  • Rylan C Paye

    • North Carolina State University

  • Dmitiry Y Anistratov

    • North Carolina State University

  • James S Warsa

    • Los Alamos National Laboratory

  • Jim E Morel

    • Texas A&M University

  • Joseph M Coale

    • Los Alamos National Laboratory