High-Order Finite Elements for Thermal Radiative Transfer on Curved Meshes

Terry Haut | 18-ERD-002

Project Overview

Our research team developed efficient and robust algorithms for simulating thermal radiative transfer using high-order finite elements on high-order (curved) meshes. The need for high-order thermal radiative transfer is motivated by Lawrence Livermore National Laboratory's next-generation high-order multi-physics codes, which solve the hydrodynamics equations on high-order (curved) meshes.

The Laboratory's current production deterministic transport solver can only solve the thermal radiative transfer equations on low-order (straight-edged) meshes. Coupling the high-order hydrodynamics to this low-order code entails an increase in the degrees of freedom by 4 times in two dimensions and 8 times in three dimensions. When the high-order mesh is very Lagrangian, the increase in degrees of freedom can be many orders of magnitude. In contrast, our project developed the methods to efficiently solve the high-order thermal radiative transfer equations on the native high-order mesh without an increase in degrees of freedom. Given thermal radiative transfer's enormous memory footprint and runtime within a multi-physics simulation, decreasing the number of degrees of freedom needed to represent the system can have a significant impact on the Laboratory's multi-physics simulation capabilities. In addition, solving the thermal radiative transfer equations on the hydrodynamics mesh avoids potential instability and physics degradation resulting from mappings.

Mission Impact

Developing a high-order, thermal radiative transfer capability is crucial for the Laboratory's ability to efficiently and robustly solve multi-physics problems with Livermore's next-generation hydrodynamics code, enabling critical missions at Livermore including stockpile stewardship and high-energy-density science. This project also supports the Laboratory's core competency in high-performance computing, simulation, and data science.


Publications, Presentations, and Patents

Haut, T. S., et al. 2018. "An Efficient Sweep-based Solver for the SN Equations on High-Order Meshes." 2018 ANS Annual Meeting, Philadelphia, PA, May 2018. LLNL-PROC-744912

——— 2019. "An Efficient Sweep-Based Solver for the SN Equations on High-Order Meshes." Nuclear Science and Engineering 193 (7): 746–759. LLNL-JRNL-759880

——— 2020. "DSA Preconditioning For DG Discretizations of SN Transport and High-Order Curved Meshes." SIAM Journal of Scientific Computing. LLNL-ABS-772019

Holec, M., et al. 2021. "Multi-Group Nonlinear Diffusion Synthetic Acceleration of Thermal Radiative Transfer." International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Raleigh, NC, October 2021. LLNL-ABS-813971

Yee, B. C., et al. 2020. "A Quadratic Programming Flux Fixup Method for High-Order Discretizations of SN Transport." Journal of Computational Physics. LLNL-PRES-787891