Moment-based adaptive time integration for thermal radiation transport

TL;DR

This paper introduces a moment-based adaptive time integration framework for multifrequency thermal radiation transport, enhancing efficiency and accuracy by dynamically adjusting timesteps across different physical regimes.

Contribution

It generalizes semi-implicit-explicit IMEX schemes to multifrequency TRT and develops new embedded methods for adaptive, high-order low-order representations with minimal computational overhead.

Findings

Adaptive algorithm varies timestep over 4-5 orders of magnitude.

Successfully captures dynamics from streaming to diffusion regimes.

Demonstrates robustness and efficiency in test problems.

Abstract

In this paper we develop a framework for moment-based adaptive time integration of deterministic multifrequency thermal radiation transpot (TRT). We generalize our recent semi-implicit-explicit (IMEX) integration framework for gray TRT to multifrequency TRT, and also introduce a semi-implicit variation that facilitates higher-order integration of TRT, where each stage is implicit in all components except opacities. To appeal to the broad literature on adaptivity with Runge--Kutta methods, we derive new embedded methods for four asymptotic preserving IMEX Runge--Kutta schemes we have found to be robust in our previous work on TRT and radiation hydrodynamics. We then use a moment-based high-order-low-order representation of the transport equations. Due to the high dimensionality, memory is always a concern in simulating TRT. We form error estimates and adaptivity in time purely based on temperature and radiation energy, for a trivial overhead in computational cost and memory usage compared with the base second order integrators. We then test the adaptivity in time on the tophat and Larsen problem, demonstrating the ability of the adaptive algorithm to naturally vary the timestep across 4--5 orders of magnitude, ranging from the dynamical timescales of the streaming regime to the thick diffusion limit.