Recent work on algorithms for solving thermal radiative transfer (TRT) problems has employed the high-order/low-order (HOLO) approach to gain significant acceleration and accuracy [1]. In [2] it was demonstrated that the predictor-corrector approach could obtain second-order accuracy in time for 1-D gray problems, however extra iterations were required in order to obtain second-order accuracy for multifrequency problems. In this talk, we will consider applying nonlinear solver methodology to this iteration in order to reduce computational costs. Traditionally, a Jacobian-free Newton-Krylov method has been used to solve the low-order system. We will consider alternative nonlinear solver technology for solving the low-order system, namely nonlinear Krylov acceleration (NKA) or Anderson Acceleration (AA).
[1] H. Park , D. A. Knoll , R. M. Rauenzahn , A. B. Wollaber and J. D. Densmore, A Consistent, Moment-Based, Multiscale Solution Approach for Thermal Radiative Transfer Problems, Transport Theory and Statistical Physics, 41:3-4, 284-303, 2012.
[2] H. Park, D. A. Knoll, R. M. Rauenzahn, C. K. Newman, J. D. Densmore, and A. B. Wollaber, An Efficient and Time Accurate Moment-Based Scale-Bridging Algorithm for Thermal Radiative Transfer Problems, SIAM J. Sci. Comp., vol 35-5, pp 18 - 41, 2013.