Moment-Based Acceleration of Monte Carlo Solution for Multifrequency Thermal Radiative Transfer Problems

Abstract

We have extended a Monte Carlo-based, moment-based acceleration algorithm to the solution of multifrequency thermal radiative transfer problems. This study focuses on two aspects. First, we consider stability/accuracy issues for a predictor-corrector time-stepping. It is demonstrated that with a consistent Planckian-weighted opacity the predictor-corrector algorithm can run stably with a larger time-step size compared to a fixed (or lagged) opacity case. With this advancement, consistency improves by about two orders of magnitude, while additional computational cost is kept minimal (< 10%).

We also extend the “asymptotic assistance” concept to multifrequency problems. This technique replaces the multifrequency Monte Carlo solution with an asymptotic solution of the O(ε) accurate solution of the equilibrium diffusion limit in optically thick regions. With this technique, the computational time is reduced about a factor of four in a one-dimensional problem. Furthermore, the solution with asymptotic assistance can become more accurate for a similar computational time because it enables a finer group structure in the high-order problem.

Keywords:

• thermal radiative transfer
• moment-based acceleration
• Monte Carlo method