A multi-dimensional, moment-accelerated deterministic particle method for time-dependent, multi-frequency thermal radiative transfer problems

Abstract

Thermal Radiative Transfer (TRT) is the dominant energy transfer mechanism in high-energy density physics with applications in inertial confinement fusion and astrophysics. The stiff interactions between the material and radiation fields make TRT problems challenging to model. In this study, we propose a multi-dimensional extension of the deterministic particle (DP) method. The DP method combines aspects from both particle and deterministic methods. If the emission source is known a priori, and no physical scattering is present, the intensity of a particle can be integrated analytically. This introduces no statistical noise compared to Monte-Carlo methods, while maintaining the flexibility of particle methods. The method is closely related to the popular method of long characteristics. The combination of the DPmethod with a discretely-consistent, nonlinear, gray low-order system enables an efficient solution algorithm for multi-frequency TRT problems. We demonstrate with numerical examples that the use of a linear-source approximation based on spatial moments improves the behavior of our method in the thick diffusion limit significantly.

Unified Gas-Kinetic Particle Method for Frequency-dependent Radiation Transport

“…The contour plots of the UGKP solution for the radiation temperature and the material temperature at the simulation time 10ns are shown in Figure 8. The UGKP solutions are in rough agreement with the solutions presented in [8], verifying the accuracy of our method. Also, we observe a smooth material temperature profile, both at the lower wall and the lower side of the center block, which shows that unlike the deterministic particle method discussed in [8], the UGKP method does not suffer from ray effects.…”

“…The UGKP solutions are in rough agreement with the solutions presented in [8], verifying the accuracy of our method. Also, we observe a smooth material temperature profile, both at the lower wall and the lower side of the center block, which shows that unlike the deterministic particle method discussed in [8], the UGKP method does not suffer from ray effects. The UGKP solution for the radiation temperature also does not show ray effects [28], though the solution is noisier than the solutions presented in [8].…”

“…Though limited in scope, equation (2.1) is nevertheless useful in many applications and has been studied widely in literature [15,39,8]. We impose the initial condition…”

“…The final example we present is the hohlraum problem for the multi-frequency radiative transfer equation. The setup of this problem is the same as that studied in [8]. The layout of this problem is shown in Figure 7.…”

MOCMC: Method of Characteristics Moment Closure, a Numerical Method for Covariant Radiation Magnetohydrodynamics

“…As in VET approaches, we evolve the frequency-integrated (gray) moments of the specific intensity, closed by a solution of the full transport equation. However, instead of using a Monte Carlo or discrete ordinates method to obtain the transport solution, we adopt a Method of Characteristics approach (Askew 1972, Pandya & Adams 2009, Hammer et al 2019). In our method, the radiation is discretized into samples with different positions and directions, with each sample carrying an array of specific intensities discretized in frequency.…”