Multi-Frequency Implicit Semi-analog Monte-Carlo (ISMC) Radiative Transfer Solver in Two-Dimensions (without Teleportation)

TL;DR

This paper extends a semi-analog implicit Monte Carlo radiative transfer scheme to two-dimensional and multi-frequency problems, demonstrating it effectively eliminates teleportation errors and improves convergence in complex geometries.

Contribution

It introduces a multi-frequency extension of the ISMC scheme for 2D problems, validating its accuracy and error-free performance in complex geometries.

Findings

Eliminates teleportation errors in 2D radiative transfer simulations.

Shows improved convergence over classic IMC schemes.

Validates the scheme's effectiveness in multi-frequency and multi-dimensional benchmarks.

Abstract

We study the multi-dimensional radiative transfer phenomena using the ISMC scheme, in both gray and multi-frequency problems. Implicit Monte-Carlo (IMC) schemes have been in use for five decades. The basic algorithm yields teleportation errors, where photons propagate faster than the correct heat front velocity. Recently [Po\"ette and Valentin, J. Comp. Phys., 412, 109405 (2020)], a new implicit scheme based on the semi-analog scheme was presented and tested in several one-dimensional gray problems. In this scheme, the material energy of the cell is carried by material-particles, and the photons are produced only from existing material particles. As a result, the teleportation errors vanish, due to the infinite discrete spatial accuracy of the scheme. We examine the validity of the new scheme in two-dimensional problems, both in Cartesian and Cylindrical geometries. Additionally, we introduce an expansion of the new scheme for multi-frequency problems. We show that the ISMC scheme presents excellent results without teleportation errors in a large number of benchmarks, especially against the slow classic IMC convergence.