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 (Poëtte and Valentin, 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.
Bibliographical noteFunding Information:
We would like to thank Gaël Poëtte for taking the time to read and comment on this paper, as well as fruitful discussions, and for amazing presentation on the ISMC algorithm in the 26th International Conference on Transport Theory (ICTT-26) in Sep. 2019, Paris.
© 2021 Elsevier Inc.
- Boltzmann equation
- Monte-Carlo schemes
- Radiative transfer