In benchmark solutions the performance of radiation algorithms is normally studied
by comparisons with the Monte Carlo method (MCM), since the latter is the only technique that can
return both a solution and an estimate of its uncertainty. In recent work, we have developed sharp
error bounds for the surface irradiation in the discrete transfer method (DTM). This paper explores
the idea that the study of sequences of DTM results with systematic angular refinement can provide
an alternative basis for error estimation. We present detailed comparisons of the DTM and MCM
with two of Hsu and Farmer’s benchmarks for a cubic enclosure with nonhomogeneous extinction,
and add some additional problems. We find consistently good agreement between our error theory
and observed convergence trends. Careful analysis of our findings also reveals excellent agreement
between highly resolved DTM and MCM surface heat flux estimates. Since the DTM economically
provides an accurate, deterministic solution and error bounds, our work highlights its potential as an
alternate benchmarking tool.
History
School
Mechanical, Electrical and Manufacturing Engineering
Citation
VERSTEEG, H.K., HENSON, J.C. and MALALASEKERA, W., 2001. A comparison of convergence and error estimates for the Monte Carlo and discrete transfer methods. IN: Menguc, M.P. and Selcuk, C.N. (eds.), ICHMT Third International Symposium on Radiative Transfer, Antalya, Turkey, 17th-22nd June, pp. 92-101
This article is closed access. The conference proceedings are available from Begell House: http://www.begellhouse.com/references/1bb331655c289a0a,4d127640467b6621,79bbb77356de52c1.html