Implicit Monte Carlo with a Linear Discontinuous Finite Element Material Solution and Piecewise Non-Constant Opacity. Issue 1 (23rd February 2016)

• Record Type: Journal Article
• Authors: Wollaeger, Ryan T.; Wollaber, Allan B.; Urbatsch, Todd J.; Densmore, Jeffery D.
• Is Part Of: Journal of computational and theoretical transport. Volume 45:Issue 1/2(2016)
• Page Start: 123
• Page End: 157
• Publication Date: 2016-02-23
• Subjects: Implicit Monte Carlo (IMC) -- finite element -- teleportation error -- opacity; Transport theory -- Periodicals; Statistical physics -- Periodicals; Statistical physics; Transport theory; Periodicals; 530.138
• DOI: 10.1080/23324309.2016.1157491
• Languages: English
• ISSNs: 2332-4309

Abstract

ABSTRACT: The non-linear thermal radiative-transfer equations can be solved in various ways. One popular way is the Fleck and Cummings Implicit Monte Carlo (IMC) method. The IMC method was originally formulated with piecewise-constant material properties. For domains with a coarse spatial grid and large temperature gradients, an error known as numerical teleportation may cause artificially non-causal energy propagation and consequently an inaccurate material temperature. Source tilting is a technique to reduce teleportation error by constructing sub-spatial-cell (or sub-cell) emission profiles from which IMC particles are sampled. Several source tilting schemes exist, but some allow teleportation error to persist. We examine the effect of source tilting in problems with a temperature-dependent opacity. Within each cell, the opacity is evaluated continuously from a temperature profile implied by the source tilt. For IMC, this is a new approach to modeling the opacity. We find that applying both source tilting along with a source tilt-dependent opacity can introduce another dominant error that overly inhibits thermal wavefronts. We show that we can mitigate both teleportation and under-propagation errors if we discretize the temperature equation with a linear discontinuous (LD) trial space. Our method is for opacities ∼ 1/ T 3, but we formulate and test a slight extension for opacities ∼ 1/ T 3.5, where T is temperature. We find our method avoids errors that can be incurred by IMC with continuous source tilt constructions and piecewise-constant material temperature updates.