For over 30 years, the Implicit Monte Carlo (IMC) method has been used to
solve challenging problems in thermal radiative transfer. These problems are typically optically thick and di ffusive, as a consequence of the high degree of "pseudo-scattering" introduced to model the absorption and reemission of photons from a tightly-coupled, radiating material. IMC has several well-known features which could be improved: a) it can be prohibitively computationally expensive, b) it introduces statistical noise into the material and radiation temperatures, which
may be problematic in multiphysics simulations, and c) under certain conditions,
solutions can be unphysical and numerically unstable, in that they violate a maximum principle - IMC calculated temperatures can be greater than the maximum
temperature used to drive the problem.
We have developed a variant of IMC called "iterative thermal emission" IMC,
which is designed to be more stable than IMC and have a reduced parameter
space in which the maximum principle is violated. ITE IMC is a more implicit
method version of the IMC in that it uses the information obtained from a series
of IMC photon histories to improve the estimate for the end of time-step material
temperature during a time step. A better estimate of the end of time-step material
temperature allows for a more implicit estimate of other temperature dependent
quantities: opacity, heat capacity, Fleck Factor (probability that a photon absorbed during a time step is not reemitted) and the Planckian emission source.
The ITE IMC method is developed by using Taylor series expansions in material
temperature in a similar manner as the IMC method. It can be implemented in a
Monte Carlo computer code by running photon histories for several sub-steps in a
given time-step and combining the resulting data in a thoughtful way. The ITE IMC
method is then validated against 0-D and 1-D analytic solutions and compared
with traditional IMC. We perform an in finite medium stability analysis of ITE
IMC and show that it is slightly more numerically stable than traditional IMC.
We find that significantly larger time-steps can be used with ITE IMC without
violating the maximum principle, especially in problems with non-linear material
properties. We also compare ITE IMC to IMC on a two-dimensional, orthogonal
mesh, x-y geometry problem called the "crooked pipe" and show that our new
method reproduces the IMC solution. The ITE IMC method yields results with
larger variances; however, the accuracy of the solution is improved in comparison
with IMC, for a given choice of spatial and temporal grid. / Graduation date: 2013
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/33215 |
| Date | 01 June 2012 |
| Creators | Long, Alex R. |
| Contributors | Palmer, Todd S. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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