The Quasidiffusion Method for Transport Problems on Unstructured Meshes
No Thumbnail Available
Files
Date
2009-02-11
Authors
Journal Title
Series/Report No.
Journal ISSN
Volume Title
Publisher
Abstract
In this work, we develop a quasidiffusion (QD) method for solving radiation
transport problems on unstructured quadrilateral meshes in 2D Cartesian geometry,
for example hanging-node meshes from adaptive mesh refinement
(AMR) applications or skewed quadrilateral meshes from
radiation hydrodynamics with Lagrangian meshing.
The main result of the work is a new low-order quasidiffusion (LOQD) discretization
on arbitrary quadrilaterals and a strategy for the
efficient iterative solution which uses Krylov methods and
incomplete LU factorization (ILU) preconditioning.
The LOQD equations are a non-symmetric set of first-order PDEs that in
second-order form resembles convection-diffusion with a diffusion tensor, with the
difference that the LOQD equations contain extra cross-derivative terms.
Our finite volume (FV) discretization of the LOQD equations is compared with three
LOQD discretizations from literature.
We then present a conservative, short characteristics
discretization based on subcell balances (SCSB) that uses polynomial exponential moments
to achieve robust behavior in various limits (e.g. small cells and voids) and is
second-order accurate in space.
A linear representation of the isotropic component of the
scattering source based on face-average and cell-average scalar fluxes is also proposed
and shown to be effective in some problems.
In numerical tests, our QD method with linear scattering source representation shows
some advantages compared to other transport methods. We conclude with avenues
for future research and note that this QD method
may easily be extended to arbitrary meshes in 3D Cartesian geometry.
Description
Keywords
arbitrary quadrilaterals, characteristic methods, subcell balance, cartesian, radiation, particle transport
Citation
Degree
PhD
Discipline
Nuclear Engineering