The Quasidiffusion Method for Transport Problems on Unstructured Meshes

arbitrary quadrilaterals;characteristic methods;subcell balance;cartesian;radiation;particle transport

Wieselquist, William Adam ; Semyon V. Tsynkov, Committee Member,Robin P. Gardner, Committee Member,Paul J. Turinsky, Committee Member,Yousry Y. Azmy, Committee Member,Dmitriy Y. Anistratov, Committee Chair,Wieselquist, William Adam ; Semyon V. Tsynkov ; Committee Member ; Robin P. Gardner ; Committee Member ; Paul J. Turinsky ; Committee Member ; Yousry Y. Azmy ; Committee Member ; Dmitriy Y. Anistratov ; Committee Chair

University:North Carolina State University

关键词: arbitrary quadrilaterals;    characteristic methods;    subcell balance;    cartesian;    radiation;    particle transport;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/3291/etd.pdf?sequence=1&isAllowed=y

美国|英语

来源: null

【 摘 要 】

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 fromradiation 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 theefficient 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 insecond-order form resembles convection-diffusion with a diffusion tensor, with thedifference that the LOQD equations contain extra cross-derivative terms.Our finite volume (FV) discretization of the LOQD equations is compared with threeLOQD 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 issecond-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 proposedand 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 methodmay easily be extended to arbitrary meshes in 3D Cartesian geometry.