Spatial approximation of the radiation transport equation using a subgrid-scale finite element method

被引:27
|
作者
Avila, Matias [1 ]
Codina, Ramon [1 ]
Principe, Javier [1 ]
机构
[1] Univ Politecn Cataluna, ES-08034 Barcelona, Spain
关键词
Radiative transfer equation; Stabilized finite element methods; SUPG; Orthogonal subscales; Discrete ordinates method; ORTHOGONAL SUBSCALES; FORMULATION; CONVECTION; FLOWS;
D O I
10.1016/j.cma.2010.11.003
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper we present stabilized finite element methods to discretize in space the monochromatic radiation transport equation. These methods are based on the decomposition of the unknowns into resolvable and subgrid scales, with an approximation for the latter that yields a problem to be solved for the former. This approach allows us to design the algorithmic parameters on which the method depends, which we do here when the discrete ordinates method is used for the directional approximation. We concentrate on two stabilized methods, namely, the classical SUPG technique and the orthogonal subscale stabilization. A numerical analysis of the spatial approximation for both formulations is performed, which shows that they have a similar behavior: they are both stable and optimally convergent in the same mesh-dependent norm. A comparison with the behavior of the Galerkin method, for which a non-standard numerical analysis is done, is also presented. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码:425 / 438
页数:14
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