Solution of the 2-D steady-state radiative transfer equation in participating media with specular reflections using SUPG and DG finite elements

被引：15

作者：

Le Hardy, D. ^{[1
]}

Favennec, Y. ^{[1
]}

Rousseau, B. ^{[1
]}

机构：

[1] Univ Nantes, LTN, UMR 6607, CNRS, F-44035 Nantes, France

来源：

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER | 2016年 / 179卷

关键词：

Specular reflection; Discontinuous Galerkin; Streamline-upwind Petrov-Galerkin; Jacobi; Gauss-Seidel; Successive over-relaxation; HEAT-TRANSFER; OPTICAL TOMOGRAPHY; FREQUENCY-DOMAIN; FORMULATION; RECONSTRUCTION; APPROXIMATION; SOLVER;

D O I：

10.1016/j.jqsrt.2016.03.027

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

The 2D radiative transfer equation coupled with specular reflection boundary conditions is solved using finite element schemes. Both Discontinuous Galerkin and Streamline Upwind Petrov-Galerkin variational formulations are fully developed. These two schemes are validated step-by-step for all involved operators (transport, scattering, reflection) using analytical formulations. Numerical comparisons of the two schemes, in terms of convergence rate, reveal that the quadratic SUPG scheme proves efficient for solving such problems. This comparison constitutes the main issue of the paper. Moreover, the solution process is accelerated using block SOR-type iterative methods, for which the determination of the optimal parameter is found in a very cheap way. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：149 / 164

页数：16

共 22 条

[1] An improved regularized fundamental solution to the 2-D steady-state Stokes equation
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[2] Discontinuous finite element solution of 2-D radiative transfer with and without axisymmetry
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Li, BQ
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Girdinio, P
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[9] 2-D Exact Analytical Method for Steady-State Heat Transfer Prediction in Rotating Electrical Machines
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[10] COUPLED RADIATIVE AND CONDUCTIVE HEAT-TRANSFER IN A TWO-DIMENSIONAL RECTANGULAR ENCLOSURE WITH GRAY PARTICIPATING MEDIA USING FINITE-ELEMENTS
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