An Unstructured Discontinuous Finite Element Method for Three-Dimensional Radiative Transfer in Participating Media

2004 ◽  
Author(s):  
X. Cui ◽  
B. Q. Li
Keyword(s):  
Finite Element ◽  
Radiative Transfer ◽  
Discontinuous Galerkin ◽  
Radiation Heat Transfer ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Participating Media ◽  
Discontinuous Finite Element ◽  
Computational Procedures ◽  
Discontinuous Finite Element Method

This paper presents a discontinuous finite element (or discontinuous Galerkin) computational methodology for the numerical solution of internal thermal radiation problems in three-dimensional geometries using unstructured meshes. Mathematical formulation and numerical details using the discontinuous Galerkin method for internal radiation heat transfer calculations are given. Computational procedures are presented. Numerical examples are given for radiative transfer in 3-D geometries filled with a non-scattering or scattering medium. The computed results are given and are compared well with analytical solutions whenever available or the data reported in references.

A Mixed-Mesh and New Angular Space Discretization Scheme of Discontinuous Finite Element Method for Three-Dimensional Radiative Transfer in Participating Media

2005 ◽  
Vol 127 (11) ◽  
pp. 1236-1244 ◽  
Author(s):  
X. Cui ◽  
B. Q. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Three Dimensional ◽  
Scattering Media ◽  
Participating Media ◽  
Discontinuous Finite Element ◽  
Space Discretization ◽  
Discontinuous Finite Element Method ◽  
Element Method

This paper presents a discontinuous finite element method for the numerical solution of internal thermal radiation problems in three-dimensional (3D) geometries using an unstructured mesh of mixed elements. Mathematical formulation, numerical implementation, and computational details are given. The different domain discretization methods are presented, and a new angular space discretization is also given. Numerical examples are presented for 3D radiative transfer in emitting, absorbing, and scattering media. Computed results compare well with analytical solutions whenever available. The localized formulation intrinsic in discontinuous finite elements is considered particularly useful for computational radiation heat transfer in participating media.

Discontinuous Finite Element Approach for Transient Radiative Transfer Equation

2007 ◽  
Vol 129 (8) ◽  
pp. 1069-1074 ◽  
Author(s):  
L. H. Liu ◽  
L. J. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Radiative Transfer ◽  
Scattering Media ◽  
Participating Media ◽  
Element Discretization ◽  
Discontinuous Finite Element ◽  
Transfer Problems ◽  
Discontinuous Finite Element Method ◽  
Element Method

A discontinuous finite element method based on the discrete ordinates equation is extended to solve transient radiative transfer problems in absorbing, emitting, and scattering media. The fully implicit scheme is used to discretize the transient term. Three numerical examples are studied to illustrate the performance of this discontinuous finite element method. The numerical results are compared to the other benchmark approximate solutions. By comparison, the results show that the discontinuous finite element method is efficient, accurate, and stable, and can be used for solving transient radiative transfer problems in participating media. Because the continuity at interelement boundaries is relaxed in discontinuous finite element discretization so that field variable is considered discontinuous across the element boundaries. This feature makes the discontinuous finite element method able to predict the correct propagation speed within medium and accurately capture the sharp drop in the incident radiation and the radiative heat flux at the penetration front.

A Discontinuous Finite Element Method for Non-Fourier Heat Conduction Problems

2003 ◽  
Author(s):  
X. Ai ◽  
B. Q. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Discontinuous Galerkin Finite Element ◽  
Discontinuous Finite Element ◽  
Fourier Heat Conduction ◽  
Computational Procedures ◽  
Element Method

A discontinuous Galerkin finite element method is presented for the solution of non-Fourier heat conduction problems that arise from the thermal processing of thin films using the ultra-short pulsed lasers. Mathematical formulation is described in detail and computational procedures are given. Numerical example are given and compare with available solutions where available. The numerical solutions exhibit strong wave behavior and reflection and interactions of thermal waves at the boundaries in multi-dimensions.

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