A Methodology to Solve 2D and Axisymmetric Radiative Transfer Problems Using a General 3D Solver

2013 ◽  
Vol 135 (12) ◽  
Author(s):  
P. Kumar ◽  
V. Eswaran
Keyword(s):  
Radiative Transfer ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Special Treatment ◽  
Dimensional Problem ◽  
Scattering Media ◽  
Special Cases ◽  
Axisymmetric Problems ◽  
Transfer Problems ◽  
Benchmark Solutions

A method to solve the radiative transfer equation (RTE) for absorbing-emitting and/or scattering media for 2-D and axisymmetric geometries using a general 3-D solver with a special treatment of the boundary condition in the third direction is presented. It allows a choice of first- or second- order schemes and can be used with non-orthogonal hexahedral grids for complex domains. Two-dimensional or axisymmetric problems are treated as different special cases of a three-dimensional problem. The method is tested on axisymmetric problems with absorbing-emitting and/or scattering media and on a 2D planar problem with a transparent medium and validated by comparisons with benchmark solutions.

Axisymmetric Solutions in Elastostatics and Elastic Wave Propagation by Ascent Methods

1984 ◽  
Vol 51 (3) ◽  
pp. 630-635
Author(s):  
F. R. Norwood
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Three Dimensional ◽  
Elastic Wave Propagation ◽  
Laplacian Operator ◽  
Dimensional Problem ◽  
Axisymmetric Problems ◽  
Axisymmetric Solutions ◽  
Transfer Problems ◽  
Theoretical Results

In the present paper a method of ascent for axisymmetric problems is developed. It is shown that, for problems where the vector or scalar Laplacian operator specifies the space behavior of the potential functions, the three-dimensional axisymmetric problems may be solved by operating on the solution to an associated two-dimensional problem. Hence, the theoretical results presented here may be applied to heat transfer problems, to problems in elastostatics, and to elastic wave propagation problems.

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

2009 ◽  
Author(s):  
Gisela Widmer
Keyword(s):  
Linear System ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Degrees Of Freedom ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Five Dimensions ◽  
Computational Costs ◽  
Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

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