An Approximate Solution to Radiative Transfer in Two-Dimensional Rectangular Enclosures

1997 ◽  
Vol 119 (4) ◽  
pp. 738-745 ◽  
Author(s):  
J. B. Pessoa-Filho ◽  
S. T. Thynell
Keyword(s):  
Radiative Transfer ◽  
Iterative Solution ◽  
Anisotropic Scattering ◽  
Solution Procedure ◽  
Two Dimensional ◽  
Scattering Media ◽  
Discontinuous Nature ◽  
Selection Of ◽  
Iterative Solution Procedure ◽  
Numerical Approaches

The application of a new approximate technique for treating radiative transfer in absorbing, emitting, anisotropically scattering media in two-dimensional rectangular enclosures is presented. In its development the discontinuous nature of the radiation intensity, stability of the iterative solution procedure, and selection of quadrature points have been addressed. As a result, false scattering is eliminated. The spatial discretization can be formed without considering the chosen discrete directions, permitting a complete compatibility with the discretization of the conservation equations of mass, momentum, and energy. The effects of anisotropic scattering, wall emission, and gray-diffuse surfaces are considered for comparison with results available in the literature. The computed numerical results are in excellent agreement with those obtained by other numerical approaches.

scholarly journals Self-updated four-node finite element using deep learning

2021 ◽  
Author(s):  
Jaeho Jung ◽  
Hyungmin Jun ◽  
Phill-Seung Lee
Keyword(s):  
Finite Element ◽  
Deep Learning ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Element Formulation ◽  
Zero Energy ◽  
Energy Mode ◽  
Bending Modes ◽  
Solution Accuracy ◽  
Iterative Solution Procedure

AbstractThis paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

An Iterative Solution for Anisotropic Radiative Transfer in a Slab

1979 ◽  
Vol 101 (4) ◽  
pp. 695-698 ◽  
Author(s):  
W. H. Sutton ◽  
M. N. O¨zis¸ik
Keyword(s):  
Radiative Transfer ◽  
Iterative Method ◽  
Integral Form ◽  
Iterative Solution ◽  
Single Scattering ◽  
Anisotropic Scattering ◽  
Initial Guess ◽  
Isotropic Scattering ◽  
Wide Range ◽  
Reflecting Boundaries

An iterative method is applied to solve the integral form of the equation of radiative transfer for the cases of isotropic scattering, highly forward, and backward anisotropic scattering in plane-parallel slab with reflecting boundaries. Calculations are performed for the values of single scattering albedo from ω = 0.7 to 1.0 where the convergence was previously reported to be poor. It is found that the convergence is significantly improved for most cases if the P-1 approximation of the spherical harmonics method is used for the initial guess. Results are presented for the hemispherical reflectivity and transmissivity of the slab over a wide range of parameters.

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