THREE-DIMENSIONAL PHONON TRANSPORT SIMULATION FOR NANO/MICROSTRUCTURED MATERIALS

2008 ◽  
Vol 07 (02n03) ◽  
pp. 103-112 ◽  
Author(s):  
A. SAKURAI ◽  
S. MARUYAMA ◽  
A. KOMIYA ◽  
K. MIYAZAKI
Keyword(s):  
Radiative Transfer ◽  
Heat Transport ◽  
Characteristic Length ◽  
Transport Phenomena ◽  
Three Dimensional ◽  
Phonon Transport ◽  
Discrete Ordinates ◽  
Complex Geometries ◽  
Transport Mechanisms ◽  
Length Scales

The Discrete Ordinates Radiation Element Method (DOREM), which is radiative transfer code, is applied for solving phonon transport of nano/microscale materials. The DOREM allows phonon simulation with multi-dimensional complex geometries. The objective of this study is to apply the DOREM to the nano/microstructured materials. It is confirmed that significant changes of the heat transport phenomena with different characteristic length scales and geometries are observed. This study also discusses further variations for understanding of heat transport mechanisms.

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.

Solution of the Radiative Transfer Equation in Three-Dimensional Participating Media Using a Hybrid Discrete Ordinates: Spherical Harmonics Method

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Maathangi Sankar ◽  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Spherical Harmonics ◽  
Hybrid Method ◽  
Transfer Equation ◽  
Large Range ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Medium Component

In this article, a new hybrid solution to the radiative transfer equation (RTE) is proposed. Following the modified differential approximation (MDA), the radiation intensity is first split into two components: a “wall” component, and a “medium” component. Traditionally, the wall component is determined using a viewfactor-based surface-to-surface exchange formulation, while the medium component is determined by invoking the first-order spherical harmonics (P1) approximation. Recent studies have shown that although the MDA approach is accurate over a large range of optical thicknesses, it is prohibitive for complex three-dimensional geometry with obstructions, both from a computational efficiency as well as memory standpoint. The inefficiency stems from the use of the viewfactor-based approach for determination of the wall-emitted component. In this work, instead, the wall component is determined directly using the control angle discrete ordinates method (CADOM). The new hybrid method was validated for both two-dimensional (2D) and three-dimensional (3D) geometries against benchmark Monte Carlo results for gray media in which the optical thickness was varied over a large range. In all cases, the accuracy of the hybrid method was found to be within a few percent of Monte Carlo results, and comparable to the solutions of the RTE obtained directly using CADOM. Finally, the new hybrid method was explored for 3D nongray media in the presence of reflecting walls and various scattering albedos. As a noteworthy advantage, irrespective of the conditions used, it was always found to be computationally more efficient than standalone CADOM and up to 15 times more efficient than standalone CADOM for optically thick media with strong scattering.

scholarly journals Development of a GOES-R Advanced Baseline Imager Solar Channel Radiance Simulator for Ice Clouds

2013 ◽  
Vol 52 (4) ◽  
pp. 872-888 ◽  
Author(s):  
Shouguo Ding ◽  
Ping Yang ◽  
Bryan A. Baum ◽  
Andrew Heidinger ◽  
Thomas Greenwald
Keyword(s):  
Radiative Transfer ◽  
Spectral Response ◽  
Three Dimensional ◽  
Gas Absorption ◽  
Radiative Transfer Model ◽  
Discrete Ordinates ◽  
Transfer Model ◽  
Water Vapor Absorption ◽  
Ice Clouds ◽  
Ice Cloud

AbstractThis paper describes the development of an ice cloud radiance simulator for the anticipated Geostationary Operational Environmental Satellite R (GOES-R) Advanced Baseline Imager (ABI) solar channels. The simulator is based on the discrete ordinates radiative transfer (DISORT) model. A set of correlated k-distribution (CKD) models is developed for the ABI solar channels to account for atmospheric trace gas absorption. The CKD models are based on the ABI spectral response functions and also consider when multiple gases have overlapping absorption. The related errors of the transmittance profile are estimated on the basis of the exact line-by-line results, and it is found that errors in transmittance are less than 0.2% for all but one of the ABI solar channels. The exception is for the 1.378-μm channel, centered near a strong water vapor absorption band, for which the errors are less than 2%. For ice clouds, the band-averaged bulk-scattering properties for each ABI [and corresponding Moderate Resolution Imaging Spectroradiometer (MODIS)] solar channel are derived using an updated single-scattering property database of both smooth and severely roughened ice particles, which include droxtals, hexagonal plates, hexagonal hollow and solid columns, three-dimensional hollow and solid bullet rosettes, and several types of aggregates. The comparison shows close agreement between the radiance simulator and the benchmark model, the line-by-line radiative transfer model (LBLRTM)+DISORT model. The radiances of the ABI and corresponding MODIS measurements are compared. The results show that the radiance differences between the ABI and MODIS channels under ice cloud conditions are likely due to the different band-averaged imaginary indices of refraction.

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

2009 ◽  
Vol 132 (2) ◽  
Author(s):  
Gisela Widmer
Keyword(s):  
Finite Elements ◽  
Linear System ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Degrees Of Freedom ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Five Dimensions ◽  
Dimensional Domain

The stationary monochromatic radiative transfer equation is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For nonscattering radiative transfer, sparse finite elements [2007, “Sparse Finite Elements for Non-Scattering Radiative Transfer in Diffuse Regimes,” ICHMT Fifth International Symposium of Radiative Transfer, Bodrum, Turkey; 2008, “Sparse Adaptive Finite Elements for Radiative Transfer,” J. Comput. Phys., 227(12), pp. 6071–6105] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared with 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 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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