Elementary Solutions and Analytical Discrete-Ordinates for Radiative Transfer

Author(s):  
Laurent Gosse
Author(s):  
Gisela Widmer

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.


2000 ◽  
Author(s):  
M. Sakami ◽  
K. Mitra ◽  
P.-F. Hsu

Abstract This research work deals with the analysis of transient radiative transfer in one-dimensional scattering medium. The time-dependant discrete ordinates method was used with an upwind monotonic scheme: the piecewise parabolic scheme. This scheme was chosen over a total variation diminishing version of the Lax-Wendroff scheme. These schemes were originally developed to solve Eulerian advection problem in hydrodynamics. The capability of these schemes to handle sharp discontinuity in a propagating electromagnetic wave front was compared. The accuracy and the efficiency of the discrete ordinates method associated with the piecewise parabolic advection scheme were studied. Comparisons with Monte Carlo and integral formulation methods show the accuracy and the efficiency of this proposed method. Parametric study for optically thin and thick medium, different albedos and phase functions is then made in the unsteady state zone.


2013 ◽  
Vol 70 (3) ◽  
pp. 794-808 ◽  
Author(s):  
Feng Zhang ◽  
Zhongping Shen ◽  
Jiangnan Li ◽  
Xiuji Zhou ◽  
Leiming Ma

Abstract Although single-layer solutions have been obtained for the δ-four-stream discrete ordinates method (DOM) in radiative transfer, a four-stream doubling–adding method (4DA) is lacking, which enables us to calculate the radiative transfer through a vertically inhomogeneous atmosphere with multiple layers. In this work, based on the Chandrasekhar invariance principle, an analytical method of δ-4DA is proposed. When applying δ-4DA to an idealized medium with specified optical properties, the reflection, transmission, and absorption are the same if the medium is treated as either a single layer or dividing it into multiple layers. This indicates that δ-4DA is able to solve the multilayer connection properly in a radiative transfer process. In addition, the δ-4DA method has been systematically compared with the δ-two-stream doubling–adding method (δ-2DA) in the solar spectrum. For a realistic atmospheric profile with gaseous transmission considered, it is found that the accuracy of δ-4DA is superior to that of δ-2DA in most of cases, especially for the cloudy sky. The relative errors of δ-4DA are generally less than 1% in both the heating rate and flux, while the relative errors of δ-2DA can be as high as 6%.


2008 ◽  
Vol 07 (02n03) ◽  
pp. 103-112 ◽  
Author(s):  
A. SAKURAI ◽  
S. MARUYAMA ◽  
A. KOMIYA ◽  
K. MIYAZAKI

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.


2005 ◽  
Vol 38 (22) ◽  
pp. 4053-4065 ◽  
Author(s):  
Mohamed Bouaoun ◽  
Hatem Elloumi ◽  
Kamel Charrada ◽  
Mounir Ben El Hadj Rhouma ◽  
Mongi Stambouli

2020 ◽  
Author(s):  
Patrick Irwin ◽  
Simon Calcutt ◽  
Jack Dobinson ◽  
Juan Alday ◽  
Arjuna James ◽  
...  

<p>The NASA Ice Giants Pre-Decadal Survey Mission Report (2017) recommended the high scientific importance of sending a mission with an orbiter and a probe to one of the Ice Giants, with preferential launch dates in the 2029-2034 timeframe. Such a mission concept is equally well supported by European scientists and Mousis et al (P&SS, 155, 12, 2018) give compelling scientific rationales for the exploration of these worlds with missions carrying in situ probes.</p> <p>In this presentation we will outline the conceptual design of the Advanced Ice Giants Net Flux Radiometer (IG-NFR) instrument, currently being designed by NASA Goddard Space Flight Center to make in situ observations of the upward and downward fluxes of solar and thermal radiation in the atmospheres of Uranus and Neptune. The IG-NFR is designed to: (i) accommodate seven filter bandpass channels in the spectral range 0.25-300 µm (ii) measure up and down radiation flux in a clear unobstructed 10° FOV for each channel; (iii) use thermopile detectors that can measure a change of flux of at least 0.5 W/m<sup>2</sup> per decade of pressure; (iv) view five distinct view angles (±80°, ±45°, and 0°); (v) predict the detector response with changing  temperature environment; (vi) use application-specific integrated circuit technology for the thermopile detector readout; (vii) be able to integrate radiance for 2s or longer, and (vii) sample each view angle including calibration targets. The IG-NFR system noise equivalent power at 298 K is 73 pW in a 1 Hz electrical bandwidth.</p> <p>We present initial simulations of the anticipated observations using two radiative transfer and retrieval tools, NEMESIS (Irwin et al., JQSRT, 109, 1136, 2008) and the Planetary Spectrum Generator (PSG, Villanueva et al., 2017, https://psg.gsfc.nasa.gov). For the NEMESIS modelling the radiative fluxes observable at varying pressure levels were calculated with a Matrix-Operator plane-parallel multiple-scattering model, using between 5 and 21 zenith angle quadrature points and up to 38 Fourier components for the azimuth decomposition. We also employed PSG to further validate our flux estimates, providing an important benchmarking and comparison test between both models. PSG solves the scattering radiative transfer employing the discrete ordinates method, with the scattering phase function described in terms of an expansion in terms of Legendre Polynomials. Molecular cross-sections are solved via the correlated-k method employing the latest HITRAN database (Gordon et al., 2017), which are completed with the latest collision-induced-absorption (CIA, Karman et al., 2019), and UV/optical cross-sections from the MPI database (Keller-Rudek et al., 2013). For the nominal case the Sun was assumed to be at an altitude of 10° above the horizon. The internal radiance field was calculated at each internal level for a standard reference Uranus atmosphere (e.g., Irwin et al., 2017) with the addition of a single cloud layer, based at 3 bar and composed of particles with a mean radius of 1.0 µm (and size variance 0.1) and assumed complex refractive index of 1.4 + 0.001i at all wavelengths. The opacity and fractional scale height of this cloud were fitted in both models to match the combined near-infrared observations of HST/WFC3, IRTF/SpeX and VLT/SINFONI analyzed by Irwin et al. (2017). The internal radiance fields were calculated from 0.4 to 300 µm using this atmospheric model.</p> <p>We will show how these simulations are being used to guide the choice of spectral filter bandwidths and centres to optimize the scientific return of such an instrument. We will show that observations with such an instrument can be used to constrain effectively the radiation energy budget in the atmospheres of the Ice Giants and can also be used to determine the pressures of cloud and haze layers and broadly constrain particle size. Such modelling also allows us to simulate the visible appearance of Uranus’ atmosphere during a descent and to perform detailed validations of the simulations by comparing the two radiative transfer models (NEMESIS and PSG).</p>


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