INTERACTIVE RENDERING OF MULTIPLE SCATTERING IN PARTICIPATING MEDIA USING SEPARABLE PHASE FUNCTION

AbstractThe Dawn spacecraft orbited Asteroid (4) Vesta for a year, and returned disk-resolved images and spectra covering visible and near-infrared wavelengths at scales as high as 20 m/pix. The visible geometric albedo of Vesta is ~ 0.36. The disk-integrated phase function of Vesta in the visible wavelengths derived from Dawn approach data, previous ground-based observations, and Rosetta OSIRIS observations is consistent with an IAU H-G phase law with H=3.2 mag and G=0.28. Hapke's modeling yields a disk-averaged single-scattering albedo of 0.50, an asymmetry factor of -0.25, and a roughness parameter of ~20 deg at 700 nm wavelength. Vesta's surface displays the largest albedo variations observed so far on asteroids, ranging from ~0.10 to ~0.76 in geometric albedo in the visible wavelengths. The phase function of Vesta displays obvious systematic variations with respect to wavelength, with steeper slopes within the 1- and 2-micron pyroxene bands, consistent with previous ground-based observations and laboratory measurement of HED meteorites showing deeper bands at higher phase angles. The relatively high albedo of Vesta suggests significant contribution of multiple scattering. The non-linear effect of multiple scattering and the possible systematic variations of phase function with albedo across the surface of Vesta may invalidate the traditional algorithm of applying photometric correction on airless planetary surfaces.

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Angular False Scattering in Radiative Heat Transfer Analysis Using the Discrete-Ordinates Method With Higher-Order Quadrature Sets

Volume 4: Heat and Mass Transfer Under Extreme Conditions; Environmental Heat Transfer; Computational Heat Transfer; Visualization of Heat Transfer; Heat Transfer Education and Future Directions in Heat Transfer; Nuclear Energy ◽

10.1115/ht2013-17249 ◽

2013 ◽

Author(s):

Brian Hunter ◽

Zhixiong Guo

Keyword(s):

Monte Carlo ◽

Radiative Transfer ◽

Phase Function ◽

Radiative Heat ◽

Higher Order ◽

Heat Transfer Analysis ◽

Discrete Ordinates ◽

Equal Weight ◽

Participating Media ◽

Discrete Ordinates Method

The SN quadrature set for the discrete-ordinates method is limited in overall discrete direction number in order to avoid physically unrealistic negative directional weight factors. Such a limitation can adversely impact radiative transfer predictions. Directional discretization results in errors due to ray effect, as well as angular false scattering error due to distortion of the scattering phase function. The use higher-order quadrature schemes in the discrete-ordinates method allows for improvement in discretization errors without an overall directional limitation. In this analysis, four higher-order quadrature sets (Legendre-Equal Weight, Legendre-Chebyshev, Triangle Tessellation, and Spherical Ring Approximation) are implemented for determination of radiative transfer in a 3-D cubic enclosure containing participating media. Radiative heat fluxes, calculated at low direction number, are compared to the SN quadrature and Monte Carlo predictions to gauge quadrature accuracy. Additionally, investigation into the reduction of angular false scattering with sufficient increase in direction number using higher-order quadrature, including heat flux accuracy with respect to Monte Carlo and computational efficiency, is presented. While higher-order quadrature sets are found to effectively minimize angular false scattering error, it is found to be much more computationally efficient to implement proper phase function normalization for accurate radiative transfer predictions.

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