Improved Treatment of Anisotropic Scattering for Ultrafast Radiative Transfer Analysis

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Energy Deposition ◽  
Anisotropic Scattering ◽  
Heat Fluxes ◽  
Asymmetry Factor ◽  
Discrete Ordinates ◽  
Improve Treatment ◽  
Scattered Energy ◽  
Volume Method

The necessity of conserving both scattered energy and asymmetry factor for ballistic incidence after finite volume method (FVM) or discrete-ordinates method (DOM) discretization is shown. A phase-function normalization technique introduced previously by the present authors is applied to scattering of ballistic incidence in 3D FVM/DOM to improve treatment of anisotropic scattering through reduction of angular false scattering errors. Ultrafast radiative transfer predictions generated using FVM and DOM are compared to benchmark Monte Carlo to illustrate the necessity of ballistic phase-function normalization. Proper ballistic phase-function treatment greatly improves predicted heat fluxes and energy deposition for anisotropic scattering and for situations where accurate numerical modeling is crucial.

Normalization for Ultrafast Radiative Transfer Analysis With Collimated Irradiation

2012 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Function Approximation ◽  
Energy Deposition ◽  
Heat Fluxes ◽  
Asymmetry Factor ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Scattered Energy ◽  
The Impact

Normalization of the scattering phase function is applied to the transient discrete ordinates method for ultrafast radiative transfer analysis in a turbid medium subject to a normal collimated incidence. Previously, the authors have developed a normalization technique which accurately conserves both scattered energy and phase function asymmetry factor after directional discretization for the Henyey-Greenstein phase function approximation in steady-state diffuse radiative transfer analysis. When collimated irradiation is considered, additional normalization must be applied to ensure that the collimated phase function also satisfies both scattered energy and asymmetry factor conservation. The authors’ technique is applied to both the diffuse and collimated components of scattering using the general Legendre polynomial phase function approximation for accurate and efficient ultrafast radiative transfer analysis. The impact of phase function normalization on both predicted heat fluxes and overall energy deposition in a model tissue cylinder is investigated for various phase functions and optical properties. A comparison is shown between the discrete ordinates method and the finite volume method. It is discovered that a lack of conservation of asymmetry factor for the collimated component of scattering causes over-predictions in both energy deposition and heat flux for highly anisotropic media.

Improved Treatment of Anisotropic Scattering for Ultrafast Radiative Transfer Analysis

2013 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Energy Deposition ◽  
Radiant Energy ◽  
Diffuse Radiation ◽  
Anisotropic Scattering ◽  
Heat Fluxes ◽  
Asymmetry Factor ◽  
Conservation Of Energy ◽  
Numerical Predictions

The necessity of conserving both scattered energy and asymmetry factor for ballistic incidence after either FVM or DOM discretization is convincingly shown by analyzing ultrafast laser radiative transfer in a cubic enclosure housing a participating medium. A phase-function normalization technique introduced previously by the present authors to correct for non-conservation of energy and asymmetry factor in diffuse radiant energy scattering is applied to scattering of ballistic incidence for the first time in 3-D FVM/DOM in order to improve treatment of anisotropic scattering through reduction of angular false scattering errors. Treatment of only the diffuse radiation will not conserve ballistic properties if the direction of ballistic incidence differs from a predetermined discrete direction. Our ultrafast radiative transfer predictions generated using the FVM and DOM are compared to benchmark Monte Carlo predictions in the literature to gauge accuracy and to illustrate the necessity of ballistic phase-function normalization. Additionally, numerical predictions of energy deposition in a tissue-phantom medium are analyzed to further clarify the importance of accurate numerical predictions. It is shown that the addition of proper ballistic phase-function treatment greatly improves predicted heat fluxes and energy deposition for anisotropic scattering and for situations where accurate numerical modeling is crucial.

A New Phase Function Normalization Approach for Radiative Transfer Analysis in Highly Anisotropic Scattering Media

2011 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Phase Function ◽  
Solid Angle ◽  
Scaling Law ◽  
Anisotropic Scattering ◽  
Convergence Time ◽  
Extreme Condition ◽  
Asymmetry Factor ◽  
Scattering Media ◽  
Scattered Energy ◽  
New Phase

A new phase function normalization approach is applied to both the DOM and FVM for predicting radiative heat transfer in an extreme condition — highly anisotropic scattering media. Previous attempts to normalize the DOM result in a distortion of the overall phase function asymmetry factor. The splitting of each solid angle into numerous sub-angles in the FVM is shown to also produce a lack of conservation of asymmetry factor, even though scattered energy is conserved. The current normalization technique is crafted such that scattered energy and asymmetry factor are accurately conserved after both DOM and FVM discretization. The change in scattering effect when asymmetry factor is not conserved is examined for both methods. Wall flux profiles generated by DOM with old and new normalization techniques as well as FVM with and without phase function normalization are compared to isotropic scaling law profiles to gauge the accuracy of the techniques. The effects of changes in both optical thickness and scattering albedo are investigated. It is found that the current normalization approach vastly improves accuracy of flux profiles. The current procedure also greatly decreases FVM convergence time by eliminating the need for large amounts of solid angle splitting.

scholarly journals A Theoretical Model of Radiative Transfer in Young Sea Ice

1982 ◽  
Vol 28 (99) ◽  
pp. 341-356
Author(s):  
Donald K. Perovich ◽  
Thomas C. Grenfell
Keyword(s):  
Theoretical Model ◽  
Radiative Transfer ◽  
Phase Function ◽  
Incident Radiation ◽  
Single Scattering ◽  
Anisotropic Scattering ◽  
Discrete Ordinates ◽  
Ice Thickness ◽  
Surface Layers ◽  
Beam Incident

AbstractA four stream discrete-ordinates photometric model including both anisotropic scattering and refraction at the boundaries is presented which treats the case of a floating ice slab. The effects of refraction and reflection on the redistribution of the incident radiation field as it enters the ice are examined in detail. Using one- and two-layer models, theoretical albedos and transmittances are compared to values measured in the laboratory for thin salt ice. With an experimentally determined three-parameter Henyey–Greenstein phase function, comparisons at 650 nm yield single-scattering albedos ranging from 0.95 to 0.9997. The models are then used to compare the effects of diffuse and direct-beam incident radiation, to investigate the dependence of spectral albedo and transmittance on ice thickness, and to determine the influence of very cold and melted surface layers.

Comparison of Phase Function Normalization Techniques for Radiative Transfer Analysis Using DOM

2014 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo ◽  
Matthew Frenkel
Keyword(s):  
Phase Function ◽  
Radiation Heat Transfer ◽  
Mathematical Formulation ◽  
Diffuse Radiation ◽  
Asymmetry Factor ◽  
Participating Media ◽  
Scattered Energy ◽  
Volume Method ◽  
The Impact ◽  
Angular Discretization

Five phase-function (PF) normalization techniques are compared using the discrete-ordinate method (DOM) for modeling diffuse radiation heat transfer in participating media. Both the mathematical formulation and the impact on the conservation of both scattered energy and PF asymmetry factor for both Henyey-Greenstein (HG) and Legendre PF distributions are presented for each technique. DOM radiation transfer predictions generated using the five normalization techniques are compared to high-order finite-volume method, to gauge their accuracy. The commonly implemented scattered energy averaging technique cannot correct asymmetry factor distortion after angular discretization, and thus large errors due to angular false scattering are prevalent. Another three simple techniques via correction of one or two terms in the PF are shown to reduce normalization complexity whilst retaining diffuse radiation computation accuracy for HG PFs. However, for Legendre PFs, such simple normalization is found to result in unphysical negative PF values at one or few correction directions. The relatively complex Hunter and Guo 2012 technique, in which normalization is realized through a correction matrix covering all discrete directions, is shown to be highly applicable for both PF types.

scholarly journals A Theoretical Model of Radiative Transfer in Young Sea Ice

1982 ◽  
Vol 28 (99) ◽  
pp. 341-356 ◽  
Author(s):  
Donald K. Perovich ◽  
Thomas C. Grenfell
Keyword(s):  
Theoretical Model ◽  
Radiative Transfer ◽  
Phase Function ◽  
Incident Radiation ◽  
Single Scattering ◽  
Anisotropic Scattering ◽  
Discrete Ordinates ◽  
Ice Thickness ◽  
Surface Layers ◽  
Beam Incident

AbstractA four stream discrete-ordinates photometric model including both anisotropic scattering and refraction at the boundaries is presented which treats the case of a floating ice slab. The effects of refraction and reflection on the redistribution of the incident radiation field as it enters the ice are examined in detail. Using one- and two-layer models, theoretical albedos and transmittances are compared to values measured in the laboratory for thin salt ice. With an experimentally determined three-parameter Henyey–Greenstein phase function, comparisons at 650 nm yield single-scattering albedos ranging from 0.95 to 0.9997. The models are then used to compare the effects of diffuse and direct-beam incident radiation, to investigate the dependence of spectral albedo and transmittance on ice thickness, and to determine the influence of very cold and melted surface layers.

Modified δ-M Scaling Results for Mie-Anisotropic Scattering Media

1990 ◽  
Vol 112 (4) ◽  
pp. 988-994 ◽  
Author(s):  
T.-K. Kim ◽  
H. S. Lee
Keyword(s):  
Phase Function ◽  
Anisotropic Scattering ◽  
Asymmetry Factor ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Scattering Problems ◽  
Anisotropic Scaling ◽  
M Phase ◽  
Phase Functions ◽  
Transfer Problems

A modified δ-M scaling method, which adjusts the δ-M scaled phase functions to be always positive, is applied to radiative transfer problems in two-dimensional square enclosures. The scaled anisotropic results are compared with the results obtained from an accurate model of the full anisotropic scattering problems using the S-N discrete ordinates method. The modified δ-M anisotropic scaling is shown to improve the isotropic scaled results of a collimated incidence problem, but the required number of terms increases as the phase function complexity and the asymmetry factor increase. For the diffuse incidence problems, even a low-order modified δ-M phase function significantly improves the accuracy of scaled solutions over the isotropic scaling. Significant savings in the computer times are observed when the modified δ-M method is applied.

Sign in / Sign up

Export Citation Format

Share Document