scholarly journals A Comparison of Angular Discretization Techniques for the Radiative Transport Equation

2015 ◽  
Author(s):  
John Tencer
Keyword(s):  
Spherical Harmonics ◽  
Radiation Transport ◽  
Radiative Flux ◽  
Benchmark Problems ◽  
Discrete Ordinates ◽  
Flux Divergence ◽  
Discontinuous Boundary ◽  
All Solutions ◽  
Mesh Resolution ◽  
Ray Effects

Two of the most popular deterministic radiation transport methods for treating the angular dependence of the radiative intensity for heat transfer: the discrete ordinates and simplified spherical harmonics approximations are compared. A problem with discontinuous boundary conditions is included to evaluate ray effects for discrete ordinates solutions. Mesh resolution studies are included to ensure adequate convergence and evaluate the effects of the contribution of false scattering. All solutions are generated using finite element spatial discretization. Where applicable, any stabilization used is included in the description of the approximation method or the statement of the governing equations. A previous paper by the author presented results for a set of 2D benchmark problems for the discrete ordinates method using the PN-TN quadrature of orders 4, 6, and 8 as well as the P1, M1, and SP3 approximations. This paper expands that work to include the Lathrop-Carlson level symmetric quadrature of order up to 20 as well as the Lebedev quadrature of order up to 76 and simplified spherical harmonics of odd orders from 1 to 15. Two 3D benchmark problems are considered here. The first is a canonical problem of a cube with a single hot wall. This case is used primarily to demonstrate the potentially unintuitive interaction between mesh resolution, quadrature order, and solution error. The second case is meant to be representative of a pool fire. The temperature and absorption coefficient distributions are defined analytically. In both cases, the relative error in the radiative flux or the radiative flux divergence within a volume is considered as the quantity of interest as these are the terms that enter into the energy equation. The spectral dependence of the optical properties and the intensity is neglected.

A Parametric Study of the Accuracy of Several Radiative Transport Solution Methods for a Set of 2-D Benchmark Problems

2013 ◽  
Author(s):  
John Tencer ◽  
John R. Howell
Keyword(s):  
Radiation Transport ◽  
Benchmark Problems ◽  
Discrete Ordinates ◽  
Test Problems ◽  
Governing Equations ◽  
Element Discretization ◽  
Discontinuous Boundary ◽  
All Solutions ◽  
Solution Methods ◽  
Ray Effects

Several of the most popular deterministic radiation transport methods for heat transfer are compared. Relative solution error is compared as a function of optical thickness and scattering albedo. The test problems are chosen to represent a range of problem types. Problems with discontinuous boundary conditions are included to evaluate ‘ray effects’ for discrete ordinates solutions. A brief derivation and a statement of the governing equations for each method is included so that the details of the precise method used is clear. All solutions are generated using finite element discretization. Where applicable, any stabilization used is included in the statement of the governing equations.

Verification for Ray Effects Elimination Module of Radiation Shielding Code ARES by Kobayashi Benchmarks

2014 ◽  
Author(s):  
Mengteng Chen ◽  
Bin Zhang ◽  
Yixue Chen
Keyword(s):  
Radiation Transport ◽  
Source Region ◽  
Anisotropic Scattering ◽  
Relative Difference ◽  
Radiation Shielding ◽  
Benchmark Problems ◽  
Discrete Ordinates ◽  
Ray Effects ◽  
Good Agreement

ARES is a multi-group of anisotropic scattering transport shielding code based on discrete ordinates method. The 3D radiation transport benchmark problems proposed by Kobayashi were calculated by ARES with sub-module ARES_RayEffect which using first collision method for ray effects mitigation. ARES_RayEffect calculates uncollided flux and first collision source moments for ARES. The uncollided flux is obtained by a ray tracing calculation between a source point and a target mesh center. In addition, ARES_RayEffect has a modifying factor function to improve the quality of uncollided flux calculation. For verification, the results of MCNP code are used as reference solution and the results of TORT with FNSUNCL3 are compared. ARES_RayEffect introduced the modifying factor to reduce the relative difference of meshes near the source region. For example, at the position (15,15,15) in Problem 1 case i, the relative difference of the result of ARES with ARES_RayEffect is −2.34%, while relative difference of the result of TORT with FNSUNCL3 is −11.92%. The calculated total neutron fluxes show good agreement with the MCNP solutions. For the pure absorber cases, the maximum differences are less than 3%. For the half scattering cases, the maximum differences are less than 11%. Numerical results demonstrate that ray effects can be effectively mitigated.

scholarly journals DAPHNE-3D: A NEW TRANSPORT SOLVER FOR UNSTRUCTURED TETRAHEDRAL MESHES

2021 ◽  
Vol 247 ◽  
pp. 03004
Author(s):  
Evangelia Diamantopoulou ◽  
Daniele Sciannandrone
Keyword(s):  
Radiation Transport ◽  
Benchmark Problems ◽  
Discrete Ordinates ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Tetrahedral Meshes ◽  
Discontinuous Galerkin Finite Element ◽  
Unstructured Tetrahedral Meshes ◽  
The One ◽  
Good Agreement

A new Discrete Ordinates transport solver for unstructured tetrahedral meshes is presented. The solver uses the Discontinuous Galërkin Finite Element Method with linear or quadratic expansion of the flux within each cell. The solution of the one-group problem is obtained with non-preconditioned fixed-point or GMRES iterations. Precision and performances of the solver are evaluated on the 3D Radiation Transport Benchmark Problems proposed by Kobayashi, showing very good agreement with the reference and good computing times in serial execution.

On the influence of CO2 on the radiative flux divergence

Tellus ◽  
1968 ◽  
Vol 20 (2) ◽  
pp. 294-299
Author(s):  
Wilford G. Zdunkowski ◽  
Larry L. Stowe
Keyword(s):  
Radiative Flux ◽  
Flux Divergence

A Statistical Model of Cloud Vertical Structure Based on Reconciling Cloud Layer Amounts Inferred from Satellites and Radiosonde Humidity Profiles

2005 ◽  
Vol 18 (17) ◽  
pp. 3587-3605 ◽  
Author(s):  
William B. Rossow ◽  
Yuanchong Zhang ◽  
Junhong Wang
Keyword(s):  
Statistical Model ◽  
Vertical Structure ◽  
Atmospheric Temperature ◽  
Radiative Flux ◽  
Cloud Layer ◽  
Cloud Base ◽  
Polar Regions ◽  
Flux Divergence ◽  
Climate Scale ◽  
Humidity Profiles

Abstract To diagnose how cloud processes feed back on weather- and climate-scale variations of the atmosphere requires determining the changes that clouds produce in the atmospheric diabatic heating by radiation and precipitation at the same scales of variation. In particular, not only the magnitude of these changes must be quantified but also their correlation with atmospheric temperature variations; hence, the space–time resolution of the cloud perturbations must be sufficient to account for the majority of these variations. Although extensive new global cloud and radiative flux datasets have recently become available, the vertical profiles of clouds and consequent radiative flux divergence have not been systematically measured covering weather-scale variations from about 100 km, 3 h up to climate-scale variations of 10 000 km, decadal inclusive. By combining the statistics of cloud layer occurrence from the International Satellite Cloud Climatology Project (ISCCP) and an analysis of radiosonde humidity profiles, a statistical model has been developed that associates each cloud type, recognizable from satellite measurements, with a particular cloud vertical structure. Application of this model to the ISCCP cloud layer amounts produces estimates of low-level cloud amounts and average cloud-base pressures that are quantitatively closer to observations based on surface weather observations, capturing the variations with latitude and season and land and ocean (results are less good in the polar regions). The main advantage of this statistical model is that the correlations of cloud vertical structure with meteorology are qualitatively similar to “classical” information relating cloud properties to weather. These results can be evaluated and improved with the advent of satellites that can directly probe cloud vertical structures over the globe, providing statistics with changing meteorological conditions.

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