A modified version of the discrete ordinates method for radiative heat transfer modelling

Abstract

The standard discrete ordinates method (SDOM) suffers from two major sources of inaccuracy, the ray effects and false scattering. False scattering may be significantly reduced using high order discretization schemes, while ray effects originated from abrupt changes of wall temperatures are mitigated by the modified discrete ordinates method (MDOM). However, the MDOM is insensitive to ray effects caused by sharp gradients of the emissive power of the medium. Therefore, a new version (NMDOM) is proposed to overcome this shortcoming. The accuracy of the SDOM, MDOM and NMDOM are investigated, along with the interaction between ray effects and false scattering. It is concluded that the NMDOM yields accurate solutions even for coarse spatial and angular discretizations. IntroductionThe discrete ordinates method [1-3] and the finite volume method [4,5] for the solution of radiative heat transfer problems have received significant attention and development in the last decade, owing to their good compromise between accuracy, flexibility and moderate computational requirements. They can be applied to non-isothermal, non-homogeneous, anisotropically scattering, non-gray media in complex geometries. However, several limitations of these methods have also been identified. Among them, ray effects and false scattering are perhaps the two most important ones. These two problems have been discussed in [6], and several proposals have been made to overcome them.False scattering, also referred to in the literature as numerical scattering or numerical smearing, is related to the spatial discretization. It is the counterpart of false diffusion in computational fluid dynamics (CFD). False scattering may be reduced by refining the grid or by using more accurate spatial discretization schemes (SDS). An evaluation of SDS was presented in [7]. The STEP and the diamond schemes are probably the most widely used ones. These are the counterpart of the upwind and central difference schemes in CFD, respectively. It is well known that the diamond scheme may predict unphysical negative radiation intensities. These may be removed, but often at the expense of spurious wiggles in the predictions. The STEP scheme never yields negative radiation intensities, but it originates excessive false scattering, smoothing out steep gradients of the radiation intensity field. A few other SDS, namely the positive, variable weight and exponential schemes were discussed in [7], but the STEP scheme was recommended for future applications.Improved versions of the exponential scheme, accounting for the multidimensional nature of radiation, were used in [4] and [8][9][10][11]. Bounded high order resolution differencing schemes, formerly developed for CFD, have also been applied to the radiative transfer equation (RTE). These include the SMART scheme [12], and the MINMOD, MUSCL, CLAM and SMART schemes [13]. The STEP and the CLAM [14] schemes are used in the present work. Although the CLAM scheme is not as accurate as the MUSCL and SMART schemes, it converges faster and...

The State of the Art in Interactive Global Illumination

“…Second, the angular discretization allows light to only travel at a finite number of directions (hence the name of the method), causing the so‐called ray effect that is particularly noticeable in media where no or little scattering takes place. Nevertheless, DOMs are widely used by radiative transfer engineers [Coe04, LBC94] and in atmospheric radiative transfer [Eva98] (where these effects are not as severe as for light transport in vacuum, for example). Evans [Eva98] describes spherical harmonics DOMs (SHDOMs) where the directional distribution of light within every cell is stored as a spherical harmonics (SH) approximation.…”

Parallel MDOM for light transport in participating media

“…False scattering or numerical smearing is related to the spatial discretization and can be reduced by using a more refined and accurate grid scheme. The MDOM [Ramankutty and Crosbie 1997;Coelho 2004] reduces the ray effects by splitting the final solution into direct and indirect components. The direct component is calculated analytically and the DOM is used for computing the indirect component.…”

Beitrag zur Lösung des Problems der Algenbildung auf Außenwänden mit Wärmedämmverbundsystemen (WDVS)

“…Die grundlegende Gleichung für die langwellige Strahlung, unter Berücksichtigung eines emissions-, absorptionsund extinktionsfähigen grauen Mediums kann in folgender Form aus [2] S. 376, (vgl. auch [8], S. 561) geschrieben werden: …”