Study on Interpolation Schemes of the Discrete Ordinates Interpolation Method for Three-Dimensional Radiative Transfer With Nonorthogonal Grids

Seo, Seok-Ho; Kim, Tae-Kuk

doi:10.1115/1.2825897

Cited by 16 publications

(11 citation statements)

References 7 publications

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“…Finally, to achieve a converged solution, it was often necessary to underrelax the deferred correction term given by Eq. (14). This is required for both the HR and the SHR schemes, although the SHR schemes generally require stronger underrelaxation.…”

Section: Computational Detailsmentioning

confidence: 96%

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Bounded Skew High-Order Resolution Schemes for the Discrete Ordinates Method

Coelho¹

2002

Journal of Computational Physics

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Section: Computational Detailsmentioning

confidence: 96%

“…The interpolation of the upstream intensity from grid node values must be done carefully to ensure conservation. Similar high-order exponential schemes have been employed in [13,14]. These authors use the discrete ordinates interpolation method, a modification of the standard discrete ordinates method which does not use the control-volume formulation.…”

mentioning

confidence: 98%

Bounded Skew High-Order Resolution Schemes for the Discrete Ordinates Method

Coelho¹

2002

Journal of Computational Physics

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“…It includes two terms, as observed in Eq. (11), one due to radiative energy leaving the wall, denoted by S w , and the other due to emission of the medium, denoted by S m . The contribution from the top wall to S w is given by…”

Section: Homogeneous Isotropic Scattering Medium Bounded By Black Wallsmentioning

confidence: 99%

“…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).…”

Section: Introductionmentioning

confidence: 99%

“…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).…”

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confidence: 99%

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

Coelho

2004

Computational Mechanics

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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...

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Narrow band radiative solutions within a cubical enclosure filled with real gas mixtures

Park

Kim

2002

KSME International Journal

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Study on Interpolation Schemes of the Discrete Ordinates Interpolation Method for Three-Dimensional Radiative Transfer With Nonorthogonal Grids

Cited by 16 publications

References 7 publications

Bounded Skew High-Order Resolution Schemes for the Discrete Ordinates Method

Bounded Skew High-Order Resolution Schemes for the Discrete Ordinates Method

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

Narrow band radiative solutions within a cubical enclosure filled with real gas mixtures

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