The combined Monte-Carlo and finite-volume method for radiation in a two-dimensional irregular geometry

Baek, Seung Wook; Byun, Do-Young; Kang, Sung Goon

doi:10.1016/s0017-9310(99)00288-4

Cited by 50 publications

(18 citation statements)

References 19 publications

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“…(7a). Different boundary conditions have been used in [24,25] for the MDOM. These authors use I 1 instead of I in the second term on the right of Eq.…”

Section: Modified Discrete Ordinates Methods (Mdom)mentioning

confidence: 99%

“…It would be necessary to change the solution method of Eq. 9(a), as it was done in [24] and [25], where the zonal or the Monte Carlo methods were employed to solve Eq. 6(a).…”

Section: Test Casementioning

confidence: 99%

“…Anisotropic scattering was also considered in [24]. Two-dimensional irregular geometries were studied in [25] using similar ideas, but applying the Monte-Carlo method instead of the zonal method to calculate the in-scattering term, and the finite volume method instead of the discrete ordinates method.…”

Section: Introductionmentioning

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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“…(7a). Different boundary conditions have been used in [24,25] for the MDOM. These authors use I 1 instead of I in the second term on the right of Eq.…”

Section: Modified Discrete Ordinates Methods (Mdom)mentioning

confidence: 99%

“…It would be necessary to change the solution method of Eq. 9(a), as it was done in [24] and [25], where the zonal or the Monte Carlo methods were employed to solve Eq. 6(a).…”

Section: Test Casementioning

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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“…Nowadays it is used directly to solve problems including complex physics, such as turbulenceradiation interaction [12][13][14], scattering [15], polarized radiative transfer [16,17] or complex geometry, sometimes in conjunction with deterministic methods [18,19].…”

Section: Introductionmentioning

confidence: 99%

An optimized reciprocity Monte Carlo method for the calculation of radiative transfer in media of various optical thicknesses

Dupoirieux¹,

Tessé²,

Avila³

et al. 2006

International Journal of Heat and Mass Transfer

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“…Therefore, Baek et al [10] suggested a simple numerical method, i.e., combined Monte-Carlo and finite volume method (CMCFVM), for analyzing radiative heat transfer in arbitrary configurations. In their work, the CMCFVM is proposed to deal with the ray effects in absorbing, emitting, and isotropic scattering medium which is surrounded by diffusely reflecting walls.…”

Section: Introductionmentioning

confidence: 99%

Radiative heat transfer in discretely heated irregular geometry with an absorbing, emitting, and anisotropically scattering medium using combined Monte-Carlo and finite volume method

Byun¹,

Lee²,

Baek³

2004

International Journal of Heat and Mass Transfer

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The combined Monte-Carlo and finite-volume method for radiation in a two-dimensional irregular geometry

Cited by 50 publications

References 19 publications

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

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

An optimized reciprocity Monte Carlo method for the calculation of radiative transfer in media of various optical thicknesses

Radiative heat transfer in discretely heated irregular geometry with an absorbing, emitting, and anisotropically scattering medium using combined Monte-Carlo and finite volume method

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