A Finite-Volume/Newton Method for a Two-Phase Heat Flow Problem Using Primitive Variables and Collocated Grids

Liang, Mao-Chang; Lan, C.W.

doi:10.1006/jcph.1996.0179

Cited by 25 publications

(30 citation statements)

References 14 publications

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“…(6) was discretized using a fully conservative finite-volume method with a nonstaggered arrangement of the variables [38,39]. Central difference was used for all spatial derivatives and firstorder forward difference for the time derivatives.…”

Section: Discretization and Numerical Methodsmentioning

confidence: 99%

Numerical studies of wave pattern in an oxide melt in the Czochralski crystal growth

Jing

Tsukada

Hozawa

et al. 2004

Journal of Crystal Growth

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Section: Discretization and Numerical Methodsmentioning

confidence: 99%

Numerical studies of wave pattern in an oxide melt in the Czochralski crystal growth

Jing

Tsukada

Hozawa

et al. 2004

Journal of Crystal Growth

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“…However, the actual physical processes show that the convection type of heat transfer may be present in the liquid and often plays an important role (Brewster and Gebhart, 1988;Chellaiah and Viskanta;1989;Zhang and Bejan, 1989;Gobin and Benard, 1992;Fukusako and Yamada, 1993). There have been more rigorous modelling studies in the recent years (Liang and Lan, 1996;Zhang et al, 1996;Chang and Yang, 1996;Sasaguchi et al, 1996;Iyer and Vafai, 1998;Amin and Greif, 1999;Harris et al, 2001). Most of the models, however, use constant liquid density approximation in some or all terms of the governing equations of the phase change process and/or lack a quantitative comparison with experiments.…”

Section: Introductionmentioning

confidence: 94%

Numerical and experimental investigation of melting of ice involving natural convection

Kahraman

2002

Int. J. Energy Res.

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SUMMARYTwo-dimensional transient melting of ice in a rectangular enclosure was numerically and experimentally investigated. Natural convection in the liquid phase due to the temperature dependency of water density was considered in the numerical model. The implicit "nite di!erence method with "xed staggered grid approach was utilized. The SIMPLER algorithm was followed for the solution of pressure and velocity "elds in the liquid phase. The prediction of the model was found to be satisfactory through preliminary experimentation.

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“…(6) was discretized using a fully conservative finite-volume method with a non-staggered arrangement of the variables [15,16]. Central difference was used for all spatial derivatives and first-order forward difference for the time derivatives.…”

Section: Discretization and Numerical Methodsmentioning

confidence: 99%

Role of characteristic modes in the dynamics of wave pattern in the Czochralski oxide crystal growth

Jing

Chen

et al. 2012

Journal of Crystal Growth

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a b s t r a c tWave pattern is a flow pattern observed on the free surface of oxide melt in the Czockralski crucible. Wave pattern exhibits regular folds in the azimuthal direction. In this paper three-dimensional flows of the LiNbO 3 melt in a Czockralski crucible of radius r c ¼ 100 mm and crystal radius r s ¼ 50 mm were investigated. The crucible is still and the crystal is rotating at a rate O s . The flow is assumed to be laminar. The governing equations of the melt flows were solved by a block-structured boundary-fittedcoordinate method. Massive numerical simulations were first conducted to obtain several stable n-folded wave patterns by changing aspect ratio A¼ h/r c and O s , where h is the depth of the oxide melt. The proper orthogonal decomposition was then applied to extract the characteristic modes of the n-folded original wave patterns. The spatial feature of the characteristic modes and the role of the characteristic modes in the dynamic process of the original wave patterns were finally analyzed. Some interesting conclusions are obtained. The characteristic modes of the wave patterns show strong spatial feature. The characteristic modes have more folds in the azimuthal direction than the original wave patterns; the characteristic modes appear in group; with the increase of group order, the number of folds in the azimuthal direction is increased regularly by n for the n-folded original wave pattern. The study of the dynamic process shows that the original wave pattern is a traveling wave, which is formed by the dominant characteristic modes.

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A Finite-Volume/Newton Method for a Two-Phase Heat Flow Problem Using Primitive Variables and Collocated Grids

Cited by 25 publications

References 14 publications

Numerical studies of wave pattern in an oxide melt in the Czochralski crystal growth

Numerical studies of wave pattern in an oxide melt in the Czochralski crystal growth

Numerical and experimental investigation of melting of ice involving natural convection

Role of characteristic modes in the dynamics of wave pattern in the Czochralski oxide crystal growth

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