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http://dx.doi.org/10.3795/KSME-B.2003.27.1.135

A Study of n Multigrid Finite-Volume Method for Radiation  

Kim, Man-Young (현대자동차 승용디젤엔진시험팀)
Do, Young-Byun (한국과학기술기획평가원)
Baek, Seung-Wook (KAIST 기계공학과 항공우주공학 전공)
Publication Information
Transactions of the Korean Society of Mechanical Engineers B / v.27, no.1, 2003 , pp. 135-140 More about this Journal
Abstract
The convergence of finite volume method (FVM) or discrete ordinate method (DOM) is known to degrade for optical thickness greater than unity and large scattering albedo. The present article presents a convergence acceleration procedure for the FVM based on a full approximation storage (FAS) multigrid method. Among a variety of multigrid cycles, the V-cycle is used and the full multigrid algorithm (FMG) is applied to an analysis of radiation in irregular two-dimensional geometry. Solution convergence is discussed for the several cases of various optical thickness and scattering albedo. At small scattering albedo and optical thickness, there is no advantage to using the multigrid method for calculation CPU time. For large scattering albedo greater than 0.5 and optical thickness greater than unity, however, the multigrid method improves the convergence and the solution is rapidly obtained.
Keywords
Multigrid Method; Radiative Heat Transfer; Finite Volume Method; Convergence; CPU Time;
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1 Chui, E. H. and Raithby, G. D., 1993, 'Computation of Radiant Heat Transfer on a Nonorthogonal Mesh Using the Finite-Volume Method,' Numer. Heat Transfer, B, Vol. 23, pp. 269-288   DOI   ScienceOn
2 Chai, J. C., Lee, H. S., and Patanker, S. V., 1995, 'Finite Volume Radiative Heat Transfer Procedure for Irregular Geometries,' J. Thermophysics Heat Transfer, Vol. 9, No. 3, pp. 410-415   DOI   ScienceOn
3 Baek, S. W., Kim, M. Y., and Kim, J. S., 1998, 'Nonorthogonal Finite-Volume Solutions of Radiative Heat Transfer in a Three-Dimensional Enclosure,' Numer. Heat Transfer, B, Vol. 34, No. 4, pp. 419-437   DOI   ScienceOn
4 Fiveland, W. A., 1984, 'Discrete Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures,' J. Heat Transfer, Vol. 106, No. 4, pp. 699-706   DOI
5 Fiveland, W. A. and Jessee, J. P., 1996, 'Acceleration Schemes for the Discrete Ordinates Method,' J. Thermodynamics Heat Transfer, Vol. 10, No. 3, pp. 445-451   DOI   ScienceOn
6 Lewis, E. E. and Miller, Jr, W. F., 1984, Computational Methods of Neutron Transport, John Wiley & Sons, Inc.
7 Mathur, S. R. and Murthy, J. Y., 1999, 'A Point Coupled Multi-Grid Acceleration Scheme for Radiative Heat Transfer,' AIAA 99-0872, $37^{th}$ Aerospace Sciences Meetings & Exhibit, Jan. 11-14, 1999, Reno
8 Hortmann, M., Peric, M., and Scheuerer, G., 1990, 'Finite Volume Multigrid Prediction of Laminar Natural Convection: Bench-Mark Solutions,' Int. J. for Numerical Methods in Fluids, Vol. 11, pp. 189-207   DOI
9 Shyy, W. and Sun, C.S., 1993, 'Development of a Pressure-Correction/Staggered-Grid Based Multigrid Solver for Incompressible Recirculating Flows,' Computers and Fluids, Vol. 22, No. 1, pp. 51-76   DOI   ScienceOn
10 Cheong, K. B. and Song, T. H., 1997, 'An Alternative Discrete Ordinates Method with Interpolation and Source Differencing for Two-Dimensional Radiative Transfer Problems,' Numer. Heat Transfer, B, Vol. 32, pp. 107-125   DOI   ScienceOn
11 Kim, T. K., 1990, 'Radiation and Combined Mode Heat Transfer Analyses in Absorbing, Emitting, and Mie-Anisotropic Scattering Media using the S-N Discrete Ordinates Method,' Ph. D Thesis, University of Minnesota, Minneappolis, MN
12 Cha, H. and Song, T.-H., 2000, 'Discrete Ordinates Interpolation Method Applied to Irregular Three-Dimentional Geometries,' Trans. KSME(B). Vol. 24, No. 6, pp. 814-821
13 Kim, M. Y., and Baek, S. W., 1996, 'Numerical Analysis of Conduction, Convection, and Radiation in a Gradually Expanding Channel,' Numer. Heat Transfer. A, Vol. 29, No. 7, pp. 725-740   DOI   ScienceOn
14 Byun, D. Y., Baek, S. W., and Kim. M. Y., 2000, 'Radiation in Discretely Heated Irregular Geometry Using Monte-Carlo, Finite-Voulme, and Modified Discrete-Ordinate Interpolation Method,' Numer. Heat Transfer. A. Vol. 37, pp. 1-18   DOI   ScienceOn