Abstract
A Seperation of Variables (SoV) scheme has been developed in order to obtain a direct solution to the Poisson problem arising from Chorin’s projection method within rectangular enclosures. The algorithm is compared to the previously used FFT with periodic boundaries and methods to improve the performace of the required transformations are presented. Finally, first results of thermal convection obtained in a closed box geometry are compared to results obtained in a periodic rectangular cell.
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References
A. J. Chorin. Numerical solution of the Navier-Stokes equations. Mathematics of Computations, 22:745–762, 1968.
Z. A. Daya and R. E. Ecke. Does turbulent convection feel the shape of the container? Phys. Rev. Lett, 87(18): 184501, 2001.
J. Driscoll, J. D. M. Healy, and D. Rockmore. Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs. SIAMJ. Comput, 26:1066–1099, 1997.
S. Grossmann and D. Lohse. Fluctuations in turbulent Rayleigh-Bénard convection: The role of plumes. Phys. Fluids, 16(12):4462–4472, Dezember 2004.
O. Shishkina and C. Wagner. Analysis of thermal dissipation in turbulent Rayleigh-Bénard convection. J. Fluid Mech., 546:51–60, 2006.
O. Shishkina and C. Wagner. A fourth order finite volume scheme for turbulent flow simulations in cylindrical domains. Computers and Fluids, 2006.
P. N. Swarztrauber. A direct method for the discrete solution of separable elliptic equations. SIAMJ. Numer. Anal, 11:1136–1150, 1974.
P. N. Swarztrauber and R. Sweet. Efficient Fortran subprograms for the solution of elliptic equations. Technical Report IA-109, National Center for Atmospheric Research, 1975.
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Kaczorowski, M., Shishkin, A., Shishkina, O., Wagner, C. (2007). Developement of a Numerical Procedure for Direct Simulations of Turbulent Convection in a Closed Rectangular Cell. In: Tropea, C., Jakirlic, S., Heinemann, HJ., Henke, R., Hönlinger, H. (eds) New Results in Numerical and Experimental Fluid Mechanics VI. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 96. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74460-3_47
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DOI: https://doi.org/10.1007/978-3-540-74460-3_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74458-0
Online ISBN: 978-3-540-74460-3
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