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A Pressure-Correction Scheme for Rotational Navier-Stokes Equations and Its Application to Rotating Turbulent Flows

Published online by Cambridge University Press:  20 August 2015

Dinesh A. Shetty ,
Jie Shen ,
Abhilash J. Chandy  and
Steven H. Frankel
Dinesh A. Shetty*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
Jie Shen*
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, China Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Abhilash J. Chandy*
Affiliation:
Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA
Steven H. Frankel*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
*
Email:dshetty@purdue.edu
Corresponding author.Email:shen7@purdue.edu
Email:ac76@uakron.edu
Email:frankel@ecn.purdue.edu
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Abstract

The rotational incremental pressure-correction (RIPC) scheme, described in Timmermans et al. [Int. J. Numer. Methods. Fluids., 22 (1996)] and Shen et al. [Math. Comput., 73 (2003)] for non-rotational Navier-Stokes equations, is extended to rotating incompressible flows. The method is implemented in the context of a pseudo Fourier-spectral code and applied to several rotating laminar and turbulent flows. The performance of the scheme and the computational results are compared to the so-called diagonalization method (DM) developed by Morinishi et al. [Int. J. Heat. Fluid. Flow., 22 (2001)]. The RIPC predictions are in excellent agreement with the DM predictions, while being simpler to implement and computationally more efficient. The RIPC scheme is not in anyway limited to implementation in a pseudo-spectral code or periodic boundary conditions, and can be used in complex geometries and with other suitable boundary conditions.

Keywords

52B1065D1868U0568U07Rotating turbulent flowpressure-correctionNavier-Stokes equationsFourier-spectral method
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 3 , March 2011 , pp. 740 - 755
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Luo, H., Rutland, C. J. and Smith, L. M., A-priori tests of one-equation LES modeling of rotating turbulence, J. Turbul., 37 (2007).Google Scholar
[2]Yeung, P. K. and Zhou, Ye, Numerical study of rotating turbulence with external forcing, Phys. Fluids., 10(DOI:10.1063/1.869810), 1998.Google Scholar
[3]Smith, L. M. and Waleffe, F., Transfer of energy to two-dimensional large scales in forced rotating three-dimensional turbulence, Phys. Fluids., 11 (1999), 1608–1622.CrossRefGoogle Scholar
[4]Morinishi, Y., Nakabayashi, K. and Ren, S. Q., A new DNS algorithm for rotating homogeneous decaying turbulence, Int. J. Heat. Fluid. Flow., 22 (2001), 30–38.CrossRefGoogle Scholar
[5]Chorin, A. J., Numerical solution of the Navier-Stokes equations, Math. Comput., 22 (1968), 745–762.CrossRefGoogle Scholar
[6]Temam, R., Sur l’approximation de la solution des équations de Navier-Stokes par la méthode des pas fractionnaires II, Arch. Rat. Mech. Anal., 33 (1969), 377–385.Google Scholar
[7]Guermond, J. L., Minev, P. and Shen, J., An overviewof projection methods for incompressible flows, Comput. Methods. Appl. Mech. Engrg., 195 (2006), 6011–6045.Google Scholar
[8]Timmermans, L. J. P., Minev, P. D. and Van De Vosse, F. N., An approximate projection scheme for incompressible flow using spectral elements, Int. J. Numer. Methods. Fluids., 22 (1996), 673–688.Google Scholar
[9]Guermond, J. L. and Shen, J., On the error estimates for the rotational pressure-correction projection methods, Math. Comput., 73 (2003), 1719–1737.Google Scholar
[10]Shen, J., Efficient spectral-Galerkin method I, direct solvers for second- and fourth-order equations by using Legendre polynomials, SIAM J. Sci. Comput., 15 (1994), 1489–1505.Google Scholar
[11]Shen, J., Efficient spectral-Galerkin method II, direct solvers for second- and fourth-order equations by using Chebyshev polynomials, SIAM J. Sci. Comput., 16 (1995), 74–87.Google Scholar
[12]Temam, R., Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, 1984.Google Scholar
[13]Chen, F. and Shen, J., Efficient spectral methods for solving systems of coupled elliptic equations, preprint, 2010.Google Scholar
[14]Rogallo, R. S., Numerical experiments in homogeneous turbulence, NASA TM., 81315, 1981.Google Scholar
[15]Chandy, A. J. and Frankel, S. H., Regularization-based sub-grid scale (SGS) models for large eddy simulations (LES) of high-Re decaying isotropic turbulence, J. Turbul., 10 (2009).CrossRefGoogle Scholar
[16]Lu, H., One Equation LES Modeling of Rotating Turbulence, Ph.D Thesis, University of Wisconsin Madison, 2007.Google Scholar