Commun. Comput. Phys., 9 (2011), pp. 740-755.

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

Dinesh A. Shetty 1, Jie Shen 2*, Abhilash J. Chandy 3, Steven H. Frankel 1

1 School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA.
2 School of Mathematical Sciences, Xiamen University, Xiamen, China; and Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA.
3 Department of Mechanical Engineering, University of Akron, Akron, OH 44325, USA.

Received 30 November 2009; Accepted (in revised version) 4 March 2010
Available online 17 September 2010


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.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Rotating turbulent flow, pressure-correction, Navier-Stokes equations, Fourier-spectral method.

*Corresponding author.
Email: (D. A. Shetty), (J. Shen), (A. J. Chandy), (S. H. Frankel)

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