Commun. Comput. Phys., 6 (2009), pp. 247-268.


Complex Transition of Double-Diffusive Convection in a Rectangular Enclosure with Height-to-Length Ratio Equal to 4: Part I

Xian Liang 1*, Xinliang Li 2, Dexun Fu 2, Yanwen Ma 2

1 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, No. 149 Yanchang Road, Shanghai 200072, China.
2 LNM, Institute of Mechanics, Chinese Academy of Sciences, No. 15 Beisihuanxi Road, Beijing 100190, China.

Received 2 June 2008; Accepted (in revised version) 29 August 2008
Available online 15 December 2008

Abstract

This is the first part of direct numerical simulation (DNS) of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients. We consider the case with the thermal Rayleigh number of $10^{5}$, the Pradtle number of 1, the Lewis number of 2, the buoyancy ratio of composition to temperature being in the range of [0,1], and height-to-width aspect ration of 4. A new 7th-order upwind compact scheme was developed for approximation of convective terms, and a three-stage third-order Runge-Kutta method was employed for time advancement. Our DNS suggests that with the buoyancy ratio increasing form 0 to 1, the flow of transition is a complex series changing from the steady to periodic, chaotic, periodic, quasi-periodic, and finally back to periodic. There are two types of periodic flow, one is simple periodic flow with single fundamental frequency (FF), and another is complex periodic flow with multiple FFs. This process is illustrated by using time-velocity histories, Fourier frequency spectrum analysis and the phase-space trajectories.

AMS subject classifications: 65Y20, 34C28, 70K50

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Key words: Double diffusive convection, transition, periodic motion, chaotic motion, high order compact.

*Corresponding author.
Email: liangx_yan@126.com (X. Liang), lixl@lnm.imech.ac.cn (X. L. Li), fudx@lnm.imech.ac.cn (D. X. Fu), mayw@lnm.imech.ac.cn (Y. W. Ma)
 

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