Numerical simulation for thermohaline multiple equilibrant system in non-rectangular domains
Zhan Jie-Min (詹杰民)a, Li Yok-Sheung (李毓湘)b
a Department of Applied Mechanics and Engineering, Zhongshan University, Guangzhou 510275, China; b Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Hong Kong, China
Abstract In this paper, incompressible, double-diffusive convection is simulated using finite-difference schemes. The Navier--Stokes equations are expressed in terms of stream function and vorticity. Because of the existence of large velocity, temperature and salinity gradients in boundary layers, a boundary-fitted coordinate system is used to concentrate the grid points near the wall and fit complex boundaries. The finite-difference methods used include the high-order accurate upwind difference scheme. It is shown that the scheme is a good candidate for direct simulations of double-diffusive convection flows. The proposed method is first applied to symmetry breaking and overturning states in thermohaline-driven flows in trapezoid basins. The basic phenomena agree well with those by Dijkstra and Molemaker (1997 J. Fluid Mech.331 169) and Quon and Ghil (1992 J. Fluid Mech. 245 449), but symmetry breaking and overturning states can occur in an asymmetric geometrical region without perturbations. Then the method is applied to double-diffusive convections in a cavity with opposing horizontal temperature and concentration gradients at large thermal ($Rt$), solutal ($Rs$) Rayleigh numbers and Lewis number. There are three straight sides and a sine curve side in the cavity. Basically, numerical results are in agreement with those of Lee and Hyun (1990 Int. J. Heat Mass Transfer33 1619) qualitatively, but eddies mixing in the top left-hand corner near the curved wall affects the layered structure.
Received: 10 May 2002
Revised: 30 August 2002
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 40276011), and the Scientific Research Found-ation for the Returned Overseas Chinese Scholars from the Ministry of Education of China (Grant No [1998]679).
Cite this article:
Zhan Jie-Min (詹杰民), Li Yok-Sheung (李毓湘) Numerical simulation for thermohaline multiple equilibrant system in non-rectangular domains 2003 Chinese Physics 12 60
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