Numerical simulation of unsteady flow in natural and thermosolutal convection using boundary-fitted coordinate system

摘要

A numerical scheme is proposed to solve double-diffusive problems using a boundary-fitted coordinate system to introduce finer grids in the boundary layer regions and an accurate high-order difference method. Numerical stability is improved by using fourth-order accurate upwind-biased differences to approximate the convection terms. The other terms in the governing differential equations are discretized using fourth-order central difference. To demonstrate the versatility of the boundary-fitted coordinate system, natural convection in an eccentric annulus is first simulated. The numerical results are consistent with the experimental results by Kuehn and Goldstein and better than the numerical results by Projahn et al. for eccentric cases. Secondly, the symmetry breaking and overturning states in thermohaline-driven flows in a two-dimensional rectangular cavity are simulated first to validate the numerical scheme. The numerical results agree well with those the Dijkstra and Molemaker and Quon and Ghil. Finally, the effect of the Lewis number on the flow system is investigated in detail. Depending on the value of the Lewis number, the flow pattern is either stable and symmetric, periodic and oscillatory, or unsymmetric and random.