High accuracy numerical investigation of double-diffusive convection in a rectangular enclosure with horizontal temperature and concentration gradients

Double-diffusive convection of a binary mixed fluid in a rectangular enclosure with horizontal temperature and concentration gradients is numerically investigated. The problem with thermal Rayleigh numbers of 104 and 105, the Prandtl number being range of [0.015, 12], the Lewis number being range of [0.05, 100], the buoyancy ratio of 0.8, and the height-to-width aspect ratio of 2 are considered. A compact difference method with fully fourth-order accuracy and high resolution in space, involving a, at least, fourth-order upwind compact scheme suggested for approximation of the nonlinear convective terms, a fourth-order symmetrical compact scheme to discretize the viscous terms and the third-order TVD Runge-Kutta method employed for time discretization, is proposed for solving this unsteady double-diffusive convection problem. The effects of Prandtl and Lewis numbers on flow structure, the temperature and concentration distribution are investigated and discussed for Ra=104 and 105 respectively in a rectangular enclosure with the aspect ratio A=2. A bifurcation for the double-diffusive convection is captured with the variation of Prandtl number, and two different types of periodic flow motion with Lewis number in different ranges are observed.