High-order compact projection method for solving unsteady Navier-Stokes/Boussinesq equations

A new fourth-order combined compact upwind (CCU) scheme which improves the capability of capturing the small scale structures greatly was employed for solving the NavierStokes/Boussinesq equations based on the projection method. The method was employed to conduct the numerical study of natural convection and the associated mode-transition in a two-dimensional differentially heated inclined enclosure. The Boussenesq air flow with the Prandtl number Pr = 0.71 was chosen as the flow model to examine the effect of the inclination at various Rayleigh numbers in the enclosure of As = 4. The angle of inclination of enclosure satisfying 0 degrees <= gamma <= 90 degrees and Rayleigh number satisfying 1500 <= Ra <= 10(5), and the steady flow was treated in simulation. The results are good agreement with those reported. In general, the present study provides an effective way to understand the physical mechanism of the natural convection in enclosures.