Streamfunction-velocity computation of natural convection around heated bodies placed in a square enclosure

Abstract

In the study of natural convection around embedded bodies in a square enclosure, most of the previous studies have used the primitive variable or the streamfunction-vorticity(ψ−ω) form of the Navier-Stokes (N-S) equations along with grid transformation for the computations. In the current study, we reconstruct a recently developed compact finite difference scheme for the biharmonic form of the N-S equations and combine it with a high order compact (HOC) scheme for the energy equation to compute the flow around heated circular and diamond cylinders inside a square enclosure. Our computed results on nonuniform grids without transformation are excellent match with available numerical results for both adiabatic and isothermal walls of the square. In the process, we have also been able to capture flow structures for certain configurations and range of parameters that were not reported earlier in the existing literature.