Solving 2-D buoyancy-driven cavity flow on collocated meshes by perturbational finite volume scheme

The buoyancy-driven cavity flow in the case ofRa=10^3 to Ra=10^8 is numerically simulated with the upwind typeof perturbation finite volume (UPFV) scheme for the convective and diffusiveequations initiated by the second author. The UPFV scheme for diffusive andconvective equations takes the same concise expressions and uses thesame nodes as the upwind scheme of the first order and high approximateaccuracy of reconstruction can be achieved. Especially, theUPFV scheme is identical for uniform grid and non-uniform grid regardlessof the distance from the CV center to the common face. The results of numericalsimulations to buoyancy-driven cavity flows by UPFV are consistent withthese by spectral method and finite element method and DSC in the range from Ra=10^3 toRa=10^8 with uniform or non-uniform structured grid. It shows that thePFV scheme is valid and can be applied for the heat convection and transferproblems.