Numerical study of three-dimensional incompressible thermal flows in complex geometries .1. Theory and benchmark solutions

In part I uses an iterative point successive over-relaxation (PSOR) finite difference scheme to solve the coupled unsteady Navier-Stokes and energy equations for incompressible, viscous and laminar flows in their primitive variable form. Presents the details concerning the derivation of the solution scheme, as well as details on its computer implementation. For validation purposes, includes the results of the two-dimensional and three-dimensional benchmark problem of natural convection in a cavity with differentially heated vertical walls. Benchmark computations have been performed for a Prandtl number of 0.71, and different values of the Rayleigh number ranging between 10(3) and 10(6) depending on the problem. By comparison with other approaches in the literature, the scheme has been found to be accurate even for large Rayleigh numbers.