NUMERICAL STUDY OF 3-DIMENSIONAL INCOMPRESSIBLE THERMAL-FLOWS IN COMPLEX GEOMETRIES .1. THEORY AND BENCHMARK SOLUTIONS

In part I uses an iterative point successive over-relaxation (PSOR) fi nite difference scheme to solve the coupled unsteady Navier-Stokes and energy equations for incompressible, viscous and laminar flows in the ir primitive variable form. Presents the details concerning the deriva tion of the solution scheme, as well as details on its computer implem entation. For validation purposes, includes the results of the two-dim ensional and three-dimensional benchmark problem of natural convection in a cavity with differentially heated vertical walls. Benchmark comp utations have been performed for a Prandtl number of 0.71, and differe nt values of the Rayleigh number ranging between 10(3) and 10(6) depen ding on the problem. By comparison with other approaches in the litera ture, the scheme has been found to be accurate even for large Rayleigh numbers.