NUMERICAL SOLUTION OF PROBLEMS IN INCOMPRESSIBLE FLUID FLOW: TREATMENT OF THE TEMPERATURE-VELOCITY COUPLING

Abstract

The cost of obtaining solutions to fluid flows depends strongly on how well the solution procedure treats the interequation couplings. For natural convection flows, treatment of the temperature-velocity coupling is often of the utmost importance. The first purpose of the present paper is to report the conditions under which the temperature-velocity coupling is important in natural convection flows, and the improvement in convergence rate that may be achieved by implicitly accounting for this coupling within the discrete equations of motion. It is shown that the strength of the coupling depends on the Prandtl number, and that substantial acceleration of the convergence rate can be achieved by appropriate treatment of the coupling. To translate improved convergence rate into computational savings requires that an efficient method be found for solution of the coupled linear set of equations. The second purpose of the paper is to present such a method, and to report the computation effort required to obtain solutions to the nonlinear set of equations with this solver compared to “standard” methods.