Buoyant Convection Computed in a Vorticity, Stream-Function Formulation

Model equations describing large scale buoyant convection in an enclosure are formulated with the vorticity and stream function as dependent variables. The mathematical model, based on earlier work of the authors, is unique in two respects. First, it neglects viscous and thermal conductivity effects. Second the fluid is taken to be thermally expandable: large density variations are allowed while acoustic waves are filtered out. A volumetric heat source of specified spatial and temporal variation drives the flow in a two-dimensional rectangular enclosure. An algorithm for solution of the equations in this voticity, stream-function formulation is presented. Results of computations using this algorithm are presented. Comparison of these results with those obtained earlier by the authors using a finite difference code to integrate the primitive equations show excelent agreement. A method for periodically smoothing the computational results during a calculation, using Lanczos smoothing, is also presented. Computations with smoothing at different time intervals are presented and discussed.