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Buoyant Convection Computed in a Vorticity, Stream-Function Formulation

Ronald G Rehm¹, Howard R Baum¹, P Darcy Barnett¹

¹National Bureau of Standards, Washington, DC 20234.

Journal of Research of the National Bureau of Standards (1977)

|September 27, 2021

Abstract:

Model equations describing large scale buoyant convection in an enclosure are formulated with the vorticity and stream function as dependent variahles. 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 vorlicily, 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 excellent 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.

Keywords:

Lanezos smoothing buoyant convection finite difference computations fire-enclosure fluid flow partial differential equations stream function vorticity

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Articles linked to this work by shared authors, journal, and citation graph.

The Equations of Motion for Thermally Driven, Buoyant Flows.

Journal of research of the National Bureau of Standards (1977)·2021

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