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Boussinesq Algorithm for Buoyant Convection in Polygonal Domains.



Kevin B. McGrattan, Ronald G. Rehm, Hai C. Tang, Howard R. Baum


A 2-D Boussinesq model describing heat-driven buoyant convection in a polygonal enclosure is presented. The hydrodynamics is based on the time-dependent Navier-Stokes equations with constant viscosity and thermal conductivity; no turbulence model or other empirical parameters are introduced. The polygonal domain is mapped via a Schwarz-Christoffel transformation onto a rectangle. A finite difference scheme second-order in space and first-order in time is used to integrate the evolution equations, and an elliptic solver is used to solve the pressure equation. Computational results for high Reynolds numbers are presented through the use of Lagrangian particles which allow one to visualize the flow patterns.
NIST Interagency/Internal Report (NISTIR) - 4831
Report Number


bossinesq approximation, algorithms, convection, computational fluid dynamics, mapping, thermal conductivity


McGrattan, K. , Rehm, R. , Tang, H. and Baum, H. (1992), Boussinesq Algorithm for Buoyant Convection in Polygonal Domains., NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed July 13, 2024)


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Created April 1, 1992, Updated June 2, 2021