Open Access

ARTICLE

2D Mixed Convection Viscous Incompressible Flows with Velocity-Vorticity Variables

Alfredo Nicolás¹, Blanca Bermúdez²
1 Depto. Matemáticas, UAM-I; 09340 México D:F:, México. E-mail: anc@xanum.uam.mx
2 F. C.C.,Benemérita Universidad Autónoma de Puebla; Puebla, Pue., México. E-mail: bbj@solarium.cs.buap.mx

Computer Modeling in Engineering & Sciences 2011, 82(3&4), 163-178. https://doi.org/10.32604/cmes.2011.082.163

Abstract

Mixed convection viscous incompressible fluid flows, under a gravitational system, in rectangular cavities are reported using the unsteady Boussinessq approximation in velocity-vorticity variables. The results are obtained using a numerical method based on a fixed point iterative process to solve the nonlinear elliptic system that results after time discretization; the iterative process leads to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems for which efficient solvers exist regardless of the space discretization. Results with different aspect ratios A up to Grashof numbers Gr = 100000 and Reynolds numbers Re = 1000 for the lid driven cavity problem are reported. The validation of the results is given through mesh size and time-step independence studies.

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Keywords

velocity-vorticity formulation, mixed convection flows, aspect ratio, Reynolds and Grashof numbers, fixed point iterative process

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