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

Alfredo Nicolás1, Blanca Bermúdez2
Depto. Matemáticas, UAM-I; 09340 México D:F:, México. E-mail:
F. C.C.,Benemérita Universidad Autónoma de Puebla; Puebla, Pue., México. E-mail:

Computer Modeling in Engineering & Sciences 2011, 82(3&4), 163-178.


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.


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

Cite This Article

Nicolás, A., Bermúdez, B. (2011). 2D Mixed Convection Viscous Incompressible Flows with Velocity-Vorticity Variables. CMES-Computer Modeling in Engineering & Sciences, 82(3&4), 163–178.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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