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Hybrid Methods in Engineering

ISSN Imprimer: 1099-2391
ISSN En ligne: 2641-7359

Archives: Volume 1, 1999 to Volume 4, 2002

Hybrid Methods in Engineering

DOI: 10.1615/HybMethEng.v1.i4.30
26 pages

A PROJECTION METHOD COMBINED WITH A FINITE-VOLUME METHOD FOR UNSTEADY NAVIER-STOKES EQUATIONS COMPARED WITH BENCHMARK SOLUTIONS

J. E. Rengel Hernandez
Department of Mechanical Engineering, University of Oriente, Puerto La Cruz, Anzodtegui, Venezuela
Sergio Hamilton Sphaier
Ocean Engineering Department - EP/COPPE/UFRJ, CP50508, 21945-970, Rio de Janeiro, RJ, Brazil

RÉSUMÉ

The advance in the development of numerical methods in fluid flow problems is evident. Finite-difference, finite-volume, finite-element, spectral, and spectral element methods and generalized integral transform techniques are some of them to be mentioned. Nevertheless, limitations and difficulties persist. Herein one looks for the development of a procedure to simulate fluid problems in ocean engineering, in particular, vortex-induced vibrations due to the incidence of ocean currents about risers when installed in floating systems in deep waters to pipe oil from the sea floor to free surface equipment.
Having this objective, a numerical procedure to simulate the flow of incompressible viscous fluids around two-dimensional bluff bodies is presented. It is based on the projection method [1], combined with a finite-volume scheme in curvilinear coordinates having as independent variables the Cartesian velocity and pressure. Due to its splitting characteristic independent of the spatial discretization, the projection method can be associated to different numerical methods for the Burgers and for the Poisson equations.
To verify the accuracy and the efficiency of the procedure presented, it is applied to three problems with existing benchmark solutions and some experimental results containing characteristics such as recirculation, separation, change of contour form, and open boundaries. These are the vortex shedding behind a circular cylinder, the lid-driven cavity, and the backward-facing step. Particularly the fluid flow about a circular cylinder has a variety of applications in many different branches of engineering. The numerical results agree very well with the benchmark solutions.


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