The description of the flow that takes place in clarifiers and other wastewater treatment basins may be a powerful tool to attain an optimum design of these structures, in order to make the most of the wastewater treatment plant resources. Some authors have attempted so by making use of the potential flow or the Stokes equations. Whan these simplifications are used, an approximation of the flow for slow creeping conditions is obtained, but only the resolution of the all-term-including Navier-Stokes equations will allow us to detect the real streamlines and the vortices that show up for even very slow water flows. The use of the Navier-Stokes formulae as the governing equations involves the appearance of complex stability problems that do not show up for the previously mantioned simplifications. In the present work a stable finite element method for the resolution of the Navier-Stokes equations is presented, verified, and used in the resolution of some wasterwater treatment flow problems with very interesting results.
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