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COBEM 2021
26th International Congress of Mechanical Engineering
ON THE USE OF STABILIZATION SCHEMES IN COLLOCATED GRIDS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
Submission Author:
Gustavo Choaire , SC
Co-Authors:
Gustavo Choaire, Antonio Fábio Carvalho da Silva, Clovis Maliska, Gustavo Paul Exel
Presenter: Gustavo Choaire
doi://10.26678/ABCM.COBEM2021.COB2021-0209
Abstract
The solution of the momentum conservation equations coupled with the mass conservation equation for incompressible flows plays an important role on Computational Fluid Dynamics (CFD). Numerous studies have shown different ways of dealing with the pressure-velocity coupling inherent to these set of equations while using segregated methods of solution and collocated variables. It is well documented that the pressure checkerboard problem arises when the collocated variable arrangement is used, since the nodal velocities are not located where they are need for the mass conservation balance. Thus, several stabilization schemes are reported in the literature with the purpose of preventing the oscillatory pressure fields. It is not clear, however, if these stabilization schemes are really needed, opposed to a simple nodal averaging velocity, if the system is solved simultaneously. It is fully reported in the literature the need of introducing the pressure in the mass conservation equation to avoid a zero diagonal in the linear system of equation. The first part of this study, shown in this paper, is concerned with the analysis of using weighted average of nodal velocities or a stabilization scheme for calculating the convecting velocity (mass flow) in conjunction with simultaneous solution. For the analysis, as prototype of a stabilization scheme, the Physical Influence Scheme (PIS) is used. The bidimensional lid-driven cavity flow problem, a widely known benchmark, was used. The results shows a good agreement of the velocity fields using average nodal velocities for the calculation of the advecting velocities. The results were also compared with the staggered grid arrangement, known for eliminating the spurious pressure oscillations.
Keywords
Incompressible Flow, Collocated grid, Fully coupled, Weighted average velocities, Cell-face velocities
