A COMPUTATIONAL MODELLING OF NAVIER STOKES EQUATION BY A PENALIZED FINITE ELEMENT FORMULATION
Liad Paskin1; José Luis Drummond Alves1; Carlos Eduardo da Silva1
1 LAMCE/PEC/COPPE/UFRJ
doi:10.20906/CPS/COB-2015-2200
Resumo
Engineering problems involving fluid flows are widely found in industrial fields, as for example: aeronautics, naval, chemistry, offshore, subsea, among others. Evaluation of physical quantities in a flow, such as pressure and velocities is a common practice in structure and equipment design. There are cases where the flow may exist in a level of complexity that doesn´t fit on the simplifications where analytical models rely, showing an engineering demand for experimental and numerical procedures. In this context, this work presents a numerical modelling technique for fluid mechanics, with particular attention to incompressible, two dimensional flows and Newtonian fluids. A numerical model was developed using a penalized, finite element formulation, able to treat mathematical difficulties of null divergence that translates the kinematic constraints of incompressibility. The implemented code employs quadratic triangular elements with reduced integration used for the penalized term, while full integration is used for the remaining. The convective term of the momentum conservation equation was linearly treated by the Picard method. Time discretization is accomplished by the finite difference method of Cranck Nicolson. Finally, numerical applications solved by the proposed model are presented, with particular attention to inner flow in a cavity and outer flow through the Von Karman Cylinder. Those applications showed good agreement to the available results in bibliography.
Palavras-chave: Penalized method; Incompressible flows; Computational Fluid Dynamics; Von Karman Vortex Street; Cavity flow