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Flow in a closed rectangular cavity with a moving lid and a dent at the bottom

Daniel Montez, Dambaru Bhatta

Abstract


We consider a rectangular cavity filled with viscous, incompressible, Newtonian fluid with three stationary sides and the lid on the top is moving at a constant speed. The bottom of the cavity has an elliptical dent at the center. The flow in the cavity is modeled using the conservation of mass and momentum equations with proper boundary conditions. We compute the fluid velocity for the steady state case using the finite element method. The penalty function method is used to obtain the weak formulation by eliminating the pressure. The Gaussian quadrature method is used to evaluate the integrals for the elements. We analyze the effect on the flow due to the presence of the dent using numerical results obtained for the velocity components.

Keywords


fluid flow, finite element, penalty method, viscous, Gaussain quadrature.

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