The Computation of Fluid Velocity in A Closed Cavity with A Moving Lid

Authors

Daniel A. Montez, University of Texas-Pan American

Date of Award

12-2013

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Dambaru Bhatta

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Paul Bracken

Abstract

We consider a cavity filled with fluid whose three sides are stationary and the lid at the top is moving at a constant speed. 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. We seek the weak formulation and develop a finite element model based on the Galerkin method. Furthermore we use the penalty function method to modify our weak formulation to eliminate the pressure. The Gaussian quadrature method is used to evaluate our integrals over the elements. We present numerical results for two cases. In the first case we consider a square cavity in shape while in the second case we consider a semi-elliptical bump protruding from the bottom. We present our results in tabular and graphical forms.

Comments

Copyright 2013 Daniel A. Montez. All Rights Reserved.

https://www.proquest.com/dissertations-theses/computation-fluid-velocity-closed-cavity-with/docview/1501926355/se-2

Granting Institution

University of Texas-Pan American