A finite element method for three dimensional cavity circulation
Abstract
A three dimensional finite element model was developed. It successfully predicts the velocity distribution in a rectangular cavity. The model is basically set up by the Galerkin, weighted residual method with the discretization of twentynode elements in brick shape. Two approaches were studied. One is the penalty function method which also incorporated the continuation method when the nonlinear convective term is considered. Another approach is called the mixed interpolation method. The penalty function method was shown to be the better of the two. The resulting flow velocity compares favorable with existing numerical models. One main contribution is that flexible parameters including the artificial viscosity, element size and velocity gradient on the free surface were all included in the model as nondimensional functions. Also the effect of grid refinement was shown. The second principal contribution is that the approximate numerical integration for the pressure term is two orders lower than the exact integration, instead of the usual one order lower procedure.
 Publication:

Ph.D. Thesis
 Pub Date:
 February 1984
 Bibcode:
 1984PhDT........36C
 Keywords:

 Cavities;
 Computational Fluid Dynamics;
 Finite Element Method;
 Flow Velocity;
 Computational Grids;
 Galerkin Method;
 Interpolation;
 Numerical Integration;
 Penalty Function;
 Three Dimensional Models;
 Velocity Distribution;
 Viscosity;
 Fluid Mechanics and Heat Transfer