Numerical simulation of cavity flow by using conforming and nonconforming finite elements

Abstract

This thesis presents a numerical method for solving the incompressible flow in a square cavity without smoothing the corner singularities. Since nonconforming finite element method can avoid vertex degree of freedom, the values at the upper corners of the cavity are not required to solve the problem. By taking this advantage it is possible to compute accurate numerical solution of the cavity flow without any modification of the problem. The stable nonconforming P1-P0 pair used to solve the incompressible flow problem. DSSY finite elements are added to elements which are on the top corners in the cavity to obtain a more accurate approximation of the boundary condition. Numerical solutions by using conforming finite element are computed for the purposes of comparison. The numerical results are compared with those in the literature and show good agreement. Numerical results computed by using the stable nonconforming P1-P0 pair show excellent accuracy.