Finite Element Analysis and Program for Stokes Fluid Flow

The theory and computer program for finite element analysis of Stokes (creeping) fluid flow is presented. The element is an eight node, two dimensional isoparametric quadrillateral. The element is formulated directly from the Stokes equations of motion, a special case of the Navier-Stokes equations where inertia terms are dropped, using the method of weighted residuals with Galerkin's criterion applied. Velocities in two directions are solved for at all eight nodes while pressure is solved simultaneously at the four corner nodes only. Several test cases have been run with the program. Very good accuracy was achieved in modeling velocity profiles for Couette and Poiseulle . f low and for pressure distribution of two lubrication models. In these four cases error was less than l\%. Limitations have been pointed out for the types of flow which may be successfully modeled. Flow between two concentric cylinders had an error of 31% between the finite element and exact solutions. Cascades of cylinders and turbine blades are modeled by modeling only one cylinder or blade. The cascade of turbine blades serves to illustrate the potential uses of this technique.