Finite-Element Solution of the Incompressible Navier-Stokes Equations

A finite-element procedure is presented for the calculation of two-dimensional, viscous, incompressible flows of a recirculating nature. As in finite-difference procedures, velocity and pressure are uncoupled and the equations are solved one after the other. Velocity fields are determined by first calculating intermediate velocity values based on an estimated pressure distribution and then obtaining appropriate corrections to satisfy the continuity equation. Illustrative examples involving flow in the entrance region between parallel plates, lid-driven cavity flow, and flow around an obstacle demonstrate the accuracy and capabilities of the proposed technique.