Finite element analysis for the navier - stokes equations

Abstract

The finite element method was employed to solve two-dimensional, unsteady, incompressible, viscous fluid flow problems. A practical computation procedure is presented. A complete finite element computer program has been developed. The numerical technique is based upon a general formulation for the Navier-Stokes equations making use of a combined variational principle finite element approach. Solution to the system of algebraic equations is approached by the Gaussian elimination scheme. The time-dependent Navier-Stokes equations are expressed in terras of a stream function equation and a transport equation. A variational functional of the stream function and a pseudo-variational functional of the vorticity of the respective boundary value problem is presented. The pressure distribution and velocity profile are determined from stream function. Two numerical examples are presented and compared with present papers. Some now ideas about the numerical method, obtained through numerical experiments, are presented and discussed.