A FRACTIONAL 4-STEP FINITE-ELEMENT FORMULATION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS USING SUPG AND LINEAR EQUAL-ORDER ELEMENT METHODS

A numerical algorithm using equal-order linear finite element and frac tional four-step methods is presented for the analyses of incompressib le fluid how and heat transfer problems. The SUPG (streamline upwind P etrov-Galerkin) method is used for the weighted formulation of the Nav ier-Stokes equations. With the fractional four-step method, the memory and cost requirements of computations are significantly reduced becau se the pressure is split from the momentum equation. The pressure equa tion is derived from the mass conservation without any approximation p rocedure, such as adopted in the previously developed SIMPLE algorithm based finite element method. Therefore, the present numerical algorit hm gives more accurate results than it does. Furthermore, the newly pr oposed pressure equation successfully treats the outflow boundary cond ition. The present algorithm has been applied to the well-known bench mark problems and proves to be efficient and accurate.