A fractional four-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 fractional four-step methods is presented for the analyses of incompressible fluid how and heat transfer problems. The SUPG (streamline upwind Petrov-Galerkin) method is used for the weighted formulation of the Navier-Stokes equations. With the fractional four-step method, the memory and cost requirements of computations are significantly reduced because the pressure is split from the momentum equation. The pressure equation is derived from the mass conservation without any approximation procedure, such as adopted in the previously developed SIMPLE algorithm based finite element method. Therefore, the present numerical algorithm gives more accurate results than it does. Furthermore, the newly proposed pressure equation successfully treats the outflow boundary condition. The present algorithm has been applied to the well-known bench mark problems and proves to be efficient and accurate.