A New Finite Element Formulation for Incompressible Flow

A basic objective in computational uid dynamics is the eecient solution of nonlinear systems of equations that arise in nite element modeling of convective-diiusive ow. The use of implicit Newton-like schemes to solve the coupled system of Navier-Stokes and continuity equations enables rapid convergence, although the well-known diiculty of indirect pressure linkage requires attention when forming the Jacobian matrices. Traditional approaches for overcoming this obstacle include reordering strategies, modiication of diagonal terms, and changes of variables. In contrast, we develop a primitive variable nite element formulation which employs an auxiliary pressure equation derived from the Navier-Stokes and continuity equations. This formulation extends the work of Rice and Schnipke, where a similar equation was developed in the context of a segregated solution method. Approximate Newton methods using the new nite element formulation are evaluated in terms of accuracy, convergence rate, and overall eeciency for ow problems with varying degrees of non-linearity.