A fractional-step Taylor-Galerkin method for unsteady incompressible flows

This paper describes the application of the Taylor-Galerkin method to the calculation of incompressible viscous flows. A finite element fractional-step method for the Navier-Stokes equations is combined with the Taylor-Galerkin method to achieve an accurate treatment of the convection part of the problem. A scheme of second-order accuracy in time for the nonlinear convection written in nonconservative form is presented. Numerical results are provided to illustrate the quality of the computed transient solutions in two dimensions.