A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method

A generalized-α method is developed and analyzed for linear, first-order systems. The method is then extended to the filtered Navier-Stokes equations within the context of a stabilized finite element method. The formulation is studied through the application to laminar flow past a circular cylinder and turbulent flow past a long, transverse groove. The method is formulated to obtain a second-order accurate family of time integrators whose high frequency amplification factor is the sole free parameter. Such an approach allows the replication of midpoint rule (zero damping), Gear’s method (maximal damping), or anything in between.