On the solution of the time-dependent incompressible Navier-Stokes equations via a penalty Galerkin finite element method.

The existence of an initial non-physical transient when using the penalty method in modelling the time-dependent incompressible Navier-Stokes equations is investigated theoretically and demonstrated numerically using the Galerkin finite element technique. A stable, variable step time integration scheme which can 'overlook' the initial non-physical transient while using 'reasonable-sized' time steps is described. Numerical examples illustrating the time integration scheme and concomitantly the difference in transient response of an incompressible fluid and its slightly compressible (penalty) analog are presented. (A)