Implicit Algorithms and their Linearisation for the Transient Incompressible Navier-Stokes Equations

The issue of appropriate time discretisation methods for the unsteady incompress-ible Navier-Stokes equations is considered from a practical perspective here. Conventional implicit time-stepping algorithms are not feasible for long time simulations since they inherit the quadratic nonlinearity of the steady-state equations. As a result linearised versions of the \pure" algorithms are analysed herein. These have similar stability properties and comparable accuracy to the underlying nonlinear methods.