Implicit algorithms and their linearization for the transient incompressible Navier-Stokes equations

The issue of appropriate time discretization methods for the unsteady incompressible Navier-Stokes equations is considered from a practical perspective. 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, two new linearized versions of the ‘pure’ algorithms are analyzed herein. These have similar stability properties and comparable accuracy to the underlying nonlinear methods.