Implicit Time-Discretization of the Nonstationary Incompressible Navier-Stokes Equations

This paper deals with implicit time-discretization of the nonstationary incompressible Navier-Stokes equations. The emphasis is on the so-called “fractional-step-e-scheme” in which the incompressibility constraint is treated either fully implicitly or semi-implicitly by employing operator splitting (projection method). Recently a complete mathematical analysis has become available for methods of this type which supports current computational experience. The fractional-step-θ-scheme has proven to be a robust and accurate time-stepping method which is in several respects superior to the traditional Crank-Nicolson scheme. Combined with operator splitting it is particularly suitable for the long time computation of complex flows.

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