@TechReport{	  it:2004-030,
  author	= {Wendy Kress and Per L{\"o}tstedt},
  title		= {Time Step Restrictions using Semi-Implicit Methods for the
		  Incompressible Navier-Stokes Equations},
  institution	= {Department of Information Technology, Uppsala University},
  department	= {Division of Scientific Computing},
  year		= {2004},
  number	= {2004-030},
  month		= jul,
  abstract	= {The incompressible Navier-Stokes equations are discretized
		  in space and integrated in time by the method of lines and
		  a semi-implicit method. In each time step a set of systems
		  of linear equations has to be solved. The size of the time
		  steps are restricted by stability and accuracy of the
		  time-stepping scheme, and convergence of the iterative
		  methods for the solution of the systems of equations. The
		  stability is investigated with a linear model equation
		  derived from the Navier-Stokes equations. The resolution in
		  space and time is estimated from turbulent flow physics.
		  The convergence of the iterative solvers is studied using
		  the same model equation. The stability constraints and the
		  convergence rate obtained from the model equation are
		  compared to results for a semi-implicit integrator of the
		  Navier-Stokes equations with good agreement. The most
		  restrictive bound on the time step is given by accuracy,
		  stability, or convergence depending on the flow conditions
		  and the numerical method.}
}