@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.}
}