The study of incompressible ?ows is vital to many areas of science and
te- nology. This includes most of the ?uid dynamics that one ?nds in
everyday life from the ?ow of air in a room to most weather phenomena.
Inundertakingthesimulationofincompressible?uid?ows, oneoftentakes many
issues for granted. As these ?ows become more realistic, the problems
encountered become more vexing from a computational point-of-view. These
range from the benign to the profound. At once, one must contend with
the basic character of incompressible ?ows where sound waves have been
analytically removed from the ?ow. As a consequence vortical ?ows have
been analytically "preconditioned," but the ?ow has a certain
non-physical character (sound waves of in?nite velocity). At low speeds
the ?ow will be deterministic and ordered, i.e., laminar. Laminar ?ows
are governed by a balance between the inertial and viscous forces in the
?ow that provides the stability. Flows are often characterized by a
dimensionless number known as the Reynolds number, which is the ratio of
inertial to viscous forces in a ?ow. Laminar ?ows correspond to smaller
Reynolds numbers. Even though laminar ?ows are organized in an orderly
manner, the ?ows may exhibit instabilities and bifurcation phenomena
which may eventually lead to transition and turbulence. Numerical
modelling of
suchphenomenarequireshighaccuracyandmostimportantlytogaingreater insight
into the relationship of the numerical methods with the ?ow physics.
