New finite element computational strategies for free-surface flows,
two-liquid flows, and flows with drifting cylinders are presented. These
strategies are based on the DSD/ST (Deforming-Spatial-Domain/Space-Time)
procedure. In the DSD/ST approach, the variational formulations for this
type of flow problems are written over their space-time domains. One of
the important features of the approach is that it enables one to
circumvent the difficulty involved in remeshing every time step and thus
reduces the projection errors introduced by such frequent remeshings.
Computations are performed for various test problems mainly for the
purpose of demonstrating the computational capability developed for this
class of problems. In some of the test cases, such as the liquid drop
problem, surface tension is taken into account. For flows involving
drifting cylinders, the mesh moving and remeshing schemes proposed are
convenient and reduce the frequency of remeshing.