Adaptive numerical methods for fluid mechanics

The equations of fluid mechanics can be used to describe natural
processes over a wide range of scales, from the behaviour of
micro-organisms to astrophysics. Each of these processes is in
turn often controlled by internal interactions on widely
different scales.  Numerical methods able to efficiently resolve
these interactions are -- in combination with theoretical analysis
and lab experiments -- an essential tool for advancing our
understanding.  I will give a general overview of the
hierarchical numerical methods I have worked on, as implemented
within the free software Gerris Flow Solver (http://gfs.sf.net)
and Basilisk (http://basilisk.fr)
and discuss a range of applications including microscale
high-energy droplet dynamics, multiphase and complex flows, tsunamis and
climate dynamics.