Numerical Simulations of Free-Surface Incompressible Flows

This research monograph is an excellent resource for
graduate students and senior researchers in the area
of Computational Fluid Dynamics. It develops a
numerical method for computer simulations of
multi-component flows involving capillary free
surfaces, and provides detailed algorithm
implementation notes in two and three dimensions. The
monograph
also contains a comprehensive review of relevant
solution methods for the incompressible Navier-Stokes
equations and techniques for managing moving boundaries.

Chapter one introduces a new projection method
for the incompressible Navier-Stokes equations. The
normally coupled velocity and pressure are split and
solved for in two separate steps using a low-order
Finite Element. The proposed method guarantees exact
local mass conservation at a reduced computational
cost. Chapter two presents an innovative technique to
track free-moving interfaces. The technique modifies
the computational grid in the vicinity of each
interface to avoid computational cells intersected by
the interface while preserving the connectivity of
the mesh.