Numerical Simulations of Free-Surface Incompressible Flows: Theory and Practice

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.