Level Set Calculations for Incompressible Two-Phase Flows on a Dynamically Adaptive Grid

We present a coupled moving mesh and level set method for computing incompressible two-phase flow with surface tension. This work extends a recent work of Di et al. [SIAM J. Sci. Comput., 26 (2005), pp. 1036-1056] where a moving mesh strategy was proposed to solve the incompressible Navier-Stokes equations. With the involvement of the level set function and the curvature of the interface, some subtle issues in the moving mesh scheme, in particular the solution interpolation from the old mesh to the new mesh and the choice of monitor functions, require careful considerations. In this work, a simple monitor function is proposed that involves both the level set function and its curvature. The purpose for designing the coupled moving mesh and level set method is to achieve higher resolution for the free surface by using a minimum amount of additional expense. Numerical experiments for air bubbles and water drops are presented to demonstrate the effectiveness of the proposed scheme.