Level Set Calculations for Incompressible Two - Phase 1 Flows on a Dynamically Adaptive Grid

We present a coupled moving mesh and level set method for computing incom5 pressible two-phase flow with surface tension. This work extends a recent work 6 of Di et al. [(2005). SIAM J. Sci. Comput. 26, 1036–1056] where a moving 7 mesh strategy was proposed to solve the incompressible Navier–Stokes equa8 tions. With the involvement of the level set function and the curvature of the 9 interface, some subtle issues in the moving mesh scheme, in particular the solu10 tion interpolation from the old mesh to the new mesh and the choice of mon11 itor functions, require careful considerations. In this work, a simple monitor 12 function is proposed that involves both the level set function and its curvature. 13 The purpose for designing the coupled moving mesh and level set method is to 14 achieve higher resolution for the free surface by using a minimum amount of 15 additional expense. Numerical experiments for air bubbles and water drops are 16 presented to demonstrate the effectiveness of the proposed scheme. 17