An adaptive mesh algorithm for evolving surfaces: Simulations of drop breakup and coalescence

An algorithm is presented for the adaptive restructuring of meshes on evolv ing surfaces. The resolution of the relevant local length scale is maintain ed everywhere with prescribed accuracy through the minimization of an appro priate mesh energy function by a sequence of local restructuring operations . The resulting discretization depends on the instantaneous configuration o f the surface but is insensitive to the deformation history. Application of the adaptive discretization algorithm is illustrated with three-dimensiona l boundary-integral simulations of deformable drops in Stokes flow. The res ults show that the algorithm can accurately resolve detailed features of de formed fluid interfaces, including slender filaments associated with drop b reakup and dimpled regions associated with drop coalescence. Our algorithm should be useful in a variety of fields, including computational fluid dyna mics, image processing, geographical information systems, and biomedical en gineering problems. (C) 2001 Academic Press.