An adaptive meshfree method for phase-field models of biomembranes. Part II: A Lagrangian approach for membranes in viscous fluids

摘要: We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in viscous fluid. In contrast previous approaches, where field variables are and fluid velocity, here we exploit fact that tracks material interface reformulate problem terms motion background medium, containing both biomembrane discretize equations space with maximum-entropy approximants, carefully shown perform well models biomembranes companion paper. The proposed formulation is variational, lending itself implicit time-stepping algorithms based on minimization time-incremental energy, which automatically nonlinearly stable. deals two major challenges numerical treatment coupled fluid/phase-field biomembranes, namely adaptivity grid resolve sharp features phase-field, stiffness equations, leading very small time-steps. our method, local refinement follows as advected by motion, large time-steps can be robustly chosen variational algorithm, also lends time adaptivity. presented axisymmetric setting, but it directly extended 3D.