Comparison between advected-field and level-set methods in the study of vesicle dynamics

► Phase-field and level-set modeling of phospholipidic vesicles in shear flow are compared. ► Careful and rigorous derivation of Euler-Lagrange equation in the level-set setting is carried out. ► Differences in the ways of handling the surface incompressibility are stressed. ► Links between the two approaches are expressed as a choice of constitutive law. ► Numerical simulations with the level-set approach are proposed and compared with previous studies.