TY - JOUR
T1 - An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions
JO - Communications in Computational Physics
VL - 3
SP - 640
EP - 664
PY - 2018
DA - 2018/03
SN - 23
DO - http://doi.org/10.4208/cicp.OA-2017-0090
UR - https://global-sci.org/intro/article_detail/cicp/10542.html
KW - Insoluble surfactant, a conservative scheme, mesh control, interfacial flow, Navier-Stokes flow, immersed boundary method.
AB - <p style="text-align: justify;">In this paper, an immersed boundary (IB) method for simulating the interfacial
flows with insoluble surfactant in three dimensions is developed. We consider a
doubly periodic interface separating two fluids where the surfactant exists only along
the evolving interface. An equi-arclength parametrization is introduced in order to
track the moving interface and maintain good Lagrangian meshes, so stable computations
can be performed without remeshing. This surface mesh-control technique
is done by adding two artificial tangential velocity components into the Lagrangian
marker velocity so that the Lagrangian markers can be equi-arclength distributed during
the time evolution. As a result, the surfactant equation on the interface must be
modified based on the new parametrization. A conservative scheme for solving the
modified surfactant equation has been developed and proved to satisfy the total surfactant
mass exactly in discrete level. A series of numerical experiments consisting of
the validation of Lagrangian mesh control technique, the convergence study, the study
of self-healing dynamics, and the simulations of two-layer fluids under Couette flow
have been conducted to test our present numerical scheme.</p>