TY - JOUR
T1 - An Unconditionally Energy Stable Immersed Boundary Method with Application to Vesicle Dynamics
AU - Wei-Fan Hu & Ming-Chih Lai
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 247
EP - 262
PY - 2018
DA - 2018/02
SN - 3
DO - http://doi.org/10.4208/eajam.250713.150813a
UR - https://global-sci.org/intro/article_detail/eajam/10857.html
KW - Immersed boundary method, unconditionally energy stable, inextensible vesicle, Navier-Stokes flow.
AB - <p style="text-align: justify;">We develop an unconditionally energy stable immersed boundary method,
and apply it to simulate 2D vesicle dynamics. We adopt a semi-implicit boundary forcing
approach, where the stretching factor used in the forcing term can be computed from
the derived evolutional equation. By using the projection method to solve the fluid
equations, the pressure is decoupled and we have a symmetric positive definite system
that can be solved efficiently. The method can be shown to be unconditionally stable, in
the sense that the total energy is decreasing. A resulting modification benefits from this
improved numerical stability, as the time step size can be significantly increased (the
severe time step restriction in an explicit boundary forcing scheme is avoided). As an
application, we use our scheme to simulate vesicle dynamics in Navier-Stokes flow.</p>