TY - JOUR
T1 - Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model
AU - Qin , Yuzhe
AU - Xu , Zhen
AU - Zhang , Hui
AU - Zhang , Zhengru
JO - Communications in Computational Physics
VL - 4
SP - 1389
EP - 1414
PY - 2020
DA - 2020/08
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2019-0175
UR - https://global-sci.org/intro/article_detail/cicp/18105.html
KW - Binary fluid-surfactant, scalar auxiliary variable approach, unconditional energy stability, linear scheme, decoupled.
AB - <p style="text-align: justify;">Here, we develop a first and a second order time stepping schemes for a binary fluid-surfactant phase field model by using the scalar auxiliary variable approach.
The free energy contains a double-well potential, a nonlinear coupling entropy and a
Flory-Huggins potential. The resulting coupled system consists of a Cahn-Hilliard
type equation and a Wasserstein type equation which leads to a degenerate problem.
By introducing only one scalar auxiliary variable, the system is transformed into an
equivalent form so that the nonlinear terms can be treated semi-explicitly. Both the
schemes are linear and decoupled, thus they can be solved efficiently. We further prove
that these semi-discretized schemes in time are unconditionally energy stable. Some
numerical experiments are performed to validate the accuracy and energy stability of
the proposed schemes.</p>