TY - JOUR
T1 - Decoupled, Energy Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential
AU - Jia , Hong-En
AU - Guo , Ya-Yu
AU - Li , Ming
AU - Huang , Yunqing
AU - Feng , Guo-Rui
JO - Communications in Computational Physics
VL - 4
SP - 1053
EP - 1075
PY - 2020
DA - 2020/02
SN - 27
DO - http://doi.org/10.4208/cicp.OA-2019-0034
UR - https://global-sci.org/intro/article_detail/cicp/14826.html
KW - Logarithmic potential, Cahn-Hilliard-Hele-Shaw, decoupling.
AB - <p style="text-align: justify;">In this paper, a decoupling numerical method for solving Cahn-Hilliard-Hele-Shaw system with logarithmic potential is proposed. Combing with a convex-splitting of the energy functional, the discretization of the Cahn-Hilliard equation in
time is presented. The nonlinear term in Cahn-Hilliard equation is decoupled from
the pressure gradient by using a fractional step method. Therefore, to update the pressure, we just need to solve a Possion equation at each time step by using an incremental
pressure-correction technique for the pressure gradient in Darcy equation. For logarithmic potential, we use the regularization procedure, which make the domain for
the regularized functional $F$($ф$) is extended from (−1,1) to (−∞,∞). Further, the stability and the error estimate of the proposed method are proved. Finally, a series of
numerical experiments are implemented to illustrate the theoretical analysis.</p>