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 -

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.