Decoupled, Energy Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential (Communications in Computational Physics, 2020)
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 intime is presented. The nonlinear term in Cahn-Hilliard equation is decoupled fromthe 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 incrementalpressure-correction technique for the pressure gradient in Darcy equation. For logarithmic potential, we use the regularization procedure, which make the domain forthe 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 ofnumerical experiments are implemented to illustrate the theoretical analysis.
Keywords: Logarithmic potential; Cahn-Hilliard-Hele-Shaw; decoupling.