Decoupled, Energy Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System with Logarithmic Flory-Huggins Potential

In this paper, a decoupling numerical method for solving Cahn-HilliardHele-Shaw system with logarithmic potential is proposed. Combing with a convexsplitting 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(phi) is extended from ( -1,1) to ( -infinity, infinity). 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.