an:06760785
Zbl 06760785
Han, Daozhi
A decoupled unconditionally stable numerical scheme for the Cahn-Hilliard-Hele-Shaw system
EN
J. Sci. Comput. 66, No. 3, 1102-1121 (2016).
00354510
2016
j
65M60 65M12 76T99 76D27 76S05 35J05 35Q35
Cahn-Hilliard-Hele-Shaw; decoupling; unconditional stability; convex-splitting; operator-splitting
Summary: We propose a novel decoupled unconditionally stable numerical scheme for the simulation of two-phase flow in a Hele-Shaw cell which is governed by the Cahn-Hilliard-Hele-Shaw system (CHHS) with variable viscosity. The temporal discretization of the Cahn-Hilliard equation is based on a convex-splitting of the associated energy functional. Moreover, the capillary forcing term in the Darcy equation is separated from the pressure gradient at the time discrete level by using an operator-splitting strategy. Thus the computation of the nonlinear Cahn-Hilliard equation is completely decoupled from the update of pressure. Finally, a pressure-stabilization technique is used in the update of pressure so that at each time step one only needs to solve a Poisson equation with constant coefficient. We show that the scheme is unconditionally stable. Numerical results are presented to demonstrate the accuracy and efficiency of our scheme.