A Decoupled Unconditionally Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System
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.
D. Han, "A Decoupled Unconditionally Stable Numerical Scheme for the Cahn-Hilliard-Hele-Shaw System," Journal of Scientific Computing, vol. 66, no. 3, pp. 1102-1121, Springer Verlag, Mar 2016.
The definitive version is available at https://doi.org/10.1007/s10915-015-0055-y
Mathematics and Statistics
Keywords and Phrases
Nonlinear equations; Poisson equation; Convex-splitting; Decoupling; Hele-Shaw; Operator-splitting; Unconditional stability; Two phase flow; Cahn-Hilliard-Hele-Shaw
International Standard Serial Number (ISSN)
Article - Journal
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01 Mar 2016