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Journal of Scientific Computing

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13.06.2015

A Decoupled Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Hele-Shaw System

verfasst von: Daozhi Han

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2016

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Abstract

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.

Vorheriger Artikel Spectral Method For Navier–Stokes Equations With Non-slip Boundary Conditions By Using Divergence-Free Base Functions

Nächster Artikel Some Non-monotone Schemes for Time Dependent Hamilton–Jacobi–Bellman Equations in Stochastic Control

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Titel: A Decoupled Unconditionally Stable Numerical Scheme for the Cahn–Hilliard–Hele-Shaw System
verfasst von: Daozhi Han
Publikationsdatum: 13.06.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-015-0055-y

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