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Erschienen in: Journal of Scientific Computing 3/2018

24.07.2017

Numerical Approximations for the Cahn–Hilliard Phase Field Model of the Binary Fluid-Surfactant System

verfasst von: Xiaofeng Yang

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2018

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Abstract

In this paper, we consider the numerical approximations for the commonly used binary fluid-surfactant phase field model that consists two nonlinearly coupled Cahn–Hilliard equations. The main challenge in solving the system numerically is how to develop easy-to-implement time stepping schemes while preserving the unconditional energy stability. We solve this issue by developing two linear and decoupled, first order and a second order time-stepping schemes using the so-called “invariant energy quadratization” approach for the double well potentials and a subtle explicit-implicit technique for the nonlinear coupling potential. Moreover, the resulting linear system is well-posed and the linear operator is symmetric positive definite. We rigorously prove the first order scheme is unconditionally energy stable. Various numerical simulations are presented to demonstrate the stability and the accuracy thereafter.

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Metadaten
Titel
Numerical Approximations for the Cahn–Hilliard Phase Field Model of the Binary Fluid-Surfactant System
verfasst von
Xiaofeng Yang
Publikationsdatum
24.07.2017
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 3/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-017-0508-6

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