We present a new phase-field fluid model and computation with minimized Cahn-Hilliard (CH) dynamics. Using the CH equation, the internal structure of the interface layer is determined by explicit smoothing flow discontinuities. This method greatly simplifies gridding, discretization, and handling of topological changes. The original CH equation, however, has intrinsic dynamics such as interface length minimization, i.e., the motion by minus the Laplacian of the mean curvature. When the CH equation is applied to the modeling of multiphase fluid flows, we want to minimize its interface length minimization property. The surface tension formulation also requires the multiphase fluid interface to be a hyperbolic tangent profile. Typically, under the advection of flow, the interfacial transition is not a hyperbolic tangent profile, i.e., it is too compressed or sharpened. Even though the original CH dynamics conserves the total mass, the enclosed area obtained by its interface is not preserved. To overcome these shortcomings, we propose a modified CH equation with an interfacial profile correction term. Several numerical examples are presented to show the accuracy of the proposed method. The numerical results demonstrate that the proposed modified CH equation preserves the enclosed area better than the original CH equation.
|Number of pages||17|
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|Publication status||Published - 2016 Jan 1|
Bibliographical noteFunding Information:
Y.B. Li is supported by the Fundamental Research Funds for the Central Universities, China. J.-I. Choi was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF20151009350 ). The corresponding author (J.S. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) ( NRF-2014R1A2A2A01003683 ). The authors are grateful to the reviewers whose valuable suggestions and comments significantly improved the quality of this paper.
© 2015 Elsevier B.V..
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics