A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities

By Jie Shen, Xiaofeng Yang. SIAM Journal on Scientific Computing, 2010

326 citations recorded by the source corpus.

Subfields: Computational Mechanics, Materials Chemistry, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/c4de1bc0c661b961eb5fbf3a129905503e2afbd2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Xiaofeng Yang
2. Jie Shen
3. Jia Zhao
4. Jiang Yang
5. Qi Wang
6. Tao Tang
7. Steven M. Wise
8. Cheng Wang

In Materials Chemistry

1. Xiaofeng Yang
2. Jie Shen
3. Jia Zhao
4. Jiang Yang
5. Qi Wang
6. Tao Tang
7. Xiaoming Wang
8. Steven M. Wise

In Mechanical Engineering

1. Qi Wang
2. Jia Zhao
3. Xiaofeng Yang
4. Axel Voigt
5. Sebastian Aland
6. Xiaoming Wang
7. Jie Shen
8. G. Em Karniadakis

Citations in the corpus

• Two‐phase flows in karstic geometry (2014, methodology): “The Cahn-Hilliard-Stokes system can be viewed as the low Reynolds number approximation of the better-known Cahn-Hilliard-Navier-Stokes system for two phase flow [28, 35, 34, 36, 40, 66, 67, 68, 69, 70].”
• On the maximum principle preserving schemes for the generalized Allen–Cahn equation (2016, background): “, [14, 16], in which a velocity field is involved in the Allen–Cahn phase equation.”
• Second-order Convex Splitting Schemes for Gradient Flows with Ehrlich-Schwoebel Type Energy: Application to Thin Film Epitaxy (2012, background): “(We refer to [6, 25, 26, 33, 5, 29] for other related convexity splitting schemes.”
• Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method (2017, methodology): “We note that a similar technique has been used in [3] to produce a linear scheme, where a zero term φ − φ is added, and the minuend is treated implicitly and the subtractor is treated explicitly, that is quite similar to the stabilization approach [31,38,39].”
• A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations (2016, methodology): “This is also true in case of integer order Allen–Cahn phase-field model [8].”
• Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows (2010, methodology): “The main advantage of the new formulation is that the modified Cahn-Hilliard phase-field system (2.3)-(2.8)-(2.10) now admits the following energy law (cf. [23]):”
• A novel linear second order unconditionally energy stable scheme for a hydrodynamic Q-tensor model of liquid crystals (2017, methodology): “In [25], we have designed a first and a second order semi-discrete scheme in time employing both the convex-splitting strategy [32–34] and the stabilizer approach [35,36], and showed the developed numerical schemes are unconditionally energy stable.”
• Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models (2013, background): “Other noteworthy contributions for the phase-field crystal equation and bistable epitaxial thin film equations include Xu & Tang [21], Li & Liu [14], Shen & Yang [19], Qiao et al.”
• Benchmark computations of diffuse interface models for two‐dimensional bubble dynamics (2012, methodology): “(11) Following Guermond and Quartapelle [16], an energy estimate of the model could be shown by introducing the new variable r Dp , see [7].”