Phase-Field Models for Multi-Component Fluid Flows

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A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows (2017, unknown): “The Allen-Cahn [2] and Cahn-Hilliard equations [13, 14], are widely used in the study of interfacial dynamics [2, 62, 4, 42, 46, 52, 53, 76, 1].”
Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle (2016, unknown): “, the survey articles of [7, 9].”
Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows (2015, background): “[15, 3, 25, 17, 22, 43], the recent review papers [30, 19], and the references therein).”
Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method (2017, background): “The bulk part of the free energy is simply a summation of the double-well potentials for each phase variable [6,7,26].”
Lattice Boltzmann methods for multiphase flow and phase-change heat transfer (2015, background): “es of these two forms are usually different as the variations of I and P I across the interface are different. There are also some other forms of the surface tension force, which can be found in Ref. [301]. Khan remarked that [302] the existence of so many forms of the surface tension force is becau”
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.”