In this paper, we present a brief overview of the phase-field-based lattice Boltzmann method
(LBM) that is a distinct and efficient numerical algorithm for multiphase flow problems. We …

Abstract The Molecular Beam Epitaxial model is derived from the variation of a free energy,
that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear …

How to develop efficient numerical schemes while preserving energy stability at the discrete
level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper …

In this paper, we consider the numerical solution of a binary fluid–surfactant phase field
model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg–Landau …

Ions in water are important throughout biology, from molecules to organs. Classically, ions in
water were treated as ideal noninteracting particles in a perfect gas. Excess free energy of …

In this paper, the droplet formation process at a low capillary number in a flow focusing micro-
channel is studied by performing a three-dimensional phase field benchmark based on the …

In this paper, we consider the numerical approximation for a phase field model of the
coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn …

We present and analyze a new second-order finite difference scheme for the
Macromolecular Microsphere Composite hydrogel, Time-Dependent Ginzburg-Landau …

In this paper, we consider numerical approximations for the viscous Cahn–Hilliard equation
with hyperbolic relaxation. This type of equations processes energy-dissipative structure …

We consider in this paper numerical approximations of phase-field models for two-phase
complex fluids. We first reformulate the phase-field models derived from an energetic …