The local and nonlocal Allen-Cahn equations (ACEs) have received increasing attention in
the study of the complicated interfacial problems. In this paper, we conduct a comparison …

We present a new numerical scheme for solving a conservative Allen–Cahn equation with a
space–time dependent Lagrange multiplier. Since the well-known classical Allen–Cahn …

In this paper, a comparative study of the lattice Boltzmann (LB) models for the Allen-Cahn
(AC) and Cahn-Hilliard (CH) equations is conducted. To this end, a new LB model for the AC …

In this work a phase field-lattice Boltzmann model for incompressible two-phase flows is
presented. In this model, the interface tracking equation is a linear combination of the local …

Stability is one of the main concerns in the lattice Boltzmann method (LBM). The objectives
of this study are to investigate the linear stability of the lattice Boltzmann equation with the …

In this paper a lattice Boltzmann equation (LBE) method is designed that is different from the
previous LBE for the Cahn-Hilliard equation (CHE). The starting point of the present CHE …

Fractional phase field models have been reported to suitably describe the anomalous two-
phase transport in heterogeneous porous media, evolution of structural damage, and image …

Comparing with the well-known classic Cahn–Hilliard equation, the nonlocal Cahn–Hilliard
equation is equipped with a nonlocal diffusion operator and can describe more practical …

Comparing with the classical local gradient flow and phase field models, the nonlocal
models such as nonlocal Cahn–Hilliard equations equipped with nonlocal diffusion operator …

The Cahn-Hilliard equation (CHE) is widely used in modeling two-phase fluid flows, and it is
critical to solve this equation accurately to track the interface between the two phases. In this …