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 …

This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

In this paper we construct two classes, based on stabilization and convex splitting, of
decoupled, unconditionally energy stable schemes for Cahn--Hilliard phase-field models of …

In this paper, we present a novel second order in time mixed finite element scheme for the
Cahn–Hilliard–Navier–Stokes equations with matched densities. The scheme combines a …

Numerical schemes to approximate the Cahn–Hilliard equation have been widely studied in
recent times due to its connection with many physically motivated problems. In this work we …

We present an efficient time-stepping scheme for simulations of the coupled Navier–Stokes
Cahn–Hilliard equations for the phase field approach. The scheme has several attractive …

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 …

In this paper, we focus on efficient second-order in time approximations of the Allen–Cahn
and Cahn–Hilliard equations. First of all, we present the equations, generic second-order …

In this paper, we propose several second order in time, fully discrete, linear and nonlinear
numerical schemes for solving the phase field model of two-phase incompressible flows, in …

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 …