This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

Binary fluid flows in irregular domains are common phenomena in natural and industrial
fields. To describe these physical processes, we herein present a novel fluid flow-coupled …

In this paper, we develop an unconditionally stable linear numerical scheme for the N-
component Cahn–Hilliard system with second-order accuracy in time and space. The …

In this study, we consider the numerical approximation of incompressible three-component
fluids, in which the fluid interfaces are captured by ternary Cahn–Hilliard equations and the …

Herein, we propose linear, decoupled, and energy dissipation-preserving schemes for the
ternary Cahn–Hilliard (CH) fluid models by using a modified scalar auxiliary variable …

An efficiently linear time-marching method is proposed for the incompressible fluid flows
coupled Ohta–Kawasaki model of diblock copolymer melt. Although this model satisfies the …

In this paper, we propose a generalized framework for the derivation of compact difference
schemes for the approximation of an arbitrary order derivative. We formulate a methodology …

Abstract The Cahn–Hilliard (CH) equation is a classical mathematical equation which
models the spinodal decomposition in binary fluid mixtures. In the real world, the phase …

Based on a time-dependent auxiliary variable approach, we propose linear, totally
decoupled, and energy dissipative methods for the three-phase conservative Allen–Cahn …

We develop a second-order accurate, energy stable, and linear numerical method for a
ternary Cahn–Hilliard (CH) model. The proposed scheme is an extension of typical …