In the present work, we consider the conservative Allen-Cahn model and applied it to two-
phase flows in a consistent and conservative manner. The consistent formulation is …

In this paper, a novel dimension splitting method is proposed for the numerical simulation of
the flow-coupled binary fluid-surfactant model which consists of two conserved Allen-Cahn …

In the present study, we propose a novel conservative Allen–Cahn (CAC) equation with a
curvature-dependent Lagrange multiplier. The proposed CAC equation has a superior …

In this work, we present a conservative Allen–Cahn (CAC) equation and investigate its
unconditionally maximum principle-preserving linear numerical scheme. The operator …

Droplet evaporation is an interesting physical phenomenon and it has extensive
applications in natural world or industrial fields. To investigate the evaporation of a single …

In this paper, we study a fast explicit operator splitting method for space fractional nonlinear
Schrödinger equation in one (1D), two (2D) and three dimensions (3D) with periodic …

An effective operator splitting scheme for solving the nonlocal Allen–Cahn equation with a
Lagrange multiplier is studied. Firstly, based on the operator splitting method, the original …

There are three criteria when we model with phase-field equations. The first one is the
evolution of phase separation. The second one is energy dissipation law. The last one is …

In this study, we present a novel conservative Allen–Cahn (CAC) equation and its maximum
principle preserving and unconditionally stable numerical method. There have been many …

In this study, we establish a phase-field two-phase surfactant system using two conservative
Allen–Cahn type equations. Two nonlocal Lagrange multipliers are used to achieve the …