Varieties of energy-stable numerical methods have been developed for incompressible two-
phase flows based on the Navier-Stokes–Cahn–Hilliard (NSCH) model in the Eulerian …

We propose and analyze a class of temporal up to fourth-order unconditionally structure-
preserving single-step methods for Allen–Cahn-type semilinear parabolic equations. We first …

Solving the high dimensional partial differential equations (PDEs) with the classical
numerical methods is a challenge task. As possessing the power of progressing high …

Phase transition in an irregular domain is a common phenomenon in the natural world. In
this study, we develop novel linear, temporally first-and second-order accurate, and …

A fast, accurate, and stable numerical algorithm is proposed to solve the anisotropic phase-
field dendritic crystal growth model. The algorithm combines the first-order direction splitting …

In this study, we present the stability analysis of a fully explicit finite difference method (FDM)
for solving the Allen–Cahn (AC) equation. The AC equation is a second-order nonlinear …

A biological vesicle in fluid environment is described by a conservative Allen–Cahn type
phase-field model and the incompressible Navier–Stokes equations. To accurately and …

In this paper, we consider modeling and numerical simulation of incompressible and
immiscible two‐phase flow in porous media with rock compressibility. Using the second law …

We present a systematic two-step approach to derive temporal up to the eighth-order,
unconditionally maximum-principle-preserving schemes for a semilinear parabolic sine …

This paper explores the fractal characteristics of phase value time series in phase field
models. The phase value time series are obtained from the corresponding phase separation …