Phase-field method is a density-based computational method at the mesoscale for modeling
and predicting the temporal microstructure and property evolution during materials …

Numerical models of surface tension play an increasingly important role in our capacity to
understand and predict a wide range of multiphase flow problems. The accuracy and …

We propose a new approach, which we term as scalar auxiliary variable (SAV) approach, to
construct efficient and accurate time discretization schemes for a large class of gradient …

The efficiency of perovskite solar cells has surged in the past few years, while the bandgaps
of current perovskite materials for record efficiencies are much larger than the optimal value …

We propose a new numerical technique to deal with nonlinear terms in gradient flows. By
introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable …

A droplet deposited on a solid substrate leads to the wetting phenomenon. A natural
observation is the lotus effect, known for its superhydrophobicity. This special feature is …

Over the past few decades, tremendous progress has been made in the development of
particle-based discrete simulation methods versus the conventional continuum-based …

Abstract Smoothed Particle Hydrodynamics (SPH) is a relatively new meshless numerical
approach which has attracted significant attention in the last two decades. Compared with …

Along with finite differences and finite elements, spectral methods are one of the three main
methodologies for solving partial differential equations on computers. This book provides a …

This review focuses on direct numerical simulations (DNS) of turbulent flows laden with
droplets or bubbles. DNS of these flows are more challenging than those of flows laden with …