Fluid flow in porous systems driven by capillary pressure is one of the most ubiquitous
phenomena in nature and industry, including petroleum and hydraulic engineering as well …

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

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 …

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 …

The scalar auxiliary variable (SAV) method was introduced by Shen et al. in [36] and has
been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar …

Stability analyses and error estimates are carried out for a number of commonly used
numerical schemes for the Allen-Cahn and Cahn-Hilliard equations. It is shown that all the …

In this paper, we review the recent development of phase-field models and their numerical
methods for multi-component fluid flows with interfacial phenomena. The models consist of a …

With the emergence of portable broadband seismic instrumentation, availability of digital
networks with wide dynamic range, and development of new powerful analysis techniques …

This article presents a comprehensive review of numerical methods and models for interface
resolving simulations of multiphase flows in microfluidics and micro process engineering …

We investigate the applicability of an incompressible diffuse interface model for two-phase
incompressible fluid flows with large viscosity and density contrasts. Diffuse-interface …