This chapter surveys recent numerical advances in the phase field method for geometric
surface evolution and related geometric nonlinear partial differential equations (PDEs) …

Using basic thermodynamic principles we derive a Cahn–Hilliard–Darcy model for tumour
growth including nutrient diffusion, chemotaxis, active transport, adhesion, apoptosis and …

A phase-field moving contact line model is presented for a two-phase system with soluble
surfactants. With the introduction of some scalar auxiliary variables, the original free energy …

In this paper, we consider the numerical solution of a binary fluid–surfactant phase field
model, in which the free energy contains a nonlinear coupling entropy, a Ginzburg–Landau …

Droplet dynamics on a solid substrate is significantly influenced by surfactants. It remains a
challenging task to model and simulate the moving contact line dynamics with soluble …

We propose a linear, fully decoupled, and energy stable finite difference scheme for solving
a phase-field surfactant fluid system. Inspired by the idea of multiple scalar auxiliary …

In this paper, we develop a novel phase-field model for fluid–structure interaction (FSI), that
is capable to handle very large deformations as well as topology changes like contact of the …

In this article, we develop a new linear, decoupled, second-order accurate, and energy
stable numerical method for a modified phase-field surfactant model (Xu et al., 2020). The …

In this contribution we present a new computational method for coupled bulk-surface
problems on time-dependent domains. The method is based on a space–time formulation …

In this work, we propose a novel scalar-transport model for the simulation of scalar quantities
that are confined to the interface in two-phase flows. In a two-phase flow, the scalar …