A phase field model for the mixture of two incompressible fluids is presented in this paper.
The model is based on an energetic variational formulation. It consists of a Navier–Stokes …

In this paper, we compute the equilibrium configurations of a vesicle membrane under
elastic bending energy, with prescribed volume and surface area. A variational phase field …

In this paper, we study a hydrodynamic system describing fluids with viscoelastic properties.
After a brief examination of the relations between several models, we shall concentrate on a …

A new simulation method for solving fluid–structure coupling problems has been developed.
All the basic equations are numerically solved on a fixed Cartesian grid using a finite …

We prove the existence of both local and global smooth solutions to the Cauchy problem in
the whole space and the periodic problem in the n-dimensional torus for the incompressible …

We consider the numerical approximation of the flow‐coupled phase‐field model of two‐
phase incompressible flows using the mass‐conserved Allen‐Cahn equation. Due to the …

We present an overview of the mathematical issues that arise in the modeling of polymer
electrolyte membrane fuel cells. These issues range from nanoscale modeling of network …

The dilemma in modeling the coupled dynamics of fluid-structure interaction (FSI) is that the
fluid model is normally based on an Eulerian perspective in contrast to the usual Lagrangian …

The interaction between a viscous fluid and an elastic solid is modeled by a system of
parabolic and hyperbolic equations, coupled to one another along the moving material …

We propose an Eulerian framework for modelling fluid–structure interaction (FSI) of
incompressible fluids and elastic structures. The model is based on an Eulerian approach …