Phase-field modeling is emerging as a promising tool for the treatment of problems with
interfaces. The classical description of interface problems requires the numerical solution of …

We apply the tensor train (TT) decomposition to construct the tensor product polynomial
chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with …

We present the method of direct van der Waals simulation (DVS) to study computationally
flows with liquid-vapor phase transformations. Our approach is based on a discretization of …

We consider a Euler system with dynamics generated by a potential energy functional. We
propose a form for the relative energy that exploits the variational structure and we derive a …

Compressible liquid–vapor flow with phase transitions can be described by systems of
Navier–Stokes–Korteweg type. They extend the Navier–Stokes equations by nonlinear …

Surfactants are compounds that find energetically favorable to be located at the boundaries
between fluids. They are able to modify the properties of those interfaces, for example …

Abstract The isothermal Navier-Stokes-Korteweg system is a classical diffuse interface
model for compressible two-phase flow which grounds in Van Der Waals' theory of …

Summary The Navier–Stokes–Korteweg (NSK) system is a classical diffuse‐interface model
for compressible two‐phase flow. However, the direct numerical simulation based on the …

We design consistent discontinuous Galerkin finite element schemes for the approximation
of a quasi-incompressible two phase flow model of Allen–Cahn/Cahn–Hilliard/Navier …

In this article, we develop a mesh adaptation algorithm for a local discontinuous Galerkin
(LDG) discretization of the (non)-isothermal Navier–Stokes–Korteweg (NSK) equations …