We review the paradoxes of the problem of a moving gas–liquid–solid contact line, and the ways to eliminate them by modifying both hydrodynamic equations at mesoscopic distances and boundary conditions at the solid surface. Two kinds of applicable models are represented by the Stokes equation amended by intermolecular forces and a diffuse interface model where the fluid density enters as an add...

Moving contact lines are implemented in a volume-of-fluid scheme with piecewise linear interface construction. Interfacial tension is treated as a continuous body force, computed from numerical derivatives of a smoothed volume-of-fluid function. Two methods for implementing the contact angle condition are investigated. The first extrapolates the volume-of-fluid function beyond the flow domain, ...

In this paper, we focus on the problem of adapting dynamic triangulations during numerical simulations to reduce the approximation errors. Dynamically evolving interfaces arise in many applications, such as free surfaces in multiphase flows and moving surfaces in fluid-structure interactions. In such simulations, it is often required to preserve a high quality interface discretization thus posi...

We present a new method for computing two-dimensional Stokes flow with moving interfaces that respond elastically to stretching. The interface is moved by semiLagrangian contouring: a distance function is introduced on a tree of cells near the interface, transported by a semi-Lagrangian time step and then used to contour the new interface. The velocity field in a periodic box is calculated as a...

Elliptic interface problems with multi-domains and triple junction points have wide applications in engineering and science. However, the corner singularity makes it a challenging problem for most existing methods. An accurate and efficient method is desired. In this paper, an efficient non-traditional finite element method with non-body-fitting grids is proposed to solve the elliptic interface...

Moving contact lines are implemented in a volume-ofuid scheme with piecewise linear interface construction. Interfacial tension is treated as a continuous body force, computed from numerical derivatives of a smoothed volume-ofuid function. Two methods for implementing the contact angle condition are investigated. The rst extrapolates the volume-ofuid function beyond the ow domain, on the basis ...

Effects of Hall current, ion-slip and Coriolis force on unsteady MHD Couette-Hartmann flow of a viscous incompressible electrically conducting fluid through a porous medium bounded by porous plates in the presence of a uniform transverse magnetic field which is either fixed relative to the fluid or to the moving porous plate is investigated using Laplace transform technique. The expressions for...

Finite element approximations of positive weak solutions to a onephase unidimensional moving-boundary system with kinetic condition describing the penetration of a sharp-reaction interface in concrete are considered. A priori and a posteriori error estimates for the semi-discrete fields of active concentrations and for the position of the moving interface are obtained. The important feature of ...