Related papers: Approaches for handling sloping fluid-solid interf…
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical…
Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces…
This paper presents a new method allowing for a numerical study of the interaction between a submerged solid structure and a current with surface waves. The method involves a Navier-Stokes equation solver for a two-fluid formulation with…
In recent decades novel solid substrates have been designed which change their wettability in response to light or an electrostatic field. Here, we investigate a droplet on substrates with oscillating uniform wettability by varying minimium…
Patterning the wettability of solid surfaces is a successful strategy to control the dropwise condensation of vapor onto partially wetting solid surfaces. We followed the condensation of water vapor onto electrowetting-functionalized…
In this work, we derive asymptotic interface models for an elastic Muskat free boundary problem describing Darcy flow beneath an elastic membrane. In a weakly nonlinear regime of small interface steepness, we obtain nonlocal evolution…
Currently existing energy-stable parametric finite element methods for surface diffusion flow and other flows are usually limited to first-order accuracy in time. Designing a high-order algorithm for geometric flows that can also be…
A partially-wetting liquid can deform the underlying elastic substrate upon which it rests. This situation requires the development of theoretical models to describe the wetting forces imparted by the drop onto the solid substrate,…
A method of simulating the drying process of a soft matter solution with an implicit solvent model by moving the liquid-vapor interface is applied to various solution films and droplets. For a solution of a polymer and nanoparticles, we…
We consider an viscous, incompressible Newtonian fluid flowing through a thin elastic structure. The motion of the structure is described by the equations of a linearised Koiter shell, whose motion is restricted to transverse displacements.…
The aim of this Letter is to derive explicitly the secular equation for Scholte waves at the interface between a fluid and an anisotropic crystal cut along a plane containing the normal to a single symmetry plane, that is containing only…
We have studied the effective slip length of confined fluid with nano-structured fluid-solid interfaces. A formula bridging the effective slip length and nano structures of the interfaces has been obtained analytically. For the application…
Nanofluidic systems show great promises for applications in energy conversion, where their performance can be enhanced by nanoscale liquid-solid slip. However, efficiency is also controlled by surface charge, which is known to reduce slip.…
We study a nonlinear fluid-structure interaction problem in which the fluid is described by the three-dimensional incompressible Navier-Stokes equations, and the elastic structure is modeled by the nonlinear plate equation which includes a…
We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier-Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With…
We consider the interaction between an incompressible, viscous fluid modeled by the dynamic Stokes equation and a multilayered poroelastic structure which consists of a thin, linear, poroelastic plate layer (in direct contact with the free…
Pure advection of a conservative scalar is relevant to several applications including two-phase flow. Successful numerical schemes must capture the sharp interface between the phases while maintaining a smooth (wrinkle-free) interfacial…