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Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical…
We present a method for computing fluid-structure interaction problems for multi-body systems. The fluid flow equations are solved using a fractional-step method with the immersed boundary method proposed by Uhlmann [J. Comput Phys. 209…
Depth averaged conservation equations are written for granular surface flows. Their application to the study of steady surface flows in a rotating drum allows to find experimentally the constitutive relations needed to close these equations…
Surface tension and wetting are dominating physical effects in micro and nanoscale flows. We present an efficient and reliable model of surface tension and equilibrium contact angles in Smoothed Particle Hydrodynamics for free-surface…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Bounds for stream functions as well as free-surface profiles and the total head are obtained under the…
In this paper, we determine an exact solution to the governing equations in spherical coordinates for an inviscid, incompressible fluid. This solution describes a steady, purely azimuthal equatorial flow with an associated free surface.…
Realistic fluid-solid interaction potentials are essential in description of confined fluids especially in the case of geometric heterogeneous surfaces. Correlated random field is considered as a model of random surface with high geometric…
We introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial…
The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…
Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces…
The dynamics of surface waves traveling along the boundary of a liquid medium are changed by the presence of floating plates and membranes, contributing to a number of important phenomena in a wide range of applications. Mathematically, if…
We propose a general control framework for two-phase flows with variable densities in the diffuse interface formulation, where the distribution of the fluid components is described by a phase field. The flow is governed by the diffuse…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…
We derive a set of equations in conformal variables that describe a potential flow of an ideal inviscid fluid with free surface in a bounded domain. This formulation is free of numerical instabilities present in the equations for the…
We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are…
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…