Related papers: Exponential asymptotics and Stokes surfaces in non…
Flow interaction between a plain-fluid region in contact with a porous layer attracted significant attention from modelling and analysis sides due to numerous applications in biology, environment and industry. In the most widely used…
Incompressible flows are modeled by a coupled system of partial differential equations for velocity and pressure, Starting from a divergence-free mixed method proposed in [John, Li, Merdon and Rui, Math. Models Methods Appl. Sci.…
We introduce and investigate a generalization of the Hele-Shaw flow with injection where several droplets compete for space as they try to expand due to internal pressure while still preserving their topology. Droplets are described by…
Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to greatly enhance electrokinetic phenomena. Existing theories assume either homogeneous flat…
Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among…
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…
We consider the Stokes system in a thin porous medium $\Omega_\varepsilon$ of thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $\varepsilon$. On the boundary of the cylinders we prescribe…
The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds number problems analytically and computationally. Alternatively, one can solve…
The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two…
Meshless methods inherently do not require mesh topologies and are practically used for solving continuum equations. However, these methods generally tend to have a higher computational load than conventional mesh-based methods because…
The evaporation of sessile drops in quiescent air is usually governed by vapour diffusion. For contact angles below $90^\circ$, the evaporative flux from the droplet tends to diverge in the vicinity of the contact line. Therefore, the…
In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…
In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…
The humble Petri dish is perhaps the simplest setting in which to examine the locomotion of swimming organisms, particularly those whose body size is tens of microns to millimetres. The fluid layer in such a container has a bottom no-slip…
Normalizing flows are a powerful tool for building expressive distributions in high dimensions. So far, most of the literature has concentrated on learning flows on Euclidean spaces. Some problems however, such as those involving angles,…
The goal of this work is to develop a novel splitting approach for the numerical solution of multiscale problems involving the coupling between Stokes equations and ODE systems, as often encountered in blood flow modeling applications. The…
We present a numerical study aimed at comparing two approaches to the evaluation of relative permeability curves from 3D binary images of porous media. One approach hinges on the numerical solution of Stokes equations, while the other is…
The paper deals with the Dirichlet problem for the nonstationary Stokes system in a three-dimensional cone. The auhors study the asymptotics of the solutions near the vertex of the cone.
Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order…
Local Koopman spectral problem is studied to resolve all dynamics for a nonlinear system. The proposed spectral problem is compatible with the linear spectral theory for various linear systems, and several properties of local Koopman…