Related papers: Projection Method for Solving Stokes Flow
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…
Particle-laden turbulent flow that separates due to a bump inside a channel is simulated to analyse the effects of the Stokes number and the lift force on the particle spatial distribution. The fluid friction Reynolds number is…
We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
Accurate simulations of ice sheet dynamics, mantle convection, lava flow, and other highly viscous free-surface flows involve solving the coupled Stokes/free-surface equations. In this paper, we theoretically analyze the stability and…
Analytical expressions for the velocity field and the effective slip length of pressure-driven Stokes flow through slippery pipes and annuli with rotationally symmetrical longitudinal slits are derived. Specifically, the developed models…
Under general assumptions on the velocity field, it is possible to construct a flow that is forward untangled. Once such a flow has been selected, the associated transport problem is well-posed.
We develop numerical methods to simulate the fluid-mechanical erosion of many bodies in two-dimensional Stokes flow. The broad aim is to simulate the erosion of a porous medium (e.g. groundwater flow) with grain-scale resolution. Our fluid…
Inertial particles are often observed to be trapped, temporarily or permanently, by recirculation cells which are ubiquitous in natural or industrial flows. In the limit of small particle inertia, determining the conditions of trapping is a…
Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the…
On a daily basis we stir tee or coffee with a spoon and leave it to rest. We know empirically the larger the stickiness, viscosity, of the fluid, more rapidly its velocity slows down. It is surprising, therefore, that the variation, the…
Conventional mathematical models for simulating incompressible fluid flow problems are based on the Navier-Stokes equations expressed in terms of pressure and velocity. In this context, pressure-velocity coupling is a key issue, and…
In this study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by utilizing the perturbation method originally proposed for pure waves that was recently published. The present…
In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The…
In this paper, we propose a multiscale method for heterogeneous Stokes problems. The method is based on the Localized Orthogonal Decomposition (LOD) methodology and has approximation properties independent of the regularity of the…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
We address the problem of numerically approximating the velocity and pressure governed by the Stokes system when the boundary conditions are only partially known and thus do not uniquely determine the velocity-pressure couple. We propose an…
We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…
A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the…
Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article blood is treated as an…