We investigate mortar multiscale numerical methods for coupled Stokes and Darcy flows with the Beavers–Joseph–Saffman interface condition. The domain is decomposed into a series of subdomains (coarse grid) of either Stokes or Darcy type. The subdomains are discretized by appropriate Stokes or Darcy finite elements. The solution is resolved locally (in each coarse element) on a fine scale, allow...

We consider methods for numerical simulations of variable density incompressible fluids, modelled by the Navier-Stokes equations. Variable density problems arise, for instance, in interfaces between fluids of different densities in multiphase flows such as appear in porous media problems. It is shown that by solving the Navier-Stokes equation for the momentum variable instead of the velocity, t...

Over 70 years have passed since dermatologists John H. Stokes and Donald M. Pillsbury first proposed a gastrointestinal mechanism for the overlap between depression, anxiety and skin conditions such as acne. Stokes and Pillsbury hypothesized that emotional states might alter the normal intestinal microflora, increase intestinal permeability and contribute to systemic inflammation. Among the rem...

This article is concerned with a dual mixed formulation of the Navier-Stokes system in a polygonal domain of the plane with Dirichlet boundary conditions and its numerical approximation. The gradient tensor, a quantity of practical interest, is introduced as a new unknown. The problem is then approximated by a mixed finite element method. Quasi-optimal a priori error estimates are obtained. The...

We consider the evolution of contact lines for viscous fluids in a two-dimensional open-top vessel. The domain is bounded above by a free moving boundary and otherwise by the solid wall of the vessel. The dynamics of the fluid are governed by the incompressible Stokes equations under the influence of gravity, and the interface between fluid and air is under the effect of capillary forces. Here ...

In a classic paper, Morduchow and Libby use an analytic solution for the profile of a Navier–Stokes shock to show that the equilibrium thermodynamic entropy has a maximum inside the shock. There is no general nonequilibrium thermodynamic formulation of entropy; the extension of equilibrium theory to nonequililbrium processes is usually made through the assumption of local thermodynamic equilibr...

Optimal aerodynamic shape design aims at finding the minimum of a functional by controlling the PDE modeling the flow using surface deformation techniques. As a solution to the enormous computational resources required for classical shape optimization of functionals of aerodynamic interest, probably the best strategy is to use in a systematic way, methods inspired in control theory. One of the ...

This Resource Letter provides a guide to the literature on fully developed turbulence in fluids. It is restricted to mechanically driven turbulence in an incompressible fluid described by the Navier-Stokes equations of hydrodynamics, and places greatest emphasis on fundamental physical questions. Journal articles and books are cited for the following topics: The Navier-Stokes equations, qualita...

We consider the regime of fully developed isotropic and homogeneous turbulence of the Navier-Stokes equation with a stochastic forcing. We present two gauge symmetries of the corresponding Navier-Stokes field theory and derive the associated general Ward identities. Furthermore, by introducing a local source bilinear in the velocity field, we show that these symmetries entail an infinite set of...

We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around 10(3). The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotati...