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With specific reference to the process of glass fibers drawing we review the models proposed to describe the various stages of the flow of molten glass from the furnace to the winding spool: the slow flow in the die, the jet formation under rapid cooling, the terminal fiber profile. In the course of our exposition we will present a general model for non-isothermal flows of mechanically incompressible but thermally expansible fluids (the basic model here assumed for glass), and the Oberbeck–Boussinesq limit is discussed. Both the modelling and the mathematical aspects will be illustrated in detail. An appendix is devoted to the question of stability analysis. [ABSTRACT FROM AUTHOR]

In the following we consider a class of non-linear systems that covers some well known generalized Navier-Stokes systems with shear dependent viscosity of power law type, p < 2 . We show that weak solutions to our class of systems have integrable gradient up to the boundary, with any finite exponent. This result extends, up the the boundary, some of the interior regularity results known in the literature for systems of the above power law type. Boundedness of the gradient, up to the boundary, remains an open problem. [ABSTRACT FROM AUTHOR]

We investigate the steady motion of a viscous incompressible fluid around a floating body which is rotating with a constant angular velocity. The fluid flow is described by a free boundary problem for the Navier-Stokes equations, where the free boundary consists of the capillary surface of the fluid and the wetted part of the floating body. [ABSTRACT FROM AUTHOR]

The aim of this note is twofold: we review some basic results which are at the basis of the derivation of eddy viscosity methods for large eddy simulation (LES) and we also try to combine them with the Stochastic approach to the Navier-Stokes equations. In particular, we propose a stochastic approach to the introduction of eddy viscosity LES methods and we evaluate by means of probabilistic techniques generalizations of the Lilly΄s constant. Next, we propose some heuristic for alternate modeling of sub-grid-scale terms and we apply scaling techniques to the derivation of a model for channel flows. [ABSTRACT FROM AUTHOR]

We prove that the energy equality holds for weak solutions of the Navier-Stokes equations in the functional class L3([0, T);D(A5/12)), where D(A5/12) is the domain of the fractional power of the Stokes operator. [ABSTRACT FROM AUTHOR]

Consider a weak solution u of the instationary Navier-Stokes system in a bounded domain of satisfying the strong energy inequality. Extending previous results Farwig et al., Journal of Mathematical Fluid Mechanics, 2007, to appear we prove among other things that u is regular if either the kinetic energy or the dissipation energy is (left-side) HÖlder continuous as a function of time t with HÖlder exponent and with sufficiently small HÖlder seminorm. The proofs use local regularity results which are based on the theory of very weak solutions and on uniqueness arguments for weak solutions. [ABSTRACT FROM AUTHOR]

We calculate numerically the solutions of the stationary Navier-Stokes equations in two dimensions, for a square domain with particular choices of boundary data. The data are chosen to test whether bounded disturbances on the boundary can be expected to spread into the interior of the domain. The results indicate that such behavior indeed can occur, but suggest an estimate of general form for the magnitudes of the solution and of its derivatives, analogous to classical bounds for harmonic functions. The qualitative behavior of the solutions we found displayed some striking and unexpected features. As a corollary of the study, we obtain two new examples of non-uniqueness for stationary solutions at large Reynolds numbers. [ABSTRACT FROM AUTHOR]

In this paper we will give an overview of our studies on turbulent flow over rough surfaces such as shark skin, which have a drag reducing effect known as shark-skin effect. Our mathematical model is restricted to the flow in the viscous sublayer. Here, the turbulences which occur in the flow above this layer enter through a boundary condition. The flow equations are the steady state Navier-Stokes equations with a Couette flow profile given through two boundary conditions: a diagonal flow on the top and the no-slip condition on the rough surface. Direct simulations are performed via stabilized finite elements. For a better approximation of the boundary isoparametric finite elements are used. Our first calculations give a drag reduction of rough surfaces up to 8% whereas 15% is obtained with an improved model. We will discuss this amount of drag reduction and how it can be compared with experimental results. For gaining insight in the details of the flow, how it is influenced by the different shapes of microstructures, and how their drag reducing mechanism can be explained, we used scientific flow visualization. We will present a short overview of the methods employed. [ABSTRACT FROM AUTHOR]

In this paper, we solve two problems. We prove a theorem on stability of a strong solution with respect to the norm ǁ ω ǁL2 +ǁω ǁL3 in Sect. 2. Then, in Sect.3, we show that there exist strong solutions of the Navier-Stokes initial-boundary value problem such that their initial values are arbitrarily large (in the norm of D(A¼)) and they belong to an arbitrarily chosen open set U ⊂ D(A½) at a time instant ξ > 0 which can be as small as we wish (We denote by A the Stokes operator.). [ABSTRACT FROM AUTHOR]

We consider a sequence of the Dirichlet problems for steady Navier- Stokes equations in domains perforated with channels where are closed subsets of bounded domain containedin small neighborhoods of some lines. While the number I (s) of channels tends toinfinity as these small sets are thinned.We study the asymptotic behaviorof solutions us (x) to problems in domains with thin channels. Wefind conditions on perforated domains under which sequence of solutions converges to solution of homogenized problem as. The proof is based on the asymptotic expansion of us (x) and on pointwise and integral estimates of auxiliary functions which are solutions of model boundary value problems. [ABSTRACT FROM AUTHOR]

We study the large time behavior of the energy in some slowly decreasing global strong solutions of the Navier-Stokes equations. We show as the main result of the paper that the energy concentrates in the lowest frequencies, while the middle and high frequencies die out as time goes to infinity. [ABSTRACT FROM AUTHOR]

There exists a series of other works dealing with flows in time varying domains that concern the motion of one or more bodies in a fluid. The fluid and the bodies are studied as an interconnected system so that the position of the bodies in the fluid is not apriori known. The weak solvability of such a problem, provided the bodies do not touch each other or they do not strike the boundary, was proved by B. Desjardins and M. J. Esteban [4, 5], K. H. Hoffmann and V. N. Starovoitov [13] (the 2D case), C. Conca et al. [2] and M. D. Gunzburger et al. [12]. [ABSTRACT FROM AUTHOR]

In the present paper we study local properties of suitable weak solutions to the Navier-Stokes equation in a cylinder Q = Ώ × (0, T). Using the local representation of the pressure we are able to define a positive constant ε★ such that for every parabolic subcylinder QR ⊂ Q the condition ]> implies ]> ). As one can easily check this condition is weaker then the well known Serrin's condition as well as the condition introduced by Farwig, Kozono and Sohr in a recent paper. Since our condition can be verified for suitable weak solutions to the Navier-Stokes system it improves the known results substantially. [ABSTRACT FROM AUTHOR]

In this paper, we combine a stabilized nonconforming finite element method with a two-level method to solve the stationary Navier-Stokes equations. Numerical results are presented to show the convergence performance of this combined algorithm. [ABSTRACT FROM AUTHOR]

Chimera technique has broad applications in complex flow field simulations because of its convenience of the arbitrary boundary interfaces and the easiness of gird generations of subzones. However, the main disadvantage or challenging difficulty lies in the global conservative information exchange between different zones or components. This work aims at assessing the conservation and effects of the mass flux based interpolation (MFBI) in a chimera multi-grid flow solver where Reynolds-Averaged Navier-Stokes (RANS) equations and Boldwin-Lomax turbulence model are introduced to calculate the viscous flows over a multi-element airfoil (NAWC1F2.2) with a flap. Numerical results reveal that, compared to the direct interpolation scheme, the performance of global conservation of MFBI are much better and more coincident with wind-tunnel experiments. [ABSTRACT FROM AUTHOR]

Two-dimensional stagnation-point flow in three different aspect ratios is studied by solving the full Navier-Stokes equations with the computational fluid dynamics (CFD) software of STAR-CD and results are compared with those obtained from the similarity solution. Pressure variation in the directions normal and parallel to the wall, as well as wall shear stress along the wall are investigated. Results show that pressure profiles are in good agreement for both numerical simulation and similarity solution at high aspect ratio in the stagnation-point region. Discrepancy of results in pressure profiles increases as aspect ratio decreases and in region which is away from the stagnation-point flow. It is found that wall shear stress is proportional to the distance from the stagnation-point along the wall as expected by similarity solution. [ABSTRACT FROM AUTHOR]

In this paper, a gas-kinetic solver is developed to solve Reynolds Averaged Navier-Stokes (RANS) equations in two-space dimensions generalized coordinates. The convection flux terms which appear on the left hand side of the RANS equations are discretized by a semi-discrete finite difference method. Then, the resulting inviscid flux functions are approximated by gas-kinetic BGK scheme which is based on the BGK model of the approximate collisional Boltzmann equation. The cell interface values required by the inviscid flux functions are reconstructed to second-order spatial accuracy via the MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws) variable interpolation method coupled with a minmod limiter. As for the diffusion flux terms, they are discretized by a second-order central difference scheme. To account for the turbulence effect, a combined k-ε / k-ω SST (Shear-Stress Transport) two-equation turbulence model is used in the solver. An explicit-type time integration method known as the modified fourth-order Runge-Kutta method is used to march the solution to steady-state. Computation over the RAE2822 airfoil flow corresponding to transonic speed has been solved using the developed gas-kinetic solver. Accuracy of BGK scheme in solving viscous transonic turbulent flow over the airfoil will be examined. Results obtained from the computations are also compared with experimental data and will demonstrate that a very good agreement has been achieved. [ABSTRACT FROM AUTHOR]

Hemodynamic forces including blood pressure and shear stress affect vulnerable plaque rupture in arteriosclerosis and biochemical activation of endothelium such as NO production. In this study, a method for estimating and imaging shear stress and pressure gradient distributions in blood vessel as the hemodynamic force based on viscosity estimation is presented. Feasibility of this method was investigated by applying to human carotid blood flow. Estimated results of shear stress and pressure gradient distributions coincide with the ideal distributions obtained by numerical simulation and flow-phantom experiment. [ABSTRACT FROM AUTHOR]

This paper describes simulations of feedback control of small disturbances in laminar Poiseuille flow. A polynomial-form spectral state-space model of the linearised flow with wall transpiration actuation and wall shear-stress measurements is generated, optimal controllers are synthesised, and closed-loop simulations are performed using an independent finite-volume Navier–Stokes solver. In addition, actuation via tangential wall transpiration is investigated, and LMI controllers, which minimise an upper bound on the peak transient energy growth, are synthesised and simulated. [ABSTRACT FROM AUTHOR]

Chapter ten of the book "Mathematical Aspects of Nonlinear Dispersive Equations," is presented. It explores the three-dimentional (3D) Navier-Stokes mathematical equations in a rotational frame with initial data on arbitrary periodic lattices. Further it uses harmonic analysis tools of Littlewood-Paley dyadic decomposition and lemmas on restricted convolutions in order to prove global regularity of the limit-resonant 3D Navier-Stokes equations.