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Graphical solutions to one-phase free boundary problems

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A logarithmic epiperimetric inequality for the obstacle problem

Maria Colombo

We study the regularity of the regular and of the singular set of the obstacle problem in any dimension. Our approach is related to the epiperimetric inequality of Weiss (Invent Math 138:23-50, Wei99a), which works at regular points and provides an alterna ...

2018

Propagation of a height contained hydraulic fracture in turbulent flow regimes

Brice Tanguy Alphonse Lecampion, Haseeb Zia

We investigate theoretically and numerically the impact of the transition from laminar to turbulent flow on the propagation of a height contained hydraulic fracture (i.e. PKN geometry). We account for the inertial terms in the balance of momentum and expre ...

Pergamon-Elsevier Science Ltd2017

We sharpen an estimate of [4] for the topological degree of continuous maps from a sphere Sdinto itself in the case d >= 2. This provides the answer for d >= 2 to a question raised by Brezis. The problem is still open for d = 1. (C) 2017 Academie des scien ...

2017

Systematic errors of skin-friction measurements by oil-film interferometry

Peter Monkewitz, Jean-Daniel Rüedi

In recent years, the independent measurement of wall shear stress with oil-film or oil-drop interferometry has become a cornerstone of turbulent-boundary-layer research as many arguments depend critically on a precise knowledge of the skin friction tau(w)* ...

Cambridge University Press2015

Too big to grow

Vladislav Mantic Lugo

Open flows, such as wakes, jets, separation bubbles, mixing layers, boundary layers, etc., develop in domains where fluid particles are continuously advected downstream. They are encountered in a wide variety of situations, ranging from nature to technolog ...

EPFL2015

Manipulating flow separation: sensitivity of stagnation points, separatrix angles and recirculation area to steady actuation

François Gallaire, Edouard Boujo

A variational technique is used to derive analytical expressions for the sensitivity of several topological indicators of flow separation to steady actuation. Considering the boundary layer flow above a wall-mounted bump, the six following representative q ...

Royal Soc2014

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Structure Interaction (FSI) phenomena is becoming a relevant study field for the design or revamping of hydropower plants. The generalized trend of increasing flow rates and reducing rotor blades/stay vanes thickness in order to improve the efficiency of t ...

International Association For Hydraulic Research2014

On the longitudinal optimal perturbations to inviscid plane shear flow: formal solution and asymptotic approximation

Cristobal Manuel Arratia Martinez

We study the longitudinal linear optimal perturbations (which maximize the energy gain up to a prescribed time T) to inviscid parallel shear flow, which present unbounded energy growth due to the lift-up mechanism. Using the phase invariance with respect t ...

Cambridge University Press2013

Partial slip at fluid-solid boundaries by multiparticle collision dynamics simulations

Giuseppe Foffi, Maxim Belushkin, Samuel Hanot

The understanding of the exact boundary conditions at the interface between a solid and a fluid is becoming increasingly important, as the limitations of the no-slip boundary condition are becoming apparent, especially in micro- and nanofluidics applicatio ...

Royal Soc Chemistry2013

Shedding of droplets in a flow focusing junction is standard technique in two-phase microfluidics. This break-up is driven by a capillary instability. Here we present a depth-averaged approach to simulate these complex phenomena. Since the physical mechani ...

2013