The Experts below are selected from a list of 159930 Experts worldwide ranked by ideXlab platform
Frédéric Rousset - One of the best experts on this subject based on the ideXlab platform.
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Uniform Regularity for the Navier-Stokes Equation with Navier Boundary Condition
Archive for Rational Mechanics and Analysis, 2012Co-Authors: Nader Masmoudi, Frédéric RoussetAbstract:We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes Equation with the Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in L (a). This allows us to obtain the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument.
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On a Constrained 2-D Navier-Stokes Equation
Communications in Mathematical Physics, 2009Co-Authors: Emanuele Caglioti, Mario Pulvirenti, Frédéric RoussetAbstract:The planar Navier-Stokes Equation exhibits, in absence of external forces, a trivial asymptotics in time. Nevertheless the appearence of coherent structures suggests non-trivial intermediate asymptotics which should be explained in terms of the Equation itself. Motivated by the separation of the different time scales observed in the dynamics of the Navier-Stokes Equation, we study the well-posedness and asymptotic behaviour of a constrained Equation which neglects the variation of the energy and moment of inertia.
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The 2D constrained Navier-Stokes Equation and intermediate asymptotics
Journal of Physics A: Mathematical and Theoretical, 2008Co-Authors: Emanuele Caglioti, Mario Pulvirenti, Frédéric RoussetAbstract:We introduce a modified version of the two-dimensional Navier-Stokes Equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and is related to the gradient flow structure of the 2D Navier-Stokes Equation. The hope is to understand intermediate asymptotics. The analysis we present here is purely formal. A rigorous study of this Equation will be done in a forthcoming paper
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Spectral stability implies nonlinear stability for incompressible boundary layers
Indiana University Mathematics Journal, 2008Co-Authors: François Gallaire, Frédéric RoussetAbstract:We prove the nonlinear stability of boundary layer profiles of the incompressible Navier-Stokes Equation under a spectral assumption on the linearized operator. The main result applies for example to the classical Blasius layer
Mikhael Gorokhovski - One of the best experts on this subject based on the ideXlab platform.
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group theoretical model of developed turbulence and renormalization of the navier stokes Equation
Physical Review E, 2005Co-Authors: V L Saveliev, Mikhael GorokhovskiAbstract:Received 19 June 2004; revised manuscript received 31 March 2005; published 7 July 2005On the basis of the Euler Equation and its symmetry properties, this paper proposes a model of stationaryhomogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained.An Equation for the averaged turbulent velocity field is derived from the Navier-Stokes Equation byrenormalization-group transformation.DOI: 10.1103/PhysRevE.72.016302 PACS number s : 47.27.Eq, 05.10.Cc
Bernd R Noack - One of the best experts on this subject based on the ideXlab platform.
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low dimensional modelling of high reynolds number shear flows incorporating constraints from the navier stokes Equation
Journal of Fluid Mechanics, 2013Co-Authors: Maciej Balajewicz, Earl H Dowell, Bernd R NoackAbstract:We generalize the POD-based Galerkin method for post-transient flow data by incorporating Navier–Stokes Equation constraints. In this method, the derived Galerkin expansion minimizes the residual like POD, but with the power balance Equation for the resolved turbulent kinetic energy as an additional optimization constraint. Thus, the projection of the Navier–Stokes Equation on to the expansion modes yields a Galerkin system that respects the power balance on the attractor. The resulting dynamical system requires no stabilizing eddy-viscosity term – contrary to other POD models of high-Reynolds-number flows. The proposed Galerkin method is illustrated with two test cases: two-dimensional flow inside a square lid-driven cavity and a two-dimensional mixing layer. Generalizations for more Navier–Stokes constraints, e.g. Reynolds Equations, can be achieved in straightforward variation of the presented results.
Bastian E Rapp - One of the best experts on this subject based on the ideXlab platform.
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numerics made easy solving the navier stokes Equation for arbitrary channel cross sections using microsoft excel
Biomedical Microdevices, 2016Co-Authors: Christiane Richter, Frederik Kotz, Stefan Giselbrecht, Dorothea Helmer, Bastian E RappAbstract:The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes Equation for pressure-driven Poiseuille flow can be solved analytically. From these Equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes Equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes Equation for arbitrary channel cross-sections.
Aditi Sengupta - One of the best experts on this subject based on the ideXlab platform.
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non linear instability analysis of the two dimensional navier stokes Equation the taylor green vortex problem
Physics of Fluids, 2018Co-Authors: Tapan K Sengupta, Nidhi Sharma, Aditi SenguptaAbstract:An enstrophy-based non-linear instability analysis of the Navier-Stokes Equation for two-dimensional (2D) flows is presented here, using the Taylor-Green vortex (TGV) problem as an example. This problem admits a time-dependent analytical solution as the base flow, whose instability is traced here. The numerical study of the evolution of the Taylor-Green vortices shows that the flow becomes turbulent, but an explanation for this transition has not been advanced so far. The deviation of the numerical solution from the analytical solution is studied here using a high accuracy compact scheme on a non-uniform grid (NUC6), with the fourth-order Runge-Kutta method. The stream function-vorticity (ψ, ω) formulation of the governing Equations is solved here in a periodic square domain with four vortices at t = 0. Simulations performed at different Reynolds numbers reveal that numerical errors in computations induce a breakdown of symmetry and simultaneous fragmentation of vortices. It is shown that the actual physi...
