Search results for "Stokes"
showing 10 items of 242 documents
Existence and Singularities for the Prandtl Boundary Layer Equations
2000
Prandtl's boundary layer equations, first formulated in 1904, resolve the differences between the viscous and inviscid description of fluid flows. This paper presents a review of mathematical results, both analytic and computational, on the unsteady boundary layer equations. This includes a review of the derivation and basic properties of the equations, singularity formation, well-posedness results, and infinite Reynolds number limits.
Comparative Study of the a Posteriori Error Estimators for the Stokes Problem
2007
The research presented is focused on a comparative study of a posteriori error estimation methods to various approximations of the Stokes problem. Mainly, we are interested in the performance of functional type a posterior error estimates and their comparison with other methods. We show that functional type a posteriori error estimators are applicable to various types of approximations (including non-Galerkin ones) and robust with respect to the mesh structure, type of the finite element and computational procedure used. This allows the construction of effective mesh adaptation procedures in all cases considered. Numerical tests justify the approach suggested.
ASYMPTOTIC ANALYSIS OF THE LINEARIZED NAVIER–STOKES EQUATION ON AN EXTERIOR CIRCULAR DOMAIN: EXPLICIT SOLUTION AND THE ZERO VISCOSITY LIMIT
2001
In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc.
A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures
2016
In this short paper, we formally derive the thin spray equation for a steady Stokes gas, i.e. the equation consists in a coupling between a kinetic (Vlasov type) equation for the dispersed phase and a (steady) Stokes equation for the gas. Our starting point is a system of Boltzmann equations for a binary gas mixture. The derivation follows the procedure already outlined in [Bernard-Desvillettes-Golse-Ricci, arXiv:1608.00422 [math.AP]] where the evolution of the gas is governed by the Navier-Stokes equation.
Unsteady Separation and Navier-Stokes Solutions at High Reynolds Numbers
2010
We compute the numerical solutions for Navier-Stokes and Prandtl’s equations in the case of a uniform bidimensional flow past an impulsively started disk. The numerical approx- imation is based on a spectral methods imple- mented in a Grid environment. We investigate the relationship between the phenomena of unsteady separation of the flow and the exponential decay of the Fourier spectrum of the solutions. We show that Prandtl’s solution develops a separation singularity in a finite time. Navier-Stokes solutions are computed over a range of Reynolds numbers from 3000 to 50000. We show that the appearance of large gradients of the pressure in the stream- wise direction, reveals that the visc…
Existence and uniqueness for Prandtl equations and zero viscosity limit of the Navier-Stokes equations
2002
The existence and uniqueness of the mild solution of the boundary layer (BL) equation is proved assuming analyticity of the data with respect to the tangential variable. Moreover we use the well-posedness of the BL equation to perform an asymptotic expansion of the Navier-Stokes equations on a bounded domain.
Electronic and Functional Scope of Boronic Acid Derived Salicylidenehydrazone (BASHY) Complexes as Fluorescent Dyes
2017
[EN] A series of boronic acid derived salicylidenehydrazone (BASHY) complexes was prepared and photophysically characterized. The dye platform can be modified by (a) electronic tuning along the cyanine-type axis via modification of the donor-acceptor pair and (b) functional tuning via the boronic acid residue. On the one hand, approach (a) allows the control of photophysical parameters such as Stokes shift, emission color, and two-photon absorption (2PA) cross section. The resulting dyes show emission light-up behavior in nonpolar media and are characterized by high fluorescence quantum yields (ca. 0.5-0.7) and brightness (ca. 35000-40000 M-1 cm(-1)). Moreover, the 2PA cross sections reach …
Theoretical study of a Bénard Marangoni problem
2011
[EN] In this paper we prove the existence of strong solutions for the stationary Benard-Marangoni problem in a finite domain flat on the top, bifurcating from the basic heat conductive state. The Benard-Marangoni problem is a physical phenomenon of thermal convection in which the effects of buoyancy and surface tension are taken into account. This problem is modelled with a system of partial differential equations of the type Navier-Stokes and heat equation. The boundary conditions include crossed boundary conditions involving tangential derivatives of the temperature and normal derivatives of the velocity field. To define tangential derivatives at the boundary, intended in the trace sense,…
CARS spectroscopy of CH4 for implication of temperature measurements in supercritical LOX/CH4 combustion
2007
International audience; Experimental and theoretical investigations of coherent anti-Stokes Raman spectroscopy of CH4 have been carried out. Experimental spectra were measured in a heated high-pressure test cell and compared with numerical simulations. Good agreement was obtained for the temperature and the pressure dependence of CARS spectra in the ranges 300-1100 K and 0.1-5.0 MPa. The observed dependencies provide useful guidance for CARS thermometry, allowing quantitative measurements of temperature in high-pressure combustors. Application of multiplex CH4 CARS thermometry for single-shot measurements in a LOX/CH4 combustion at high pressure was demonstrated at supercritical conditions …
Collisional line broadening and line shifting in N2-CO2 mixture studied by inverse Raman spectroscopy
1990
Abstract Collisional effects in the Raman Q-branch of N 2 perturbed by CO 2 have been studied by high-resolution stimulated Raman spectroscopy. The Raman spectra recorded in the 0.3–1.0 atm and 295–1000 K pressure and temperature ranges are fitted with a theoretical profile taking into account line broadening, frequency shift and line mixing due to rotational energy transfers. The data at low density are used as basic data for the modeling of rotationally inelastic rates through sets of adjustable parameters. We have used in this study the two main models developed in the last decade and known as modified exponential gap (MEG) and energy corrected sudden (ECS) laws. Experimental spectra rec…