Search results for " Navier-Stokes equations"

showing 5 items of 5 documents

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.

Asymptotic analysisApplied MathematicsMathematical analysisAsymptotic analysis; Boundary layer; Explicit solutions; Navier-Stokes equations; Stokes equations; Zero viscosity; Mathematics (all); Analysis; Applied MathematicsMathematics::Analysis of PDEsAnalysiStokes equationDomain (mathematical analysis)Navier-Stokes equationPhysics::Fluid DynamicsSobolev spaceAsymptotic analysiBoundary layersymbols.namesakeBoundary layerSquare rootExplicit solutionInviscid flowStokes' lawsymbolsMathematics (all)Zero viscosityNavier–Stokes equationsAnalysisMathematicsCommunications in Partial Differential Equations
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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.

Bounday layer analysis zero viscosity limit Navier-Stokes equations
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A High-Resolution Penalization Method for large Mach number Flows in the presence of Obstacles

2009

International audience; A penalization method is applied to model the interaction of large Mach number compressible flows with obstacles. A supplementary term is added to the compressible Navier-Stokes system, seeking to simulate the effect of the Brinkman-penalization technique used in incompressible flow simulations including obstacles. We present a computational study comparing numerical results obtained with this method to theoretical results and to simulations with Fluent software. Our work indicates that this technique can be very promising in applications to complex flows.

General Computer ScienceComputational fluid dynamics01 natural sciencesCompressible flow010305 fluids & plasmas[SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]Physics::Fluid DynamicsShock Waves.symbols.namesakeIncompressible flow0103 physical sciencesPenalty methodComplex geometries[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]0101 mathematicsBrinkman PenalizationChoked flowMathematicsbusiness.industry[SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environmentGeneral EngineeringMechanics[INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation010101 applied mathematicsClassical mechanicsCompressible Navier-Stokes EquationsMach numberShock WavesMesh generationCompressibilitysymbolsbusiness[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
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Formation of Coherent Structures in Kolmogorov Flow with Stratification and Drag

2014

We study a weakly stratified Kolmogorov flow under the effect of a small linear drag. We perform a linear stability analysis of the basic state. We construct the finite dimensional dynamical system deriving from the truncated Fourier mode approximation. Using the Reynolds number as bifurcation parameter we build the corresponding diagram up to Re=100. We observe the coexistence of three coherent structures.

Partial differential equationApplied MathematicsDiagramMathematical analysisReynolds numberDynamical systemPhysics::Fluid DynamicsLinear stability analysisymbols.namesakeFourier transformBifurcation theoryDragsymbolsBifurcation theoryEquilibriaTruncated Navier-Stokes equationsSettore MAT/07 - Fisica MatematicaBifurcationMathematics
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Unsteady Separation for High Reynolds Numbers Navier-Stokes Solutions

2010

In this paper we compute the numerical solutions of Navier-Stokes equations in the case of the two dimensional disk impulsively started in a uniform back- ground flow. We shall solve the Navier-Stokes equations (for different Reynolds numbers ranging from 1.5 · 10^3 up to 10^5 ) with a fully spectral numerical scheme. We shall give a description of unsteady separation process in terms of large and small scale interactions acting over the flow. The beginning of these interactions will be linked to the topological change of the streamwise pressure gradient on the disk. Moreover we shall see how these stages of separation are related to the complex singularities of the solution. Infact the ana…

Unsteady Separation Phenomena High Reynolds Flows Navier-Stokes equations Prandtl equations zero viscosity limit Boundary Layer theorySettore MAT/07 - Fisica Matematica
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