Showing papers on "Navier–Stokes equations published in 2008"

A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier-Stokes Simulations of Transitional Flow

Abstract: An eddy-viscosity turbulence model employing three additional transport equations is presented and applied to a number of transitional flow test cases. The model is based on the k- framework and represents a substantial refinement to a transition-sensitive model that has been previously documented in the open literature. The third transport equation is included to predict the magnitude of low-frequency velocity fluctuations in the pretransitional boundary layer that have been identified as the precursors to transition. The closure of model terms is based on a phenomenological (i.e., physics-based) rather than a purely empirical approach and the rationale for the forms of these terms is discussed. The model has been implemented into a commercial computational fluid dynamics code and applied to a number of relevant test cases, including flat plate boundary layers with and without applied pressure gradients, as well as a variety of airfoil test cases with different geometries, Reynolds numbers, freestream turbulence conditions, and angles of attack. The test cases demonstrate the ability of the model to successfully reproduce transitional flow behavior with a reasonable degree of accuracy, particularly in comparison with commonly used models that exhibit no capability of predicting laminar-toturbulent boundary layer development. While it is impossible to resolve all of the complex features of transitional and turbulent flows with a relatively simple Reynolds-averaged modeling approach, the results shown here demonstrate that the new model can provide a useful and practical tool for engineers addressing the simulation and prediction of transitional flow behavior in fluid systems. DOI: 10.1115/1.2979230

Simulating elliptic flow with viscous hydrodynamics

Abstract: In this work we simulate a viscous hydrodynamical model of noncentral Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance The model fluid equations were proposed by Oettinger and Grmela [Grmela, M, and Oettinger, H C, Phys Rev E, 56, 6620 (1997)] Freeze-out is signaled when the viscous corrections become large relative to the ideal terms Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest However, when these corrections are included, the elliptic flow is strongly modified at large p{sub T} We also investigate the stability of the viscous results by comparing the nonideal components of the stress tensor ({pi}{sup ij}) and their influence on the v{sub 2} spectrum to the expectation of the Navier-Stokes equations ({pi}{sup ij}=-{eta} ) We argue that when the stress tensor deviates from the Navier-Stokes form the dissipative corrections to spectra are too large for a hydrodynamic description to be reliable For typical Relativistic Heavy Ion Colloder initial conditions this happens for {eta}/s > or approx 03

Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions

Abstract: We generalize recent work to construct a map from the conformal Navier Stokes equations with holographically determined transport coefficients, in d spacetime dimensions, to the set of asymptotically locally AdSd+1 long wavelength solutions of Einstein's equations with a negative cosmological constant, for all 2$>d>2. We find simple explicit expressions for the stress tensor (slightly generalizing the recent result by Haack and Yarom (arXiv:0806.4602)), the full dual bulk metric and an entropy current of this strongly coupled conformal fluid, to second order in the derivative expansion, for arbitrary 2$>d>2. We also rewrite the well known exact solutions for rotating black holes in AdSd+1 space in a manifestly fluid dynamical form, generalizing earlier work in d = 4. To second order in the derivative expansion, this metric agrees with our general construction of the metric dual to fluid flows.

Introduction to the Numerical Analysis of Incompressible Viscous Flows

Abstract: This book treats the numerical analysis of finite element computational fluid dynamics. Assuming minimal background, the text covers finite element methods; the derivation, behavior, analysis, and numerical analysis of Navier Stokes equations; and turbulence and turbulence models used in simulations. Each chapter on theory is followed by a numerical analysis chapter that expands on the theory. The chapters contain numerous exercises. Introduction to the Numerical Analysis of Incompressible Viscous Flows provides the foundation for understanding the interconnection of the physics, mathematics, and numerics of the incompressible case, which is essential for progressing to the more complex flows not addressed in this book (e.g., viscoelasticity, plasmas, compressible flows, coating flows, flows of mixtures of fluids, and bubbly flows). With mathematical rigor and physical clarity, the book progresses from the mathematical preliminaries of energy and stress to finite element computational fluid dynamics in a format manageable in one semester. Audience: This unified treatment of fluid mechanics, analysis, and numerical analysis is intended for graduate students in mathematics, engineering, physics, and the sciences who are interested in understanding the foundations of methods commonly used for flow simulations.

Direct optimal growth analysis for timesteppers

Abstract: Methods are described for transient growth analysis of flows with arbitrary geometric complexity, where in particular the flow is not required to vary slowly in the streamwise direction. Emphasis is on capturing the global effects arising from localized convective stability in streamwise-varying flows. The methods employ the 'timestepper's approach' in which a nonlinear Navier-Stokes code is modified to provide evolution operators for both the forward and adjoint linearized equations. First, the underlying mathematical treatment in primitive flow variables is presented. Then, details are given for the inner level code modifications and outer level eigenvalue and SVD algorithms in the timestepper's approach. Finally, some examples are shown and guidance provided on practical aspects of this type of large-scale stability analysis. Copyright (C) 2008 John Wiley & Sons, Ltd.

Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations

Abstract: The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for the motion of shallow water, from the Navier-Stokes system for incompressible flows with a moving free surface [14]. These compressible systems are degenerate when vacuum state appears. We study initial-boundary-value problems for such systems for both bounded spatial domains or periodic domains. The dynamics of weak solutions and vacuum states are investigated rigorously.

An Effective Fluid-Structure Interaction Formulation for Vascular Dynamics by Generalized Robin Conditions

Abstract: In this work we focus on the modeling and numerical simulation of the fluid-structure interaction mechanism in vascular dynamics. We first propose a simple membrane model to describe the deformation of the arterial wall, which is derived from the Koiter shell equations and is applicable to an arbitrary geometry. Secondly, we consider a reformulation of the fluid-structure problem, in which the newly derived membrane model, thanks to its simplicity, is embedded into the fluid equations and will appear as a generalized Robin boundary condition. The original problem is then reduced to the solution of subsequent fluid equations defined on a moving domain and may be achieved with a fluid solver only. We also derive a stability estimate for the resulting numerical scheme. Finally, we propose new outflow absorbing boundary conditions, which are easy to implement and allow us to reduce significantly the spurious pressure wave reflections that typically appear in artificially truncated computational domains. We present several numerical results showing the effectiveness of the proposed approaches.

Regularity Criteria for the Three-dimensional Navier-Stokes Equations

Abstract: In this paper we consider the three-dimensional Navier-Stokes equations subject to periodic boundary condi- tions or in the whole space. We provide suYcient conditions, in terms of one component of the velocity field, or alternatively in terms of one component of the pressure gradient, for the regularity of strong solutions to the three-dimensional Navier- Stokes equations.

Forced Fluid Dynamics from Gravity

Abstract: We generalise the computations of arXiv:0712.2456 to generate long wavelength, asymptotically locally AdS_5 solutions to the Einstein-dilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity, our solutions are dual, under the AdS/CFT correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. These solutions turn out to be parametrised by four-velocity and temperature fields that are constrained to obey the boundary covariant Navier Stokes equations with a dilaton dependent forcing term. We explicitly evaluate the stress tensor and Lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the Weyl covariance of these expressions. We also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. As a check of our constructions we expand the exactly known solutions for rotating black holes in global AdS_5 in a boundary derivative expansion and find perfect agreement with all our results upto second order. We also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. Our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence.

Asymptotic Analysis for a Vlasov-Fokker-Planck/ Compressible Navier-Stokes System of Equations

Abstract: This article is devoted to the asymptotic analysis of a system of coupled kinetic and fluid equations, namely the Vlasov-Fokker-Planck equation and a compressible Navier-Stokes equation Such a system is used, for example, to model fluid-particle interactions arising in sprays, aerosols or sedimentation problems The asymptotic regime corresponding to a strong drag force and a strong Brownian motion is studied and the convergence toward a two phase macroscopic model is proved The proof relies on a relative entropy method

A Stochastic Lagrangian Representation of the Three-Dimensional Incompressible Navier-Stokes Equations

Abstract: In this paper we derive a probabilistic representation of the deterministic three-dimensional Navier-Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self-contained proof of local existence for the nonlinear stochastic system and can be extended to formulate stochastic representations of related hydrodynamic-type equations, including viscous Burgers equations and Lagrangian-averaged Navier-Stokes alpha models. © 2007 Wiley Periodicals, Inc.

Lower Bound on the Blow-up Rate of the Axisymmetric Navier-Stokes Equations

Abstract: Consider axisymmetric strong solutions of the incompressible Navier–Stokes equations in ℝ3 with non-trivial swirl. Let z denote the axis of symmetry and r measure the distance to the z-axis. Suppos...

On energetic variational approaches in modeling the nematic liquid crystal flows

Abstract: In this paper we present results for the existence of classical solutions of a hydrodynamical system modeling the flow of nematic liquid crystals. The system consists of a coupled system of Navier-Stokes equations and various kinematic transport equations for the molecular orientations. A formal physical derivation of the induced elastic stress using least action principle reflects the special coupling between the transport and the induced stress terms. The derivation and the analysis of the system falls into a general energetic variational framework for complex fluids with elastic effects due to the presence of nontrivial microstructures.