Showing papers on "Navier–Stokes equations published in 2004"
TL;DR: In this article, an eddy-viscosity model is proposed and applied in large-eddy simulation of turbulent shear flows with quite satisfactory results, which is essentially not more complicated than the Smagorinsky model, but is constructed in such a way that its dissipation is relatively small in transitional and near-wall regions.
Abstract: An eddy-viscosity model is proposed and applied in large-eddy simulation of turbulent shear flows with quite satisfactory results. The model is essentially not more complicated than the Smagorinsky model, but is constructed in such a way that its dissipation is relatively small in transitional and near-wall regions. The model is expressed in first-order derivatives, does not involve explicit filtering, averaging, or clipping procedures, and is rotationally invariant for isotropic filter widths. Because of these highly desirable properties the model seems to be well suited for engineering applications. In order to provide a foundation of the model, an algebraic framework for general three-dimensional flows is introduced. Within this framework several types of flows are proven to have zero energy transfer to subgrid scales. The eddy viscosity is zero in the same cases; the theoretical subgrid dissipation and the eddy viscosity have the same algebraic structure. In addition, the model is based on a fundament...
1,003 citations
TL;DR: In this paper, the authors present a framework for applying the method of proper orthogonal decomposition (POD) and Galerkin projection to compressible fluids and obtain an approximate version of the Navier-Stokes equations, valid for cold flows at moderate Mach number.
788 citations
Book•
01 Jan 2004
TL;DR: The Navier-Stokes equations under initial and boundary conditions were studied in this paper, where they were shown to be incompressible in the spatially periodic case and in the constant-coefficient case.
Abstract: Preface to the Classics Edition Introduction 1. The Navier-Stokes equations 2. Constant-coefficient Cauchy problems 3. Linear variable-coefficient Cauchy problems in 1D 4. A nonlinear example: Burgers' equations 5. Nonlinear systems in one space dimension 6. The Cauchy problem for systems in several dimensions 7. Initial-boundary value problems in one space dimension 8. Initial-boundary value problems in several space dimensions 9. The incompressible Navier-Stokes equations: the spatially periodic case 10. The incompressible Navier-Stokes equations under initial and boundary conditions Appendices References Author index Subject index.
764 citations
TL;DR: In this article, a spatially developing supersonic adiabatic flat plate boundary layer flow (at M∞=2.25 and Reθ≈4000) is analyzed by means of direct numerical simulation.
Abstract: A spatially developing supersonic adiabatic flat plate boundary layer flow (at M∞=2.25 and Reθ≈4000) is analyzed by means of direct numerical simulation. The numerical algorithm is based on a mixed weighted essentially nonoscillatory compact-difference method for the three-dimensional Navier–Stokes equations. The main objectives are to assess the validity of Morkovin’s hypothesis and Reynolds analogies, and to analyze the controlling mechanisms for turbulence production, dissipation, and transport. The results show that the essential dynamics of the investigated turbulent supersonic boundary layer flow closely resembles the incompressible pattern. The Van Driest transformed mean velocity obeys the incompressible law-of-the-wall, and the mean static temperature field exhibits a quadratic dependency upon the mean velocity, as predicted by the Crocco–Busemann relation. The total temperature has been found not to be precisely uniform, and total temperature fluctuations are found to be non-negligible. Consiste...
419 citations
Posted Content•
TL;DR: In this article, the stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are studied and the smallest closed invariant subspace for this model and the dynamics restricted to that subspace is shown to be ergodic.
Abstract: The stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are studied. We characterize the smallest closed invariant subspace for this model and show that the dynamics restricted to that subspace is ergodic. In particular, our results yield a purely geometric characterization of a class of noises for which the equation is ergodic in $Ł^2_0(\TT^2)$. Unlike previous works, this class is independent of the viscosity and the strength of the noise. The two main tools of our analysis are the \textit{asymptotic strong Feller} property, introduced in this work, and an approximate integration by parts formula. The first, when combined with a weak type of irreducibility, is shown to ensure that the dynamics is ergodic. The second is used to show that the first holds under a H{o}rmander-type condition. This requires some interesting nonadapted stochastic analysis.
340 citations
TL;DR: A new local discontinuous Galerkin method for the incompressible stationary Navier-Stokes equations is proposed and analyzed, which confirms the independence of the number of fixed point iterations with respect to the discretization parameters and works well for a wide range of Reynolds numbers.
Abstract: In this paper a new local discontinuous Galerkin method for the incompressible stationary Navier-Stokes equations is proposed and analyzed. Four important features render this method unique: its stability, its local conservativity, its high-order accuracy, and the exact satisfaction of the incompressibility constraint. Although the method uses completely discontinuous approximations, a globally divergence-free approximate velocity in H(div; Ω) is obtained by simple, element-by-element post-processing. Optimal error estimates are proven and an iterative procedure used to compute the approximate solution is shown to converge. This procedure is nothing but a discrete version of the classical fixed point iteration used to obtain existence and uniqueness of solutions to the incompressible Navier-Stokes equations by solving a sequence of Oseen problems. Numerical results are shown which verify the theoretical rates of convergence. They also confirm the independence of the number of fixed point iterations with respect to the discretization parameters. Finally, they show that the method works well for a wide range of Reynolds numbers.
301 citations
TL;DR: In this article, a detailed analysis of the dependence of drag reduction on the oscillatory parameters allows us to address conflicting results hitherto reported in the literature, and we assess the possibility for the power saved to be higher than the power spent for the movement of the walls (when mechanical losses are neglected).
Abstract: Direct numerical simulations of the incompressible Navier–Stokes equations are employed to study the turbulent wall-shear stress in a turbulent channel flow forced by lateral sinusoidal oscillations of the walls. The objective is to produce a documented database of numerically computed friction reductions. To this aim, the particular numerical requirements for such simulations, owing for example to the time-varying direction of the skin-friction vector, are considered and appropriately accounted for. A detailed analysis of the dependence of drag reduction on the oscillatory parameters allows us to address conflicting results hitherto reported in the literature. At the Reynolds number of the present simulations, we compute a maximum drag reduction of 44.7%, and we assess the possibility for the power saved to be higher than the power spent for the movement of the walls (when mechanical losses are neglected). A maximum net energy saving of 7.3% is computed. Furthermore, the scaling of the amount of drag reduction is addressed. A parameter, which depends on both the maximum wall velocity and the period of the oscillation, is found to be linearly related to drag reduction, as long as the half-period of the oscillation is shorter than a typical lifetime of the turbulent near-wall structures. For longer periods of oscillation, the scaling parameter predicts that drag reduction will decrease to zero more slowly than the numerical data. The same parameter also describes well the optimum period of oscillation for fixed maximum wall displacement, which is smaller than the optimum period for fixed maximum wall velocity, and depends on the maximum displacement itself.
287 citations
TL;DR: A conservative, second-order accurate fully implicit discretization of the Navier-Stokes and Cahn-Hilliard system that has an associated discrete energy functional is developed and convergence of the scheme numerically in both the presence and absence of flow is demonstrated.
285 citations
TL;DR: In this article, a primitive variable formulation for simulation of time-dependent incompressible flows in cylindrical coordinates is developed, where Spectral elements are used to discretise the meridional semi-plane, coupled with Fourier expansions in azimuth.
248 citations
TL;DR: In this article, the authors describe the nature of 3D separation and address the way in which topological rules based on a linear treatment of the Navier-Stokes equations can predict properties of the limiting streamlines, including the singularities which form.
Abstract: Flow separations in the corner regions of blade passages are common. The separations are three dimensional and have quite different properties from the two-dimensional separations that are considered in elementary courses of fluid mechanics. In particular the consequences for the flow may be less severe than the two-dimensional separation. This paper describes the nature of three-dimensional separation and addresses the way in which topological rules, based on a linear treatment of the Navier-Stokes equations, can predict properties of the limiting streamlines, including the singularities which form. The paper shows measurements of the flow field in a linear cascade of compressor blades and compares these with the results of 3D CFD. For corners without tip clearance, the presence of three-dimensional separation appears to be universal and the challenge for the designer is to limit the loss and blockage produced. The CFD appears capable of predicting this.Copyright © 2004 by ASME
225 citations
TL;DR: Conditional averaging is adopted for the Navier–Stokes equation, and one more parameter, based on the filter size, is introduced into the k−e model, and the filter-based model is shown to improve the predictive capability considerably.
TL;DR: The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil.
Abstract: We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around ${10}^{3}$. The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotation provides a mechanism for a brief elevation of center of mass near the cusplike turning points. The Navier-Stokes solutions further provide the missing quantity in the classical theory of lift, the instantaneous circulation, and suggest a revised model for the fluid forces.
TL;DR: Systematic numerical experiments indicate that a second order implicit time discretization of the viscous term, with the pressure and convective terms treated explicitly, is stable under the standard CFL condition.
TL;DR: The method of manufactured solutions is used to verify the order of accuracy of two finite‐volume Euler and Navier–Stokes codes, giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised.
Abstract: The method of manufactured solutions is used to verify the order of accuracy of two finite-volume Euler and Navier–Stokes codes. The Premo code employs a node-centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second-order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier–Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given. Copyright © 2004 John Wiley & Sons, Ltd.
TL;DR: In this paper, a finite-dimensional feedback controller with support in an arbitrary open subset w ⊂ Ω of positive measure was proposed to stabilize the Navier-Stokes equations on R d, d = 2, 3 with no-slip boundary conditions.
Abstract: The steady-state solutions to Navier-Stokes equations on Ω ⊂ R d , d = 2, 3, with no-slip boundary conditions, are locally exponentially stabilizable by a finite-dimensional feedback controller with support in an arbitrary open subset w ⊂ Ω of positive measure. The (finite) dimension of the feedback controller is related to the largest algebraic multiplicity of the unstable eigenvalues of the linearized equation.
TL;DR: In this paper, a hydrodynamic limit for the Vlasov-Navier-Stokes equations with non-constant density was proved using a relative entropy method, where the density involved in this system is the sum of the (constant) density of the fluid and of the macroscopic density of particles.
Abstract: The paper is devoted to the analysis of a hydrodynamic limit for the Vlasov-Navier-Stokes equations. This system is intended to model the evolution of particles interacting with a fluid. The coupling arises from the force terms. The limit problem is the Navier-Stokes system with non constant density. The density which is involved in this system is the sum of the (constant) density of the fluid and of the macroscopic density of the particles. The proof relies on a relative entropy method.
TL;DR: In this article, a method for simulating incompressible, imiscible, unsteady, Newtonian, multi-fluid flows with free surfaces is described, where a sharp interface separates fluids of different density and viscosity.
TL;DR: In this article, the authors study the nonstationary Navier-Stokes equations in the entire 3D space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.
Abstract: We study the nonstationary Navier-Stokes equations in the entire three-dimensional space and give some criteria on certain components of gradient of the velocity which ensure its global-in-time smoothness.
TL;DR: In this article, the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space time decoupled formulation where a least square minimisation procedure is performed in space at each time step.
TL;DR: The viscous slip coefficient was calculated for binary gaseous mixtures on the basis of the McCormack kinetic model of the Boltzmann equation, which was solved by the discrete velocity method as discussed by the authors.
Abstract: The viscous slip coefficient was calculated for binary gaseous mixtures on the basis of the McCormack kinetic model of the Boltzmann equation, which was solved by the discrete velocity method. The calculations were carried out for the three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. It was showed that for the mixture of helium and xenon, which has a large ration of the molecular masses, the slip coefficient significantly differs from that for a single gas. A comparison of the present results with those obtained by the moment method applied to the Boltzmann equation showed that the McCormack model equation provides reliable results with modest computational efforts. An example of application of the viscous slip coefficient was given.
TL;DR: In this paper, an approach is presented to derive transport equations for rarefied gases from the Boltzmann equation within higher orders of the Knudsen number, and the method focuses on the order of magnitude of the moments of the phase density.
Abstract: An approach is presented to derive transport equations for rarefied gases from the Boltzmann equation within higher orders of the Knudsen number. The method focuses on the order of magnitude of the moments of the phase density, and the order of accuracy of the transport equations, both measured in powers of the Knudsen number. The method is developed up to the third order, and it is shown that it yields the Euler equations at zeroth order, the Navier–Stokes–Fourier equations at first order, Grad’s 13 moment equations (with omission of a nonlinear term) at second order, and a regularization of these at third order. The method is discussed in detail, and compared with the classical methods of kinetic theory, i.e., Chapman–Enskog expansion and Grad moment method. The advantages of this method above the classical approaches are discussed conclusively. An important feature of the method presented is that the equations of any order are stable, other than in the Chapman–Enskog method, where the second and third ...
01 Jan 2004
TL;DR: In this paper, a stable equal-order finite element scheme for the Navier-Stokes equation is proposed based on filtering small-scale fluctuations of pressure and velocities by local projections.
Abstract: As an alternative to classical stabilization schemes as, for instance, Galerkin-Least-Squares or streamline diffusion techniques, a stable equal-order finite element scheme for the Navier-Stokes equation is proposed. The approach is based on filtering small-scale fluctuations of pressure and velocities by local projections. For the Stokes system, we prove stability and analyze the arising system matrix. Furthermore, the transport equation is analyzed with respect to stability and an a-priori estimate is given.
TL;DR: The linearized Navier-Stokes equations for a system of superimposed immiscible compressible ideal fluids are analyzed in this article, showing that the growth rate n obtained for an inviscid, compressible flow in an infinite domain is bounded by the growth rates obtained for the corresponding incompressible flows with uniform and exponentially varying density.
Abstract: The linearized Navier–Stokes equations for a system of superposed immiscible compressible ideal fluids are analyzed. The results of the analysis reconcile the stabilizing and destabilizing effects of compressibility reported in the literature. It is shown that the growth rate n obtained for an inviscid, compressible flow in an infinite domain is bounded by the growth rates obtained for the corresponding incompressible flows with uniform and exponentially varying density. As the equilibrium pressure at the interface p∞ increases (less compressible flow), n increases towards the uniform density result, while as the ratio of specific heats γ increases (less compressible fluid), n decreases towards the exponentially varying density incompressible flow result. This remains valid in the presence of surface tension or for viscous fluids and the validity of the results is also discussed for finite size domains. The critical wavenumber imposed by the presence of surface tension is unaffected by compressibility. However, the results show that the surface tension modifies the sensitivity of the growth rate to a differential change in γ for the lower and upper fluids. For the viscous case, the linearized equations are solved numerically for different values of p∞ and γ. It is found that the largest differences compared with the incompressible cases are obtained at small Atwood numbers. The most unstable mode for the compressible case is also bounded by the most unstable modes corresponding to the two limiting incompressible cases.
TL;DR: In this article, a two-and a three-level finite element method for numerical simulation of incompressible flow governed by the Navier-Stokes equations is presented, where the resolution of the large and small scales takes place on levels 1 and 2 with the aid of diverse approaches and the dynamic calculation of a subgrid viscosity representing the effect of the unresolved scales constitutes level 3 of the algorithm.
TL;DR: An anisotropic a posteriori error analysis of the advection-diffusion-reaction and the Stokes problems is developed, which yields an adaptive algorithm which, via an iterative process, can be used for designing the optimal mesh for the problem at hand.
TL;DR: In this article, the linearized version of the stationary Navier-Stokes equations on a subdomain Ω of a smooth, compact Riemannian manifold M is considered, where the boundary of Ω is assumed to be only C 1 and even Lipschitz.
Abstract: We consider the linearized version of the stationary Navier-Stokes equations on a subdomain Ω of a smooth, compact Riemannian manifold M. The emphasis is on regularity: the boundary of Ω is assumed to be only C1 and even Lipschitz, and the data are selected from appropriate Sobolev-Besov scales. Our approach relies on the method of boundary integral equations, suitably adapted to the variable-coefficient setting we are considering here. Applications to the stationary, nonlinear Navier-Stokes equations in this context are also discussed.
TL;DR: In this paper, the numerical approximation of Navier-Stokes equations in a domain with moving boundaries using the arbitrary Lagrangian-Eulerian (ALE) method is presented.
TL;DR: In this article, the radiation of high-order spinning modes from an unflanged duct with or without a mean flow is studied numerically, based on solutions of the linearized Euler equations (LEE) for propagation in the duct and near field and the acoustic analogy for far field radiation.
Abstract: The radiation of high-order spinning modes from an unflanged duct with or without a mean flow is studied
numerically. The application is to noise radiation from the intake duct of an aircraft engine. The numerical
method is based on solutions of the linearized Euler equations (LEE) for propagation in the duct and near field
and the acoustic analogy for far-field radiation. A formulation of the LEE is used for a single azimuthal mode,
which offers an advantage in terms of computational efficiency: in the case of an axisymmetric mean flow-field,
this model reduces computing costs connected with a three-dimensional model. In the solution process, acoustic
waves are admitted from upstream into the propagation area surrounding the exit of an axisymmetric duct and
the region immediately downstream. The wave admission is realized through an absorbing nonreflecting boundary
treatment, which admits incoming waves and damps spurious waves generated by the numerical solutions. The
wave propagation is calculated using a high-order compact scheme. Far-field directivity is estimated by solving
the Ffowcs Williams–Hawkings equations. The far-field prediction is compared with analytic solutions, and good
agreement is found.
TL;DR: In this paper, the authors considered the Navier-Stokes equations with a density-dependent viscosity in a bounded domain and proved the local existence of unique strong solutions for all initial data satisfying a natural compatibility condition.
Abstract: In this paper we consider the incompressible Navier–Stokes equations with a density-dependent viscosity in a bounded domain Ω of R n ( n = 2 , 3 ) . We prove the local existence of unique strong solutions for all initial data satisfying a natural compatibility condition. This condition is also necessary for a very general initial data. Moreover, we provide a blow-up criterion for the regularity of the strong solution. For these results, the initial density need not be strictly positive. It may vanish in an open subset of Ω .
TL;DR: In this article, a hybrid approach that combines a continuum approach solving the Navier-Stokes equations and a particle method called the information preservation (IP) method is implemented to simulate subsonic, rarefied gas flows accurately and efficiently.