Showing papers on "Navier–Stokes equations published in 2010"
TL;DR: In this paper, the impact of a fluid drop onto a planar solid surface at high speed was studied and it was shown that at impact, kinetic energy dominates over surface energy and inertia dominates over viscous effects.
Abstract: We study the impact of a fluid drop onto a planar solid surface at high speed so that at impact, kinetic energy dominates over surface energy and inertia dominates over viscous effects. As the drop spreads, it deforms into a thin film, whose thickness is limited by the growth of a viscous boundary layer near the solid wall. Owing to surface tension, the edge of the film retracts relative to the flow in the film and fluid collects into a toroidal rim bounding the film. Using mass and momentum conservation, we construct a model for the radius of the deposit as a function of time. At each stage, we perform detailed comparisons between theory and numerical simulations of the Navier–Stokes equation.
351 citations
TL;DR: A general time-discrete framework to design asymptotic-preserving schemes for initial value problem of the Boltzmann kinetic and related equations, which can capture the macroscopic fluid dynamic (Euler) limit even if the small scale determined by the Knudsen number is not numerically resolved.
340 citations
TL;DR: A new unified family of arbitrary high order accurate explicit one-step finite volume and discontinuous Galerkin schemes on unstructured triangular and tetrahedral meshes for the solution of the compressible Navier–Stokes equations is proposed.
282 citations
TL;DR: It is shown that the RBVMS formulation globally conserves angular momentum, a feature that is felt to be important for flows dominated by rotation, and that is not shared by standard stabilized formulations of fluid flow.
282 citations
TL;DR: A physically consistent phase-field model that admits an energy law is proposed, and several energy stable, efficient, and accurate time discretization schemes for the coupled nonlinear phase- field model are constructed and analyzed.
Abstract: Modeling and numerical approximation of two-phase incompressible flows with different densities and viscosities are considered. A physically consistent phase-field model that admits an energy law is proposed, and several energy stable, efficient, and accurate time discretization schemes for the coupled nonlinear phase-field model are constructed and analyzed. Ample numerical experiments are carried out to validate the correctness of these schemes and their accuracy for problems with large density and viscosity ratios.
279 citations
TL;DR: In this paper, the authors proposed a second order slip flow model to predict viscous flow over a shrinking sheet, and the closed solution is an exact solution of the full governing Navier-Stokes equations.
260 citations
TL;DR: Tezduyar et al. as mentioned in this paper showed that using the element vector-based definition of stabilization parameters circumvents the well-known instability associated with conventional stabilized formulations at small time steps.
226 citations
TL;DR: In this paper, the authors compare the characteristics of the wake of an actuator disc, modelled using a steady solution to the Reynolds-averaged Navier-Stokes (RANS) simulated equations, with the k-ω shear stress transport (SST) turbulence model, to experimental data measured behind discs of various porosities.
Abstract: The actuator disc is a useful method for parameterising a tidal stream turbine in a solution of the Reynolds-averaged Navier–Stokes equations. An actuator disc is a region where similar forces are applied to a flow as would be imposed by a turbine. It is useful where large-scale flow characteristics are of interest, such as the far wake, free surface effects, or installation of multi-turbine arrays. This study compares the characteristics of the wake of an actuator disc, modelled using a steady solution to the Reynolds-averaged Navier–Stokes (RANS) simulated equations, with the k–ω shear stress transport (SST) turbulence model, to experimental data measured behind discs of various porosities. The results show that the wake of the experimental and modelled discs has similar characteristics; in both model and experiment, velocity in the near wake decreased as thrust coefficient increased. However, the near wake region in the experiment was shorter than simulated in the model because of near wake turbulence. This, combined with lower ambient turbulence levels in the model, meant that the far wake recovered further downstream, while showing similar overall trends in velocity and turbulence intensity.
219 citations
TL;DR: In this paper, the authors considered the regularity criteria for the incompressible Navier?Stokes equations connected with one velocity component and proved that the weak solution is regular, provided,, \frac {10}{3} SRC=http://ej.iop.org/images/0951-7715/23/5/004/non327722in003.gif/> or provided, if or if s (3,?].
Abstract: We consider the regularity criteria for the incompressible Navier?Stokes equations connected with one velocity component. Based on the method from Cao and Titi (2008 Indiana Univ. Math. J. 57 2643?61) we prove that the weak solution is regular, provided , , \frac {10}{3} SRC=http://ej.iop.org/images/0951-7715/23/5/004/non327722in003.gif/> or provided , if or if s (3, ?]. As a corollary, we also improve the regularity criteria expressed by the regularity of or .
200 citations
TL;DR: In this paper, a generalization of Bjorken flow is described, where the medium has finite transverse size and expands both radially and along the beam axis, and the local four-velocity in the flow is entirely determined by the assumption of symmetry under a subgroup of the conformal group.
Abstract: I explain a generalization of Bjorken flow where the medium has finite transverse size and expands both radially and along the beam axis. If one assumes that the equations of viscous hydrodynamics can be used, with p={epsilon}/3 and zero bulk viscosity, then the flow I describe can be developed into an exact solution of the relativistic Navier-Stokes equations. The local four-velocity in the flow is entirely determined by the assumption of symmetry under a subgroup of the conformal group.
197 citations
TL;DR: The numerical results indicate that this reconstruction-based discontinuous Galerkin (RDG) method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods.
TL;DR: An immersed-boundary algorithm for incompressible flows with complex boundaries, suitable for Cartesian or curvilinear grid system, and has the property that the integrals of the force field and of its moment on the grid are conserved, independent of the grid topology.
TL;DR: In this paper, the global well-posedness issue for the barotropic compressible Navier-Stokes system in the whole space with d ≧ 2 was studied and the global existence was established for small perturbations of a stable equilibrium state.
Abstract: The present paper is dedicated to the global well-posedness issue for the barotropic compressible Navier–Stokes system in the whole space \({\mathbb{R}^d}\) with d ≧ 2. We aim at extending the work by Danchin (Inventiones Mathematicae 141(3):579–614, 2000) to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable Lp-type Besov norms, we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true. In passing, we obtain new estimates for the linearized and the paralinearized systems which may be of interest for future works on compressible flows.
TL;DR: In this article, the authors established the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow.
Abstract: We establish the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow. For the Navier-Stokes equations, there exist no natural invariant regions for the equations with the real physical viscosity term so that the uniform sup-norm of solutions with respect to the physical viscosity coefficient may not be directly controllable. Furthermore, convex entropy-entropy flux pairs may not produce signed entropy dissipation measures.
To overcome these difficulties, we first develop uniform energy-type estimates with respect to the viscosity coefficient for solutions of the Navier-Stokes equations and establish the existence of measure-valued solutions of the isentropic Euler equations generated by the Navier-Stokes equations. Based on the uniform energy-type estimates and the features of the isentropic Euler equations, we establish that the entropy dissipation measures of the solutions of the Navier-Stokes equations for weak entropy-entropy flux pairs, generated by compactly supported C2 test functions, are confined in a compact set in H−1, which leads to the existence of measure-valued solutions that are confined by the Tartar-Murat commutator relation.
A careful characterization of the unbounded support of the measure-valued solution confined by the commutator relation yields the reduction of the measurevalued solution to a Dirac mass, which leads to the convergence of solutions of the Navier-Stokes equations to a finite-energy entropy solution of the isentropic Euler equations with finite-energy initial data, relative to the different end-states at infinity. © 2010 Wiley Periodicals, Inc.
TL;DR: The present implementation of stabilization finite element methods for the resolution of the 3D time-dependent incompressible Navier-Stokes equations is able to exhibit good stability and accuracy properties for high Reynolds number flows with unstructured meshes.
04 Jan 2010
TL;DR: The HDG method inherits the geometric flexibility and arbitrary high order accuracy of Discontinuous Galerkin methods, but offers a significant reduction in the computational cost as well as improved accuracy and convergence properties.
Abstract: In this paper, we present a Hybridizable Discontinuous Galerkin (HDG) method for the solution of the compressible Euler and Navier-Stokes equations. The method is devised by using the discontinuous Galerkin approximation with a special choice of the numerical fluxes and weakly imposing the continuity of the normal component of the numerical fluxes across the element interfaces. This allows the approximate conserved variables defining the discontinuous Galerkin solution to be locally condensed, thereby resulting in a reduced system which involves only the degrees of freedom of the approximate traces of the solution. The HDG method inherits the geometric flexibility and arbitrary high order accuracy of Discontinuous Galerkin methods, but offers a significant reduction in the computational cost as well as improved accuracy and convergence properties. In particular, we show that HDG produces optimal converges rates for both the conserved quantities as well as the viscous stresses and the heat fluxes. We present some numerical results to demonstrate the accuracy and convergence properties of the method.
TL;DR: The method features an unstructured dynamic mesh capable of modeling complicated geometries, an arbitrary Lagrangian-Eulerian framework that allows for large displacements of the moving fluid domain, monolithic coupling between the fluid and structure equations, and fully implicit time discretization.
TL;DR: A conservative, second-order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered Cartesian grid, suitable for Large-Eddy Simulations of high-Reynolds number flows.
TL;DR: In this article, the authors focus on the theoretical treatment of the laminar, incompressible, and time-dependent flow of a viscous fluid in a porous channel with orthogonally moving walls.
Abstract: This paper focuses on the theoretical treatment of the laminar, incompressible, and time-dependent flow of a viscous fluid in a porous channel with orthogonally moving walls Assuming uniform injection or suction at the porous walls, two cases are considered for which the opposing walls undergo either uniform or nonuniform motions For the first case, we follow Dauenhauer and Majdalani Phys Fluids 15, 1485 2003 by taking the wall expansion ratio to be time invariant and then proceed to reduce the Navier‐Stokes equations into a fourth order ordinary differential equation with four boundary conditions Using the homotopy analysis method HAM, an optimized analytical procedure is developed that enables us to obtain highly accurate series approximations for each of the multiple solutions associated with this problem By exploring wide ranges of the control parameters, our procedure allows us to identify dual or triple solutions that correspond to those reported by Zaturska et al Fluid Dyn Res 4, 151 1988 Specifically, two new profiles are captured that are complementary to the type I solutions explored by Dauenhauer and Majdalani In comparison to the type I motion, the so-called types II and III profiles involve steeper flow turning streamline curvatures and internal flow recirculation The second and more general case that we consider allows the wall expansion ratio to vary with time Under this assumption, the Navier‐ Stokes equations are transformed into an exact nonlinear partial differential equation that is solved analytically using the HAM procedure In the process, both algebraic and exponential models are considered to describe the evolution of t from an initial 0 to a final state 1 In either case, we find the time-dependent solutions to decay very rapidly to the extent of recovering the steady state behavior associated with the use of a constant wall expansion ratio We then conclude that the time-dependent variation of the wall expansion ratio plays a secondary role that may be justifiably ignored © 2010 American Institute of Physics doi:101063/13392770
TL;DR: In this article, two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered and the existence of the trajectory attractor for both systems is proved.
Abstract: Two different models for the evolution of incompressible binary fluid mixtures in a three-dimensional bounded domain are considered. They consist of the 3D incompressible Navier-Stokes equations, subject to time-dependent external forces and coupled with either a convective Allen-Cahn or Cahn-Hilliard equation. Such systems can be viewed as generalizations of the Navier-Stokes equations to two-phase fluids. Using the trajectory approach, the authors prove the existence of the trajectory attractor for both systems.
TL;DR: In this article, an analytical solution of electro-osmotic flow (EOF) velocity distribution as functions of radial distance, periodic time and relevant parameters was derived by numerical computations, the influences of the electrokinetic width K denoting the characteristic scale of the microannulus to Debye length, the wall zeta potential ratio β denoting inner cylinder to the outer cylinder, the ratio α denoting of the annular inner radius to outer radius and the periodical EOF electric oscillating Reynolds number Re on velocity profiles are presented.
Abstract: Flow behavior of time periodic electro-osmosis in a cylindrical microannulus is investigated based on a linearized Poisson–Boltzmann equation and Navier–Stokes equation. An analytical solution of electro-osmotic flow (EOF) velocity distribution as functions of radial distance, periodic time and relevant parameters is derived. By numerical computations, the influences of the electrokinetic width K denoting the characteristic scale of the microannulus to Debye length, the wall zeta potential ratio β denoting the inner cylinder to the outer cylinder, the ratio α denoting of the annular inner radius to outer radius and the periodical EOF electric oscillating Reynolds number Re on velocity profiles are presented. Results show that when electric oscillating Reynolds number is low and the electrokinetic width K is large, the electro-osmotic velocity amplitude shows a square pluglike profile. When the Reynolds number is high, the driving effect of the electric force decreases immediately away from the two cylindr...
TL;DR: In this paper, various approximations to unsteady aerodynamics are examined for the aero-elastic analysis of a thin double-wedge airfoil in hypersonic flow.
Abstract: DOI: 10.2514/1.C000190 Various approximations to unsteady aerodynamics are examined for the aeroelastic analysis of a thin doublewedge airfoil in hypersonic flow. Flutter boundaries are obtained using classical hypersonic unsteady aerodynamic theories: piston theory, Van Dyke’s second-order theory, Newtonian impact theory, and unsteady shock-expansion theory. The theories are evaluated by comparing the flutter boundaries with those predicted using computational fluid dynamics solutions to the unsteady Navier–Stokes equations. Inaddition, several alternative approaches to the classical approximations are also evaluated: two different viscous approximations based on effective shapes and combined approximate computational approaches that use steady-state computational-fluid-dynamics-based surrogatemodelsinconjunction withpistontheory.Theresultsindicatethat,with theexceptionof first-order piston theory and Newtonian impact theory, the approximate theories yield predictions between 3 and 17% of normalized root-mean-square error and between 7 and 40% of normalized maximum error of the unsteady Navier–Stokes predictions. Furthermore, the demonstrated accuracy of the combined steady-state computational fluid dynamics and piston theory approaches suggest that important nonlinearities in hypersonic flow are primarily due to steadystate effects. This implies that steady-state flow analysis may be an alternative to time-accurate Navier–Stokes solutions for capturing complex flow effects.
TL;DR: A time-dependent flux function from a high-order discontinuous reconstruction based on the Boltzmann equation is presented, which has no specific requirement on the smoothness of the initial data and the kinetic equation has the mechanism to construct a dissipative wave structure starting from an initially discontinuous flow condition on a time scale larger than the particle collision time.
TL;DR: A posteriori error estimation and anisotropic mesh refinement for three-dimensional laminar aerodynamic flow simulations for goal-oriented refinement of the optimal order symmetric interior penalty discontinuous Galerkin discretization.
TL;DR: A stochastic model to simulate the flow of gases, which are not in thermodynamic equilibrium, and the application to the Knudsen paradox demonstrates the correctness and relevance of this development, and comparisons with existing kinetic equations and standard solution algorithms reveal its advantages.
TL;DR: In this article, a large eddy simulation of turbulent cavitating flow in a venturi nozzle is conducted, where the fully compressible Favre-filtered Navier-Stokes equations are coupled with a homogeneous equilibrium cavitation model, and the dynamic Smagorinsky subgrid-scale turbulence model is employed to close the filtered nonlinear convection terms.
Abstract: Large eddy simulation of turbulent cavitating flow in a venturi nozzle is conducted. The fully compressible Favre-filtered Navier-Stokes equations are coupled with a homogeneous equilibrium cavitation model. The dynamic Smagorinsky subgrid-scale turbulence model is employed to close the filtered nonlinear convection terms. The equations are numerically integrated in the context of a generalized curvilinear coordinate system to facilitate geometric complexities. A sixth-order compact finite difference scheme is employed for the Navier—Stokes equations with the AUSM + -up scheme to handle convective terms in the presence of large density gradients. The stiffness of the system due to the incompressibility of the liquid phase is addressed through an artificial increase in the Mach number. The simulation predicts the formation of a vapor cavity at the venturi throat with an irregular shedding of the small scale vapor structures near the turbulent cavity closure region. The vapor formation at the throat is observed to suppress the velocity fluctuations due to turbulence. The collapse of the vapor structures in the downstream region is a major source of vorticity production, resulting into formation of hairpin vortices. A detailed analysis of the vorticity transport equation shows a decrease in the vortex-stretching term due to cavitation. A substantial increase in the baroclinic torque is observed in the regions where the vapor structures collapse. A spectra of the pressure fluctuations in the far-field downstream region show an increase in the acoustic noise at high frequencies due to cavitation.
TL;DR: In this paper, the authors compute the continuum thermohydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed by Sbragaglia et al. The method is stable and reliable up to temperature jumps between top and bottom walls of the order of 50% the averaged bulk temperature.
Abstract: We compute the continuum thermohydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed by Sbragaglia et al. [J. Fluid Mech. 628, 299 (2009)]. We show that the hydrodynamical manifold is given by the correct compressible Fourier–Navier–Stokes equations for a perfect fluid. We validate the numerical algorithm by means of exact results for transition to convection in Rayleigh–Benard compressible systems and against direct comparison with finite-difference schemes. The method is stable and reliable up to temperature jumps between top and bottom walls of the order of 50% the averaged bulk temperature. We use this method to study Rayleigh–Taylor instability for compressible stratified flows and we determine the growth of the mixing layer at changing Atwood numbers up to At∼0.4. We highlight the role played by the adiabatic gradient in stopping the mixing layer growth in the presence of high stratification and we quantify the asymmetric growth rate...
TL;DR: The schemes solving the first-order advection-diffusion system give a tremendous speed-up in CPU time over traditional scalar schemes despite the additional cost of carrying extra variables and solving equations for them.
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19 Nov 2010
TL;DR: In this article, a stabilizable feedback linear controller is proposed to suppress instabilities and turbulence occurring in the dynamics of the fluid, which is a linear combination of eigenfunctions for the corresponding linearized systems.
Abstract: In this chapter we discuss the feedback stabilization of stationary (equilibrium) solutions to Navier–Stokes equations. The design of a robust stabilizing feedback control is the principal way to suppress instabilities and turbulence occurring in the dynamics of the fluid and we treat this problem in the case of internal and boundary controllers. The first case, already presented in an abstract setting in Chap. 2, is that in which the controller is distributed in a spatial domain \(O\) and has compact support taken arbitrarily small. The second case is that where the controller is concentrated on the boundary \(\partial O\). In both cases, we design a stabilizable feedback linear controller which is robust and has a finite-dimensional structure, that is, it is a linear combination of eigenfunctions for the corresponding linearized systems. From the control theory point of view, this means that the actuation, though infinite-dimensional, is confined to an arbitrary subdomain \(O_{\rm 0} \) or to the boundary.
TL;DR: This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.
Abstract: Acoustic wave propagation in flow ducts is commonly modeled with time-domain non-linear Navier–Stokes equation methodologies. To reduce computational effort, investigations of a linearized approach in frequency domain are carried out. Calculations of sound wave propagation in a straight duct are presented with an orifice plate and a mean flow present. Results of transmission and reflections at the orifice are presented on a two-port scattering matrix form and are compared to measurements with good agreement. The wave propagation is modeled with a frequency domain linearized Navier–Stokes equation methodology. This methodology is found to be efficient for cases where the acoustic field does not alter the mean flow field, i.e., when whistling does not occur.