Showing papers on "Navier–Stokes equations published in 2001"
01 Dec 2001
TL;DR: A class of automated methods for digital inpainting using ideas from classical fluid dynamics to propagate isophote lines continuously from the exterior into the region to be inpainted is introduced.
Abstract: Image inpainting involves filling in part of an image or video using information from the surrounding area. Applications include the restoration of damaged photographs and movies and the removal of selected objects. We introduce a class of automated methods for digital inpainting. The approach uses ideas from classical fluid dynamics to propagate isophote lines continuously from the exterior into the region to be inpainted. The main idea is to think of the image intensity as a 'stream function for a two-dimensional incompressible flow. The Laplacian of the image intensity plays the role of the vorticity of the fluid; it is transported into the region to be inpainted by a vector field defined by the stream function. The resulting algorithm is designed to continue isophotes while matching gradient vectors at the boundary of the inpainting region. The method is directly based on the Navier-Stokes equations for fluid dynamics, which has the immediate advantage of well-developed theoretical and numerical results. This is a new approach for introducing ideas from computational fluid dynamics into problems in computer vision and image analysis.
1,068 citations
TL;DR: In this article, the velocity boundary condition for curved boundaries in the lattice Boltzmann equation (LBE) was studied for moving boundaries by combination of the "bounce-back" scheme and spatial interpolations of first or second order.
Abstract: We study the velocity boundary condition for curved boundaries in the lattice Boltzmann equation (LBE). We propose a LBE boundary condition for moving boundaries by combination of the “bounce-back” scheme and spatial interpolations of first or second order. The proposed boundary condition is a simple, robust, efficient, and accurate scheme. Second-order accuracy of the boundary condition is demonstrated for two cases: (1) time-dependent two-dimensional circular Couette flow and (2) two-dimensional steady flow past a periodic array of circular cylinders (flow through the porous media of cylinders). For the former case, the lattice Boltzmann solution is compared with the analytic solution of the Navier–Stokes equation. For the latter case, the lattice Boltzmann solution is compared with a finite-element solution of the Navier–Stokes equation. The lattice Boltzmann solutions for both flows agree very well with the solutions of the Navier–Stokes equations. We also analyze the torque due to the momentum transfer between the fluid and the boundary for two initial conditions: (a) impulsively started cylinder and the fluid at rest, and (b) uniformly rotating fluid and the cylinder at rest.
1,063 citations
TL;DR: In this paper, the Lagrange-multiplier-based fictitious domain methods are combined with finite element approximations of the Navier-Stokes equations occurring in the global model to simulate incompressible viscous fluid flow past moving rigid bodies.
982 citations
01 Aug 2001
TL;DR: The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer graphics applications.
Abstract: In this paper, we propose a new approach to numerical smoke simulation for computer graphics applications. The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer graphics applications (as compared to the much finer grids used in the computational fluid dynamics literature). We use the inviscid Euler equations in our model, since they are usually more appropriate for gas modeling and less computationally intensive than the viscous Navier-Stokes equations used by others. In addition, we introduce a physically consistent vorticity confinement term to model the small scale rolling features characteristic of smoke that are absent on most coarse grid simulations. Our model also correctly handles the inter-action of smoke with moving objects.
937 citations
TL;DR: In this paper, the NavierStokes equations are locally well-posed for smooth enough initial data as long as one imposes appropriate boundary conditions on the pressure at ∞, where u is the velocity and p is the pressure.
860 citations
TL;DR: In this article, the authors consider the accuracy of projection method approximations to the initial-boundary-value problem for the incompressible Navier-Stokes equations and present an improved projection algorithm which is fully second-order accurate.
841 citations
TL;DR: In this paper, the existence of globally defined weak solutions to the Navier-Stokes equations of compressible isentropic flows in 3D space dimensions was proved on the condition that the adiabatic constant satisfies γ ≥ 3/2.
Abstract: We prove the existence of globally defined weak solutions to the Navier—Stokes equations of compressible isentropic flows in three space dimensions on condition that the adiabatic constant satisfies
$ \gamma > 3/2 $
.
799 citations
TL;DR: In this article, an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations is presented.
641 citations
TL;DR: In this article, the authors propose an approach to couple the original 3D equations with a convenient 1D model for the analysis of flows in compliant vessels, which allows for a dramatic reduction of the computational complexity and is suitable for ''absorbing» outgoing pressure waves.
595 citations
TL;DR: In this paper, a random flow generation (RFG) technique is presented, which can be used for initial/inlet boundary generation in LES (Large-Eddy-Simulations) or particle tracking in RANS (Reynolds-Averaged Navier-Stokes) computations of turbulent flows.
Abstract: A random flow generation (RFG) technique is presented, which can be used for initial/ inlet boundary generation in LES (Large-Eddy-Simulations) or particle tracking in LES/ RANS (Reynolds-Averaged Navier-Stokes) computations of turbulent flows. The technique is based on previous methods of synthesizing divergence-free vector fields from a sample of Fourier harmonics and allows to generate non-homogeneous anisotropic flow field representing turbulent velocity fluctuations. It was validated on the cases of boundary layer and flat plate flows. Applications of the technique to LES and particle tracking are considered
584 citations
TL;DR: In this article, an approximate deconvolution model for large-eddy simulation of incompressible flows is applied to turbulent channel flow and the effect of nonrepresented scales is modeled by a relaxation regularization involving a secondary filter operation.
Abstract: The approximate deconvolution model (ADM) for the large-eddy simulation of incompressible flows is detailed and applied to turbulent channel flow. With this approach an approximation of the unfiltered solution is obtained by repeated filtering. Given a good approximation of the unfiltered solution, the nonlinear terms of the filtered Navier–Stokes equations can be computed directly. The effect of nonrepresented scales is modeled by a relaxation regularization involving a secondary filter operation. Large-eddy simulations are performed for incompressible channel flow at Reynolds numbers based on the friction velocity and the channel half-width of Reτ=180 and Reτ=590. Both simulations compare well with direct numerical simulation (DNS) data and show a significant improvement over results obtained with classical subgrid scale models such as the standard or the dynamic Smagorinsky model. The computational cost of ADM is lower than that of dynamic models or the velocity estimation model.
01 Aug 2001
TL;DR: A catalog record for this book is available from the British Library as mentioned in this paper, where the catalog record can be found in the catalogue of the British Museum's Archives of Science and Technology.
Abstract: A catalog record for this book is available from the British Library.
TL;DR: In this paper, the authors derived the Saint-Venant system for the shallow waters including small friction, viscosity and Coriolis-Boussinesq factor departing from the Navier-Stokes system with a free moving boundary.
Abstract: We derive the Saint-Venant system for the shallow waters including small friction, viscosity and Coriolis-Boussinesq factor departing from the Navier-Stokes system with a free moving boundary. This derivation relies on the hydrostatic approximation where we follow the role of viscosity and friction on the bottom. Numerical comparisons between the limiting Saint-Venant system and direct Navier-Stokes simulation allow to validate this derivation.
TL;DR: An immersed interface method for the incompressible Navier–Stokes equations with singular forces along one or several interfaces in the solution domain is proposed based on a second-order projection method with modifications only at grid points near or on the interface.
TL;DR: In this article, a high-accuracy discrete singular convolution (DSC) approach is proposed for the numerical simulation of coupled convective heat transfer problems, where the problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures.
Abstract: This article introduces a high-accuracy discrete singular convolution (DSC) for the numerical simulation of coupled convective heat transfer problems. The problem of a buoyancy-driven cavity is solved by two completely independent numerical procedures. One is a quasi-wavelet-based DSC approach, which uses the regularized Shannon's kernel, while the other is a standard form of the Galerkin finite-element method. The integration of the Navier-Stokes and energy equations is performed by employing velocity correction-based schemes. The entire laminar natural convection range of 10 3 h Ra h 10 8 is numerically simulated by both schemes. The reliability and robustness of the present DSC approach is extensively tested and validated by means of grid sensitivity and convergence studies. As a result, a set of new benchmark quality data is presented. The study emphasizes quantitative, rather than qualitative comparisons.
TL;DR: It is shown on a variety of problems that the most cost-effective simulations can be obtained using higher-order basis functions when compared with the traditional linear basis.
Abstract: Stabilized finite element methods have been shown to yield robust, accurate numerical solutions to both the compressible and incompressible Navier-Stokes equations for laminar and turbulent flows. The present work focuses on the application of higher-order, hierarchical basis functions to the incompressible Navier-Stokes equations using a stabilized finite element method. It is shown on a variety of problems that the most cost-effective simulations (in terms of CPU time, memory, and disk storage) can be obtained using higher-order basis functions when compared with the traditional linear basis. In addition, algorithms will be presented for the efficient implementation of these methods within the traditional finite element data structures
TL;DR: It is proved existence and uniqueness of local and global solutions for a system of equations concerning an incompressible viscoelastic fluid of the Oldroyd type and a new a priori estimate for the two-dimensional Navier-Stokes system.
Abstract: We prove existence and uniqueness of local and global solutions for a system of equations concerning an incompressible viscoelastic fluid of the Oldroyd type. We also show a new a priori estimate f...
TL;DR: A finite element formulation for the numerical solution of the stationary incompressible Navier–Stokes equations including Coriolis forces and the permeability of the medium using the algebraic version of the sub-grid scale approach.
TL;DR: In this paper, the authors derive analytic criteria for the existence of hyperbolic (attracting or repelling), elliptic, and parabolic material lines in two-dimensional turbulence.
Abstract: We derive analytic criteria for the existence of hyperbolic (attracting or repelling), elliptic, and parabolic material lines in two-dimensional turbulence. The criteria use a frame-independent Eulerian partition of the physical space that is based on the sign definiteness of the strain acceleration tensor over directions of zero strain. For Navier–Stokes flows, our hyperbolicity criterion can be reformulated in terms of strain, vorticity, pressure, viscous and body forces. The special material lines we identify allow us to locate different kinds of material structures that enhance or suppress finite-time turbulent mixing: stretching and folding lines, Lagrangian vortex cores, and shear jets. We illustrate the use of our criteria on simulations of two-dimensional barotropic turbulence.
TL;DR: In this article, a simple filtering procedure for stabilizing the spectral element method (SEM) for the unsteady advection-diffusion and Navier-Stokes equations is presented.
Abstract: We present a simple filtering procedure for stabilizing the spectral element method (SEM) for the unsteady advection–diffusion and Navier–Stokes equations. A number of example applications are presented, along with basic analysis for the advection–diffusion case.
TL;DR: The key idea is the treatment of the curvature terms by a variational formulation and in the context of a discontinuous in time space–time element discretization stability in (weak) energy norms can be proved.
Abstract: The instationary Navier–Stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions. A stable finite element discretization is presented. The key idea is the treatment of the curvature terms by a variational formulation. In the context of a discontinuous in time space–time element discretization stability in (weak) energy norms can be proved. Numerical examples in 2 and 3 space dimensions are given.
TL;DR: In this paper, a number of extended hydrodynamics models have been proposed to model hypersonic flows about space vehicles in low earth orbits or flows in microchannels of microelectromechanical devices.
Abstract: In hypersonic flows about space vehicles in low earth orbits or flows in microchannels of microelectromechanical devices, the local Knudsen number lies in the continuum–transition regime Navier–Stokes equations are not adequate to model these flows since they are based on small deviation from local thermodynamic equilibrium To model these flows, a number of extended hydrodynamics or generalized hydrodynamics models have been proposed over the past fifty years, along with the direct simulation Monte Carlo (DSMC) approach One of these models is the Burnett equations which are obtained from the Chapman–Enskog expansion of the Boltzmann equation [with Knudsen number (Kn) as a small parameter] to O(Kn2) With the currently available computing power, it has been possible in recent years to numerically solve the Burnett equations However, attempts at solving the Burnett equations have uncovered many physical and numerical difficulties with the Burnett model As a result, several improvements to the conventio
TL;DR: In this paper, direct numerical simulations of three-dimensional, Rayleigh-Taylor instability between two incompressible, miscible fluids, with a 3:1 density ratio, are presented.
Abstract: Direct numerical simulations (DNS) are presented of three-dimensional, Rayleigh–Taylor instability (RTI) between two incompressible, miscible fluids, with a 3:1 density ratio. Periodic boundary conditions are imposed in the horizontal directions of a rectangular domain, with no-slip top and bottom walls. Solutions are obtained for the Navier–Stokes equations, augmented by a species transport-diffusion equation, with various initial perturbations. The DNS achieved outer-scale Reynolds numbers, based on mixing-zone height and its rate of growth, in excess of 3000. Initial growth is diffusive and independent of the initial perturbations. The onset of nonlinear growth is not predicted by available linear-stability theory. Following the diffusive-growth stage, growth rates are found to depend on the initial perturbations, up to the end of the simulations. Mixing is found to be even more sensitive to initial conditions than growth rates. Taylor microscales and Reynolds numbers are anisotropic throughout the simulations. Improved collapse of many statistics is achieved if the height of the mixing zone, rather than time, is used as the scaling or progress variable. Mixing has dynamical consequences for this flow, since it is driven by the action of the imposed acceleration field on local density differences.
TL;DR: In this paper, a new theoretical approach for turbulent flows based on Lie-group analysis is presented, which unifies a large set of "solutions" for the mean velocity of stationary parallel turbulent shear flows.
Abstract: A new theoretical approach for turbulent flows based on Lie-group analysis is presented. It unifies a large set of ‘solutions’ for the mean velocity of stationary parallel turbulent shear flows. These results are not solutions in the classical sense but instead are defined by the maximum number of possible symmetries, only restricted by the flow geometry and other external constraints. The approach is derived from the Reynolds-averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. The results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile not previously reported that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the centre and the near-wall regions in both experimental and DNS data of turbulent channel flows. In the case of the logarithmic law of the wall, the scaling with the distance from the wall arises as a result of the analysis and has not been assumed in the derivation. All solutions are consistent with the similarity of the velocity product equations to arbitrary order. A method to derive the mean velocity profiles directly from the two-point correlation equations is shown.
TL;DR: In this paper, the authors prove the global existence of weak solutions to the Cauchy problem for the compressible isentropic Navier-Stokes equations in ℝ ≥ γ ≥γγγ n ≥γghazi n ≥ 3/2 for n = 2 and γγn ≥ 9/5 for n= 3.
Abstract: We prove the global existence of weak solutions to the Cauchy problem for the compressible isentropic Navier–Stokes equations in ℝ
n
(n= 2, 3) when the Cauchy data are spherically symmetric. The proof is based on the exploitation of the one-dimensional feature of symmetric solutions and use of a new (multidimensional) property induced by the viscous flux. The present paper extends Lions' existence theorem [15] to the case 1< γ <γ
n
for spherically symmetric initial data, where γ is the specific heat ratio in the pressure, γ
n
= 3/2 for n= 2 and γ
n
= 9/5 for n= 3. Dedicated to Professor Rolf Leis on the occasion of his 70th birthday
TL;DR: In this article, the authors investigated energy amplification in parallel channel flows, where background noise is modeled as stochastic excitation of the linearized Navier-Stokes equations and showed that the energy of three-dimensional streamwise-constant disturbances achieves O(R3) amplification.
Abstract: We investigate energy amplification in parallel channel flows, where background noise is modeled as stochastic excitation of the linearized Navier–Stokes equations. We show analytically that the energy of three-dimensional streamwise-constant disturbances achieves O(R3) amplification. Our basic technical tools are explicit analytical calculations of the traces of solutions of operator Lyapunov equations, which yield the covariance operators of the forced random velocity fields. The dependence of these quantities on both the Reynolds number and the spanwise wave number are explicitly computed. We show how the amplification mechanism is due to a coupling between wall-normal velocity and vorticity disturbances, which in turn is due to nonzero mean shear and disturbance spanwise variation. This mechanism is viewed as a consequence of the non-normality of the dynamical operator, and not necessarily due to the existence of near resonances or modes with algebraic growth.
TL;DR: In this article, the truly meshless local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations and the local weak form is modi- fied in a very careful way so as to ovecome the Babuska-Brezzi conditions.
Abstract: The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modi- fied in a very careful way so as to ovecome the so-called Babuska-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems. keyword: MLPG, MLS, Babuconditions, upwinding scheme, incompressible flow, Navier-Stokes equations.
TL;DR: In this article, a Mach 3 adiabatic flat plate turbulent boundary layer is studied using large-eddy simulation (LES) on a three-dimensional unstructured grid of tetrahedral cells.
Abstract: A Mach 3 adiabatic flat plate turbulent boundary layer is studied using large-eddy simulation (LES). The filtered compressible Navier-Stokes equations are solved on a three-dimensional unstructured grid of tetrahedral cells. A compressible extension of the rescaling-reintroducing process of Lund et al. is developed to generate the inflow conditions. The effect of the subgrid-scale motion is incorporated using two approaches, namely, monotone integrated LES (MILES) and the Smagorinsky subgrid-scale model. A detailed grid refinement study is performed
TL;DR: In this paper, the problem of deriving rigorously from renormalized solutions of Boltzmann's equation, globally in time, for general initial conditions and without any additional assumption, solutions of Stokes' equations (together with the strong Boussinesq relation).
Abstract: We consider here the problem of deriving rigorously from renormalized solutions of Boltzmann's equation, globally in time, for general initial conditions and without any additional assumption, solutions of Stokes' equations (together with the strong Boussinesq relation). We also obtain similar results for Euler equations where, however, we need to make an assumption on the high velocities of the solutions of Boltzmann's equation.