Showing papers on "Navier–Stokes equations published in 1994"
Book•
01 Jan 1994
1,781 citations
TL;DR: In this article, the turbulent flow resulting from a top-hat jet exhausting into a large room was investigated and the Reynolds number based on exit conditions was approximately 105 Velocity moments to third order were obtained using flying and stationary hot-wire and burstmode laser-Doppler anemometry (LDA) techniques.
Abstract: The turbulent flow resulting from a top-hat jet exhausting into a large room was investigated The Reynolds number based on exit conditions was approximately 105 Velocity moments to third order were obtained using flying and stationary hot-wire and burst-mode laser-Doppler anemometry (LDA) techniques The entire room was fully seeded for the LDA measurements The measurements are shown to satisfy the differential and integral momentum equations for a round jet in an infinite environmentThe results differ substantially from those reported by some earlier investigators, both in the level and shape of the profiles These differences are attributed to the smaller enclosures used in the earlier works and the recirculation within them Also, the flying hot-wire and burst-mode LDA measurements made here differ from the stationary wire measurements, especially the higher moments and away from the flow centreline These differences are attributed to the cross-flow and rectification errors on the latter at the high turbulence intensities present in this flow (30% minimum at centreline) The measurements are used, together with recent dissipation measurements, to compute the energy balance for the jet, and an attempt is made to estimate the pressure-velocity and pressure-strain rate correlations
1,056 citations
TL;DR: In this article, the Navier-Stokes equation is solved using staggered finite differences on a MAC grid and a split-explicit time differencing scheme, while incompressibility is enforced using an iterative multigrid Poisson solver.
1,000 citations
TL;DR: In this article, a numerical method for solving three-dimensional, time-dependent incompressible Navier-Stokes equations in curvilinear coordinates is presented, where the Cartesian velocity components and the pressure are defined at the center of a control volume, while the volume fluxes are defined on their corresponding cell faces.
669 citations
TL;DR: In this paper, Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data are presented, and the Navier-Stokes equation is analyzed.
Abstract: (1994). Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data. Communications in Partial Differential Equations: Vol. 19, No. 5-6, pp. 959-1014.
408 citations
314 citations
TL;DR: In this article, a review of phase transitions in momentum-conserving lattice gases is presented, with particular attention given to the derivation of macroscopic constitutive equations from microscopic dynamics.
Abstract: Momentum-conserving lattice gases are simple, discrete, microscopic models of fluids. This review describes their hydrodynamics, with particular attention given to the derivation of macroscopic constitutive equations from microscopic dynamics. Lattice-gas models of phase separation receive special emphasis. The current understanding of phase transitions in these momentum-conserving models is reviewed; included in this discussion is a summary of the dynamical properties of interfaces. Because the phase-separation models are microscopically time irreversible, interesting questions are raised about their relationship to real fluid mixtures. Simulation of certain complex-fluid problems, such as multiphase flow through porous media and the interaction of phase transitions with hydrodynamics, is illustrated.
275 citations
IBM1
TL;DR: In this article, a method is described to solve the time-dependent incompressible Navier-Stokes equations with finite differences on curvilinear overlapping grids in two or three space dimensions.
255 citations
TL;DR: In this article, a fictitious domain method for the numerical solutions of three-dimensional elliptic problems with Dirichlet boundary conditions and also of the Navier-Stokes equations modeling incompressible viscous flow was discussed.
251 citations
TL;DR: In this article, the filtered Navier-Stokes equations are used to find necessary conditions on the statistical properties of the modeled subgrid-scale stress tensor, for statistical equivalence between a real and a modeled (via LES) turbulent velocity field.
Abstract: Some thoughts are presented regarding the question: when can a subgrid‐scale model yield correct statistics of resolved fields in a large‐eddy simulation (LES) of turbulent flow. The filtered Navier–Stokes equations are used to find necessary conditions on the statistical properties of the modeled subgrid‐scale stress tensor, for statistical equivalence between a ‘‘real’’ and a modeled (via LES) turbulent velocity field. When trying to formulate sufficient conditions, an unclosed hierarchy of expressions is obtained, essentially due to the ‘‘turbulence problem’’ of the resolved scales of motion. Experimental (statistical a priori) testing of subgrid‐scale models is performed, based on single‐probe measurements in grid turbulence and on several key assumptions. Three versions of the eddy‐viscosity model are considered: constant eddy viscosity, subgrid kinetic energy, and the usual Smagorinsky eddy viscosity. Measured joint moments between filtered velocity and real or modeled subgrid scale stresses show th...
231 citations
TL;DR: Methods are presented for time evolution, steady-state solving and linear stability analysis for the incompressible Navier-Stokes equations at low to moderate Reynolds numbers, and a detailed implementation is described for a pseudospectral calculation of the stability of Taylor vortices with respect to wavy vorts in the Couette-Taylor problem.
TL;DR: In this article, a 2-dimensional stochastic Navier-Stokes equation with a general white noise is considered and the authors prove the existence of invariant measures using a new dissipativity property.
Abstract: A 2-dimensional stochastic Navier-Stokes equation with a general white noise is considered. The aim is to prove the existence of invariant measures, using a new dissipativity property of the stochastic dynamic.
TL;DR: In this article, an analytical solution to the incompressible Navier-Stokes equations is presented, which is fully three-dimensional vector solutions involving all three Cartesian velocity components, each of which depends non-trivially on all three co-ordinate directions.
Abstract: SUMMARY Unsteady analytical solutions to the incompressible Navier-Stokes equations are presented. They are fully three-dimensional vector solutions involving all three Cartesian velocity components, each of which depends non-trivially on all three co-ordinate directions. Although unlikely to be physically realized, they are well suited for benchmarking, testing and validation of three-dimensional incompressible Navier-Stokes solvers. The use of such a solution for benchmarking purposes is described.
TL;DR: This work analyzes the problem of boundary-driven shear flow in detail, comparing the rigorous estimates obtained from the variational method with both recent experimental results and predictions of a conventional closure approximation from statistical turbulence theory.
Abstract: A variational principle for upper bounds on the time averaged rate of viscous energy dissipation for Newtonian fluid flows is derived from the incompressible Navier-Stokes equations. When supplied with appropriate test background'' flow fields, the variational formulation produces explicit estimates for the energy dissipation rate. This dissipation rate is related to the drag of the fluid on the boundaries, and so these estimates translate into bounds on the drag. We analyze the problem of boundary-driven shear flow in detail, comparing the rigorous estimates obtained from the variational method with both recent experimental results and predictions of a conventional closure approximation from statistical turbulence theory.
TL;DR: In this article, the Navier-Stokes equations with lattice Boltzmann equation (LBE) were solved for global quantities as well as energy spectra using spectral and LBE methods.
Abstract: Numerical solutions of the two‐dimensional Navier–Stokes equations are presented by two methods; spectral and the novel lattice Boltzmann equation (LBE) scheme. Very good agreement is found for global quantities as well as energy spectra. The LBE scheme is, indeed, providing reasonably accurate solutions of the Navier–Stokes equations with an isothermal equation of state, in the nearly incompressible limit. Relaxation to a previously reported ‘‘sinh‐Poisson’’ state is also observed for both runs.
TL;DR: In this paper, a finite element formulation for solving the compressible Navier-Stokes equations is presented, which accommodates the use of any set of variables, including primitive variables (p, u, T ), or entropy variables.
TL;DR: The generalized complex Ginzburg-Landau equation (GGLE) is a model for fluid turbulence described by the incompressible Navier-Stokes equations as mentioned in this paper, which is a dissipative version of the Hamiltonian nonlinear Schrodinger equation possessing solutions that form localized singularities.
01 Oct 1994
TL;DR: A hybrid Cartesian/body-fitted grid generation approach based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented and the most suitable viscous discretization is demonstrated for geometrically-complicated internal flows.
TL;DR: In this article, it was shown that linear growth mechanisms are necessary for transition in flows governed by the incompressible Navier-Stokes equations and that nonnormality of the linearized Navier−Stokes operator is a necessary condition for subcritical transition.
Abstract: Recent work has shown that linear mechanisms can lead to substantial transient growth in the energy of small disturbances in incompressible flows even when the Reynolds number is below the critical value predicted by linear stability (eigenvalue) analysis. In this note it is shown that linear growth mechanisms are necessary for transition in flows governed by the incompressible Navier–Stokes equations and that non‐normality of the linearized Navier–Stokes operator is a necessary condition for subcritical transition.
TL;DR: The strong shock interaction test cases show the applicability of the gas-kinetic based hydrodynamic scheme to supersonic gas flow and some Navier-Stokes solutions are exhibited.
TL;DR: A subclass of algorithms which retain these strong notions of nonlinear stability and long-term dissipative behavior is identified which, in addition, has the remarkable property of being linear within the time step.
TL;DR: In this paper, the Navier-Stokes (NS) and Euler (E) equations of incompressible flow in the whole plane are constructed, under the assumption that the initial vorticity is in L1(ℝ2)∩ Lr(ↆ) for some r>2 for (E).
Abstract: Long-time solutions to the Navier-Stokes (NS) and Euler (E) equations of incompressible flow in the whole plane are constructed, under the assumption that the initial vorticity is in L1(ℝ2) for (NS) and in L1(ℝ2)∩ Lr(ℝ2) for some r>2 for (E). It is shown that the solution to (NS) is unique, smooth and depends continuously on the initial data, and that the (velocity) solution to (E) is Holder continuous in the space and time coordinates. It is shown that as the viscosity vanishes, there is a subsequence of solutions to (NS) converging to a solution of (E).
Book•
01 Jan 1994
TL;DR: In this article, the Navier-Stokes Equations are used to solve the problem of stable state solutions of Navier and Stokes flow in bounded and unbounded domains.
Abstract: Contents: Steady-State Solutions of the Navier-Stokes Equations: Statement of the Problem and Open Questions.- Basic Function Spaces and Related Inequalities.- The Function Spaces of Hydrodynamics.- Steady Stokes Flow in Bounded Domains.- Steady Stokes Flow in Exterior Domains.- Steady Stokes Flow in Domains with Unbounded Boundaries.- Steady Oseen Flow in Exterioir Domains.
TL;DR: In this article, the velocity and pressure fields, free surface shape and wave speed are computed simultaneously as functions of the Reynolds number Re and the wave number μ, and compared with predictions of long-wave, asymptotic theories and boundary-layer approximations for the form and nonlinear transitions of finite-amplitude waves that evolve from the flat film state.
Abstract: Finite‐amplitude waves propagating at constant speed down an inclined fluid layer are computed by finite element analysis of the Navier–Stokes equations written in a reference frame translating at the wave speed. The velocity and pressure fields, free‐surface shape and wave speed are computed simultaneously as functions of the Reynolds number Re and the wave number μ. The finite element results are compared with predictions of long‐wave, asymptotic theories and boundary‐layer approximations for the form and nonlinear transitions of finite‐amplitude waves that evolve from the flat film state. Comparisons between the finite element calculations and the long‐wave predictions for fixed μ and increasing Re agree well for small‐amplitude waves. However, for larger‐amplitude waves the long‐wave results diverge qualitatively from the finite element predictions; the long‐wave theories predict limit points in the solution families that do not exist in the finite element solutions. Comparisons between the finite ele...
TL;DR: In this article, the stability of strongly decaying global strong Navier-Stokes equations in 3D space dimensions has been shown and the existence theorem for large solutions with approximately symmetric initial data has been proved.
Abstract: We prove the stability of mildly decaying global strong solutions to the Navier-Stokes equations in three space dimensions. Combined with previous results on the global existence of large solutions with various symmetries, this gives the first global existence theorem for large solutions with approximately symmetric initial data. The stability of unforced 2D flow under 3D perturbations is also obtained.
TL;DR: In this article, pressure fluctuations in incompressible turbulence are studied by direct numerical simulations of the 3D Navier-Stokes equations and the pressure probability distribution function is shown to have an exponential tail on the negative side, and to be independent of the Reynolds number for Reλ ≥ 60.
Abstract: Pressure fluctuations in incompressible turbulence are studied by direct numerical simulations of the three‐dimensional (3‐D) Navier–Stokes equations. The pressure probability distribution function (PDF) is shown to have an exponential tail on the negative side, and to be independent of the Reynolds number for Reλ≲60. At higher Reynolds numbers, the low pressure part of the pressure PDF becomes super exponential. The joint PDFs of strain, vorticity, and pressure (considered pairwise) show a strong dissymmetry between positive and negative pressure fluctuations. The results obtained from the numerical solutions of the Navier–Stokes equations are compared with a Gaussian velocity field. The two statistical ensembles are shown to lead to quantitatively different results.
TL;DR: In this article, the open boundary conditions for the incompressible Navier-Stokes equations are given from a weak formulation in velocity-pressure variables, and some natural boundary conditions involving the traction or pseudotraction and inertial terms are established.
Abstract: SUMMARY The aim of this paper is to give open boundary conditions for the incompressible Navier-Stokes equations. From a weak formulation in velocity-pressure variables, some natural boundary conditions involving the traction or pseudotraction and inertial terms are established. Numerical experiments on the flow behind a cylinder show the efficiency of these conditions, which convey properly the vortices downstream. Comparisons with other boundary conditions for the velocity and pressure are also performed.
Dissertation•
01 Oct 1994TL;DR: In this paper, a Cartesian cell-based grid generation method for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested, where the grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solutionadaptive refinement.
Abstract: A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain Where the resulting cells intersect bodies, polygonal 'cut' cells are created The geometry of the cut cells is computed using polygon-clipping algorithms The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells A multi-stage time-stepping scheme is used to reach a steady-state solution Validation of the Euler solver with benchmark numerical and exact solutions is presented An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations The error of the approach is directly compared to a structured solver formulation A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows For flows at high Reynolds numbers, both an altered grid-generation procedure and a different formulation of the viscous terms are shown to be necessary A hybrid Cartesian/body-fitted grid generation approach is demonstrated In addition, a grid-generation procedure based on body-aligned cell cutting coupled with a viscous stensil-construction procedure based on quadratic programming is presented
TL;DR: In this article, a bifurcation diagram is presented for an axisymmetric swirling flow in a constricted pipe, using the pipe geometry of Beran and Culick.
Abstract: The bifurcation structure is presented for an axisymmetric swirling flow in a constricted pipe, using the pipe geometry of Beran and Culick [J. Fluid Mech. 242, 491 (1992)]. The flow considered has been restricted to a two‐dimensional parameter space comprising the Reynolds number Re and the relative swirl V0 of the incoming swirling flow. The bifurcation diagram is constructed by solving the time‐dependent axisymmetric Navier–Stokes equations. The stability of the steady results presented by Beran and Culick, obtained from a steady axisymmetric Navier–Stokes code, has been confirmed. Further, the steady solution branch has also been extended to much larger V0 values. At larger V0, a stable unsteady solution branch has been identified. This unsteady branch coexists with the previously found stable steady solution branch and originates via a turning point bifurcation. The bifurcation diagram is of the type described by Benjamin [Proc. R. Soc. London Ser. A 359, 1 (1978)] as the canonical unfolding of a pitchfork bifurcation. This type of bifurcation structure in the two‐dimensional parameter space (Re,V0), suggests the possibility of hysteresis behavior over some part of parameter space, and this is observed in the present study. The implications of this on the theoretical description of vortex breakdown and the search for a criterion for its onset are discussed.