Showing papers on "Navier–Stokes equations published in 1992"

Development of turbulence models for shear flows by a double expansion technique

Abstract: Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)] with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (η≡SK/■) is the ratio of the turbulent to mean strain time scale. While low‐order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of η suffices−terms of all orders must be retained. Based on these ideas, a new two‐equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method.

Abstract: It is known that the Frisch-Hasslacher-Pomeau lattice-gas automaton model and related models possess some rather unphysical effects. These are (1) a non-Galilean invariance caused by a density-dependent coefficient in the convection term, and (2) a velocity-dependent equation of state. In this paper, we show that both of these effects can be eliminated exactly in a lattice Boltzmann-equation model.

Application of generalized differential quadrature to solve two-dimensional incompressible navier-stokes equations

Abstract: A global method of generalised differential quadrature is applied to solve the two-dimensional incompressible Navier-Stokes equations in the vorticity-stream-function formulation. Numerical results for the flow past a circular cylinder were obtained using just a few grid points. A good agreement is found with the experimental data.

Stabilized finite element methods. II: The incompressible Navier-Stokes equations

Abstract: Stabilized methods are proposed and analyzed for a linearized form of the incompressible Navier-Stokes equations. The methods are extended and tested for the nonlinear model. The methods combine the good features of stabilized methods already proposed for the Stokes flow and for advective-diffusive flows. These methods also generalize previous works restricted to low-order interpolations, thus allowing any combination of velocity and continuous pressure interpolations. A careful design of the stability parameters is suggested which considerably simplifies these generalizations.

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

Abstract: One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology.

Exact solution of a restricted Euler equation for the velocity gradient tensor

Abstract: The velocity gradient tensor satisfies a nonlinear evolution equation of the form (dAij/dt)+AikAkj− (1/3)(AmnAnm)δij=Hij, where Aij=∂ui/∂xj and the tensor Hij contains terms involving the action of cross derivatives of the pressure field and viscous diffusion of the velocity gradient. The homogeneous case (Hij=0) considered previously by Vielliefosse [J. Phys. (Paris) 43, 837 (1982); Physica A 125, 150 (1984)] is revisited here and examined in the context of an exact solution. First the equations are simplified to a linear, second‐order system (d2Aij/dt2)+(2/3)Q(t)Aij=0, where Q(t) is expressed in terms of Jacobian elliptic functions. The exact solution in analytical form is then presented providing a detailed description of the relationship between initial conditions and the evolution of the velocity gradient tensor and associated strain and rotation tensors. The fact that the solution satisfies both a linear second‐order system and a nonlinear first‐order system places certain restrictions on the solution path and leads to an asymptotic velocity gradient field with a geometry that is largely but not wholly independent of initial conditions and an asymptotic vorticity which is proportional to the asymptotic rate of strain. A number of the geometrical features of fine‐scale motions observed in direct numerical simulations of homogeneous and inhomogeneous turbulence are reproduced by the solution of the Hij=0 case.

The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbomachines

Abstract: The extension of a well established three dimensional flow calculation method to calculate the flow through multiple turbomachinery blade rows is described in this paper. To avoid calculating the unsteady flow, which is inherent in any machine containing both rotating and stationary blade rows, a mixing process is modelled at a calculating station between adjacent blade rows. The effects of this mixing on the flow within the blade rows may be minimised by using extrapolated boundary conditions at the mixing plane.Copyright © 1990 by ASME

On error estimates of projection methods for Navier-Stokes equations: first-order schemes

Abstract: In this paper projection methods (or fractional step methods) are studied in the semi-discretized form for the Navier–Stokes equations in a two- or three-dimensional bounded domain. Error estimates for the velocity and the pressure of the classical projection scheme are established via the energy method. A modified projection scheme which leads to improved error estimates is also proposed.

Nonlinear Water Waves Generated by Submarine and Aerial Landslides

Abstract: The two‐dimensional hydrodynamics program Nasa‐Vof2D is modified to study the generation, propagation, and run‐up on the shore of water waves created by landslides. Nasa‐Vof2D, developed by the Los Alamos National Laboratory in Los Alamos, New Mexico, is a nonlinear Eulerian code, which solves the complete incompressible Navier‐Stokes equations by a finite difference method. The modification includes making the fluid domain boundaries (i.e., the bathymetry) time‐dependent. It allows a complex geometry box to slide down any incline, provided that the body kinetic is known and that the phenomenon is two‐dimensional or axisymmetric. To verify this numerical Nasa‐Vof2D extension, an experimental study on nonlinear waves generated by a two‐dimensional triangular body sliding a 45° inclined plane is conducted. The computed wave profiles show very close agreement with the experimental ones, except when free‐surface turbulence occurs, which the present numerical method cannot simulate.

On chorin's projection method for the incompressible navier-stokes equations

Abstract: Pseudo-compressibility methods are frequently used in computational fluid dynamics in order to cope with the algebraic difficulties caused by the incompressibility constraint. A popular example is the pressure stabilization (Petrov-Galerkin) method of T.J.R. Hughes, et al., which can be applied to the stationary as well as to the nonstationary Navier-Stokes problem. Also the classical projection method of A.J. Chorin can be interpreted as a variant of this method. This observation sheds some new light on the approximation properties of the projection method, particularly for the pressure.

Relaxation in two dimensions and the "sinh-Poisson" equation

Abstract: Long‐time states of a turbulent, decaying, two‐dimensional, Navier–Stokes flow are shown numerically to relax toward maximum‐entropy configurations, as defined by the ‘‘sinh‐Poisson’’ equation. The large‐scale Reynolds number is about 14 000, the spatial resolution is (512)2, the boundary conditions are spatially periodic, and the evolution takes place over nearly 400 large‐scale eddy‐turnover times.

On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations

Abstract: This paper is a continuation of our previous work [10] on projection methods. We study first existing "higher order" projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.

Turbulence transport equations for variable-density turbulence and their relationship to two-field models

Abstract: This study gives an updated account of our current ability to describe multimaterial compressible turbulent flows by means of a one-point transport model. Evolution equations are developed for a number of second-order correlations of turbulent data, and approximations of the gradient type are applied to additional correlations to close the system of equations. The principal fields of interest are the one- point Reynolds tensor for variable-density flow, the turbulent energy dissipation rate, and correlations for density-velocity and density- density fluctuations. This single-field description of turbulent flows is compared in some detail to two-field flow equations for nonturbulent, highly dispersed flow with separate variables for each field. This comparison suggests means for improved modeling of some correlations not subjected to evolution equations.

Finite element methods for navier-stokes equations

Abstract: The main goal of this article is to address the finite element solution of the Navier-Stokes equations modeling compressible and incompressible viscous flow. It is the opinion of the authors that most general and reliable incompressible viscous flow simulators arc based on finite clement method­ ologies; these simulators, which can handle complicated geometries and boundary conditions, free surfaces, and turbulence effects, are well suited to industrial applications. On the other hand, the situation is much less satisfying concerning compressible viscous flow simulation, particularly at high Reynolds and Mach numbers and much progress must still be made in order to reach the degree of achievement obtained by the incompressible flow simulations. In this article, whose scope has been voluntarily limited, we concentrate on those topics combining our own work and the work of others with which we are familiar. The paper has been divided into two parts: In the first part (Sections I to 5) we discuss the various ingredients of a solution methodology for incompressible viscous flow based on operator splitting. Via splitting one obtains, at each time step, two families of subproblems: one of advection-diffusion type and one related to the steady Stokes

Reconnection in orthogonally interacting vortex tubes: Direct numerical simulations and quantifications

Abstract: The three‐dimensional time evolution of two orthogonally offset cylindrical vortices of equal strength is simulated by solving the hyperviscosity‐regularized incompressible Navier–Stokes equations. A Fourier pseudospectral method with a time‐split integration scheme is used for the solution. Four runs with different Reynolds numbers ranging between 690–2100 are performed, each with a resolution of 963 collocation points. The sequence of important physical processes and the evolution of local and global quantities such as vorticity, velocity, and mean‐square strain rate are presented. It is found that the growth rate of the maximum vorticity is at most exponential. The Reynolds number dependence of the time scale of reconnection, the vorticity growth rate, and the time at which the maximum vorticity is attained are examined and differences between the present results and Saffman’s essentially two‐dimensional model predictions are encountered and elucidated. The distributions of the eigenvalues α, β, γ and ...

Analysis and convergence of the MAC scheme. I : The linear problem

Abstract: The MAC (Marker and Cell) discretization of fluid flow is analysed for the stationary Stokes equations. It is proved that the discrete approximations do in fact converge to the exact solutions of the flow equations. Estimates using mesh dependent norms analogous to the standard ${\bf H}^1 $ and $L^2 $ norms are given for the velocity and pressure, respectively.

Stochastic Navier-stokes equations with multiplicative noise

Abstract: An abstract stochastic Navier-Stokes equation with multiplicative white noise is considered. 2-dimensional Navier-Stokes equations with noise depending on first order derivatives of the solution are covered by the abstract model. Existence and uniqueness of a solution is proved for small initial data, and the associated local stochastic flow is constructed

The regularized Chapman-Enskog expansion for scalar conservation laws

Abstract: Rosenau has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. The behavior of Rosenau regularization of the Chapman-Enskog expansion (RCE) is studied in the context of scalar conservation laws. It is shown that thie RCE model retains the essential properties of the usual viscosity approximation, e.g., existence of traveling waves, monotonicity, upper-Lipschitz continuity..., and at the same time, it sharpens the standard viscous shock layers. It is proved that the regularized RCE approximation converges to the underlying inviscid entropy solution as its mean-free-path epsilon approaches 0, and the convergence rate is estimated.

Global solutions to the compressible Navier-Stokes equations for a reacting mixture

Abstract: Existence theorems are established for global generalized solutions to the compressible Navier–Stokes equations for a reacting mixture with discontinuous Arrhenius functions, which describe dynamic...

Implicit Navier-Stokes Solver for Three-Dimensional Compressible Flows

Abstract: A three-dimensional numerical method based on the lower-upper symmetric-Gauss-Seidel implicit scheme in conjunction with the flux-limited dissipation model is developed for solving the compressible Navier-Stokes equations. A new computer code based on this method requires only 9 μs per grid point per iteration on a single processor of a Cray YMP computer and executes at the sustained rate of 175 MFLOPS. A reduction of three orders of magnitude in the residual for a high-Reynolds-number flow using 636K grid points is obtained in 38 min

Unsteady force on a spherical bubble at finite Reynolds number with small fluctuations in the free‐stream velocity

Abstract: Unsteady flow over a stationary spherical bubble with small fluctuations in the free‐stream velocity is considered for Reynolds number ranging from 0.1 to 200. Solutions to the Navier–Stokes equations of both steady and unsteady components are obtained using a finite‐difference method and a regular perturbation scheme based on the amplitude of the fluctuations being small. The dependence of the unsteady drag on the frequency of the fluctuations is examined at finite Reynolds number. It is shown that the quasisteady drag can be represented by using the steady‐state drag coefficient and the instantaneous velocity. Numerical results indicate that the unsteady force at low frequency, ω, increases linearly with ω rather than increasing linearly with ω1/2, which results from the creeping flow solution of the Stokes equation. The added‐mass force at finite Reynolds number is found to be the same as in creeping flow and potential flow. The history force at finite Re is identified and carefully evaluated. The imaginary component of the history force increases linearly with ω when ω is small and decays as ω−1/2 as ω becomes large. The implication is that the history force has a much shorter memory in the time domain than predicted by the solution of the unsteady Stokes equation. Numerical results suggest that the history force, which is due to the combination of the viscous diffusion of the vorticity and the acceleration of the flow field, at low frequency is finite even at large Reynolds number.