A numerical solution of the Navier-Stokes equations using the finite element technique

American Society of Mechanical Engineers

https://www.southampton.ac.uk/~nwb/lectures/GoodPracticeCFD/Articles/Validation_SAND2002-0529.pdf

Verification and Validation in Computational Fluid Dynamics

In this review, we present control methods for flow over a bluff body such as a circular cylinder, a 2D bluff body with a blunt trailing edge, and a sphere. We introduce recent major achievements in bluff-body flow controls such as 3D forcing, active feedback control, control based on local and global instability, and control with a synthetic jet. We then classify the controls as boundary-layer controls and direct-wake modifications and discuss important features associated with these controls. Finally, we discuss some other issues such as Reynolds-number dependence, the lowest possible drag by control, and control efficiency.

Control of Flow Over a Bluff Body

Regular Article: An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries

Numerical methods for steady viscous flow problems

By two separate methods, a numerical one and an experimental one, new data which support and complete one another are obtained, regarding the flow of a viscous fluid around a circular cylinder subjected, after an impulsive start, to a combined rotation and translation. The numerical method is based on the solution of the Navier-Stokes equations governing the unsteady flow. The experimental study is carried out by visualization of the quasi-instantaneous velocity fields by means of solid tracers. As an example, a comparison of the results is presented for Re=500 En developpant deux etudes paralleles, l'une numerique, l'autre experimentale, on obtient des informations nouvelles, qui se confirment et qui se completent mutuellement, concernant l'ecoulement d'un fluide visqueux autour d'un cylindre soumis, apres un depart impulsif, a une rotation combinee a une translation. L'etude numerique est basee sur la resolution des equations instationnaires de Navier-Stokes. L'etude experimentale est faite par visualisation des champs quasi instantanes des vitesses a l'aide de traceurs solides. A titre d'exemple, une comparaison des resultats est presentee pour Re=500

Sur la comparaison des calculs numériques et des visualisations de l'écoulement d'un fluide visqueux engendré par un cylindre en translation et rotation

The boundary layer on a fixed sphere on the axis of an unbounded rotating fluid

Results concerning the process of vortex formation in an example of unsteady two-dimensional flow near a moving wall are presented. The motion considered is that generated in a viscous fluid by a circular cylinder which suddenly starts from rest with a uniform translation perpendicular to and a uniform rotation about its axis. A study is made of the first vortex to form behind the cylinder over a range of Reynolds numbers. Then some features of the appearance of secondary vortices, the detachment of the primary vortex, and the ultimate coalescence of secondary vortices, are discussed. Comparisons made between results calculated respectively from unsteady boundary-layer theory and the Navier-Stokes equations for high Reynolds numbers will be presented in a later paper.

Vortex Formation in Unsteady Flow near a Moving Wall

A numerical method for treating certain classes of problems in the theory of rotating fluids is given. The uniform, slow motion of a sphere in a viscous fluid has been examined in the case where the undisturbed fluid rotates with constant angular velocity ωo and the axis of rotation is taken to coincide with the line of motion. The Navier-Stokes equations can be written in the form of three coupled, nonlinear, elliptic partial differential equations. These equations are expressed in finite-difference form using a specialized technique which is everywhere second order accurate. It is based on an expansion of a finite-difference scheme which already exists in the literature and which involves the exponential function. By expanding the exponentials in powers of their exponents an approximation is arrived at which is particularly suitable for use in obtaining numerical solutions.

S. C. R. Dennis

Papers

Numerical methods for steady viscous flow problems

Sur la comparaison des calculs numériques et des visualisations de l'écoulement d'un fluide visqueux engendré par un cylindre en translation et rotation

The boundary layer on a fixed sphere on the axis of an unbounded rotating fluid

Vortex Formation in Unsteady Flow near a Moving Wall

A finite difference method for the slow motion of a sphere in a rotating fluid