Problem Of Viscous Fluid Flow Research Articles

A new finite element technique for the analysis of steady viscous flow problems

AbstractA new finite element technique for two‐dimensional viscous incompressible fluid flow problems is presented in this paper. The vorticity transport equation is integrated in a small control volume, which results in the conservation law of vorticity. The finite element technique is applied to this equation together with the continuity equation, where simple linear triangular elements with three nodes are used for the formulation. Resulting sets of algebraic equations are solved by the use of a kind of relaxation method. Numerical results for viscous flow past a cavity show good agreement with experimental results.

The operator compact implicit method for parabolic equations

This paper attempts to trace out the broad characteristics of a class of higher order finite difference schemes which are applicable to the solution of parabolic partial differential equations associated with viscous fluid flow problems. The basic method developed here uses the approach of the compact implicit techniques applied to the full spatial operator. The resulting spatial approximation, referred to here as the operator compact implicit method can be implemented with a variety of temporal integration schemes. In particular, a simple factorization technique is employed to resolve higher space dimension problems in terms of simple tridiagonal systems. The operator compact implicit method is compared to standard techniques and to some of the newer compact implicit methods. Stability characteristics, computational efficiency and the results of numerical experiments are discussed.

Boundary condition formulation for viscous fluid flow problems

In the solution of the Navier-Stokes equations by difference methods in infinite regions, the question arises as to the nature of the approximate boundary conditions at those portions of the computational region boundary where these conditions are not determined directly by the formulation of the basic problem. In certain cases of practical importance, these boundary conditions may be obtained by coupling the N-S equations with equations which are similar to the boundary-layer equations.

Drag of a rotating sphere

We consider the problem of steady incompressible viscous fluid flow about a rotating sphere, with the flow specified on a sphere of finite radius, which reduces to the solution of the complete Navier-Stokes equations.

XCI. Some viscous fluid flow problems I: Jet emerging from a hole in a plane wall

Summary An exact solution of the equations of viscous fluid flow for axially-symmetric motion is studied for a special case : this is shown to give the flow for a jet emerging from a hole in an infinite plane wall. Some examples of the calculated streamlines are given.

The Mathematical Problems of Aerodynamics

The equations governing the motion of a viscous fluid were first obtained by Navier more than 100 years ago (“ Memoire sur les Lois du Mouvement des Fluides,” Mem. de l’Acad. des Sciences, vi. 389, 1822), and in spite of their close study by Stokes, Helmholtz, Kelvin, Rayleigh, Lamb and numerous other mathematicians of great eminence, no complete unrestricted solution for any case of practical importance has yet been discovered. As they stand, the mathematical difficulties presented by the equations have so far been found to be too formidable, and whatever progress has been achieved has been by imposing restrictions on the form of the equations, and therefore serious limitations on the nature of the fluid motion studied. It may be that the mathematical symbolism in the formulation of the problem of viscous fluid flow as usually presented is not that best adapted for its purpose, that it is not as natural a medium of expression as for example Tensor Analysis is for Relativity ; that in fact the essential factors that govern the eddying, for instance, in the wake of a moving body are not presented as governing the structure of the equations.

The Theory of Aerodynamics

THE equations governing the motion of a viscous fluid were first obtained by Navier more than 100 years ago (“Memoire sur les Lois du Mouvement des Fluides,” Mem. de l'Acad. des Sciences, vi, 389, 1822), and, in spite of their close study by Stokes, Helmholtz, Kelvin, Rayleigh, Lamb, and numerous other mathematicians of great eminence, no complete unrestricted solution for any case of practical importance has yet been discovered. As they stand, the mathematical difficulties presented by the equations have so far been found to be too formidable, and whatever progress has been achieved has been by imposing restrictions on the form of the equations, and therefore serious limitations on the nature of the fluid motion studied. It may be that the mathematical symbolism in the formulation of the problem of viscous fluid flow as usually presented is not that best adapted for its purpose, that it is not as natural a medium of expression as, for example, tensor analysis is for relativity; that, in fact, the essential factors that govern the eddying, for instance, in the wake of a moving body are not presented as governing the structure of the equations.