Perturbation Method in Fluid Mechanics

Some Regular Perturbation Solutions in Fluid Mechanics

In this paper we examine two problems in steady incompressible viscous flow with a view to generating high-order perturbation solutions as regular expansions in powers of the Reynolds number. Thus, computer-algebra techniques are used to study the motions produced (a) by a Landau momentum source placed at the centre of a fluid-filled spherical shell, and (b) by a rotating sphere in both unbound...

Superconvergent perturbation method in quantum mechanics.

An analogue of Kolmogorov’s superconvergent perturbation theory in classical mechanics is constructed for self adjoint operators. It is different from the usual Rayleigh–Schrödinger perturbation theory and yields expansions for eigenvalues and eigenvectors in terms of functions of the perturbation parameter. PACS Code: 03.65.-w, 31.15+q, 02.30.Mv, 02.90.+p

Two Perturbation Calculations in Fluid Mechanics Using Large-Expression Management

Two uid-ow problems are solved using perturbation expansions, with special emphasis on the reduction of intermediate expression swell. This is done by developing tools in Maple that contribute to the eecient representation and manipulation of large expressions. The tools share a common basis, which is the creation of a hierarchy of representation levels such that expressions located at higher l...

The Stochastic Perturbation Method for Computational Mechanics

Perturbation Theory in Celestial Mechanics

4 Classical perturbation theory 4 4.1 The classical theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 4.2 The precession of the perihelion of Mercury . . . . . . . . . . . . . . . . . . . . 6 4.2.1 Delaunay action–angle variables . . . . . . . . . . . . . . . . . . . . . . 6 4.2.2 The restricted, planar, circular, three–body problem . . . . . . . . . . . 7 4.2.3 Expansi...