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Steady vortex rings with swirl in an ideal fluid: asymptotics for some solutions in exterior domains

Tadie (1999)

Applications of Mathematics

In this paper, the axisymmetric flow in an ideal fluid outside the infinite cylinder ( r ≤ d ) where ( r , θ , z ) denotes the cylindrical co-ordinates in ℝ 3 is considered. The motion is with swirl (i.e. the θ -component of the velocity of the flow is non constant). The (non-dimensional) equation governing the phenomenon is (Pd) displayed below. It is known from e.g. that for the problem without swirl ( f q = 0 in (f)) in the whole space, as the flux constant k tends to ∞ , 1) dist ( 0 z , ∂ A ) = O ( k 1 / 2 ) ; diam A = O ( exp ( - c 0 k 3 / 2 ) ) ; 2) ( k 1 / 2 Ψ ) k ∈ ℕ converges to a vortex cylinder U m (see...

Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale

Jean-Luc Guermond (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Navier–Stokes equations are approximated by means of a fractional step, Chorin–Temam projection method; the time derivative is approximated by a three-level backward finite difference, whereas the approximation in space is performed by a Galerkin technique. It is shown that the proposed scheme yields an error of 𝒪 ( δ t 2 + h l + 1 ) for the velocity in the norm of l2(L2(Ω)d), where l ≥ 1 is the polynomial degree of the velocity approximation. It is also shown that the splitting error of projection schemes based...

Water-wave problem for a vertical shell

Nikolai G. Kuznecov, Vladimir G. Maz'ya (2001)

Mathematica Bohemica

The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for finding a solution.

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