Motivated by a range of applications (biomedical, industrial, engineering, environmental) this contribution is focussed on a mathematical study of (a) constriction/distortion and (b) branching in a vessel or network of vessels containing fluid flow. The central interest addressed is in medium-to-high Reynolds numbers where asymptotic approaches and matching yield much insight. The main reasonin...

A critical analysis of the numerous works on dolphin swimming shows that several uncertainties led to incorrect conclusions concerning the estimates of dolphin drag coefficients. Original results on dolphin kinematics and hydrodynamics indicate the existence of a drag-reduction mechanism, caused by the formation of a negative pressure gradient along the body during active swimming. The mathemat...

Computational fluid dynamics simulations of relevance to jet-engine design, for instance, are extremely computationally demanding and the use of large-scale distributed computing will allow the solution of problems that cannot be tackled using current resources. It is often appropriate to leave the large datasets generated by CFD codes local to the compute resource in use at the time. This natu...

iii Preface There is fluid flow everywhere around us: air is flowing past airplanes, cars and buildings; water is flowing past ships, through rivers and harbours; oil is flowing through pipelines and in underground reservoirs; blood is flowing through our arteries. And the most important flow around us has not even been mentioned: the air flow in the atmosphere that determines our weather. It w...

This is the first of two papers examining the critical collapse of spherically symmetric perfect fluids with the equation of state P = (Γ − 1)ρ. Here we present the equations of motion and describe a computer code capable of simulating the extremely relativistic flows encountered in critical solutions for Γ ≤ 2. The fluid equations are solved using a high-resolution shock-capturing scheme based...

I Notation: I Ω ⊂ R: domain initially occupied by a material moving under the influence of interior and exterior forces I η ∈ Ω: initial position of an arbitrary particle I x = Φ(η, t): position of particle η at time t > 0 I Ω(t) = Φ(Ω, t): domain occupied by the material at time t > 0 I Basic assumptions: I Φ(·, t) : Ω→ Ω(t) is an orientation preserving diffeomorphism for all t > 0. I Φ(·, 0) ...