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This article deals with a method to build programs in computational geometry from their specifications. It focuses on a case study namely computing incrementally the convex hull of a set of points in the plane using hypermaps. Our program to compute convex hulls is specified and proved correct using the Coq proof assistant. It performs a recursive traversal of the existing convex hull to compute the new hull each time a new point is inserted. This requires using well-founded recursion in Coq. A concrete implementation in Ocaml is then automatically extracted and an efficient C++ program is derived (by hand) from the specification.

The near wall behaviour of complex turbulent flows is investigated by dimensional considerations and a priori investigations. We consider separated incompressible and compressible flows. In incompressible turbulent flows, it is found that the flow in the immediate vicinity of the wall is dependent on two parameters, based on wall friction and local pressure gradient, respectively. In compressible turbulent flows, a third parameter based on the wall heat flux is relevant for the flow profiles in vicinity of the wall. While in the viscous sub-layer, an exact law of the wall can be formulated, the buffer and log-layer is dependent on empirical formulations. The significance of the wall scaling is shown by carefully carried out Direct Numerical Simulations and Large-Eddy Simulations of incompressible and compressible separated flows.

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Two different solution schemes are applied for the LES of compressible turbulent flows. First, a conservative LES formulation is applied with the filtered structure-function model. Solutions for a compressible channel flow at M0 = 1 are in overall agreement with DNS references. The quasi-incompressible transitional boundary layers show the establishment of a streak system well upstream of the peak of skin friction. For harmonic and subharmonic perturbations, however, a different first location of high speed regions is observed. The second method is a mixed central-upwind scheme. The results for the case of a fully turbulent boundary layer are in good agreement with reference data from other authors. The simulation of the wake with trailing edge blowing shows that the jet inhibits the generation of the regular vortex shedding. Instead only smaller and weaker spanwise vortices are generated, rapidly decaying through the interaction with streamwise vortices. Thus, the mixing in the wake with the external flow is reduced and the losses become smaller compared to the case without blowing.

The world is undergoing a revolution in information and communication technologies (ICT) that has momentous implications for the current and future social and economic situations of all countries of the world. In March 2000, an estimated 276 million persons worldwide were using the Internet with a growth rate of roughly 150,000 persons per day. 220 million devices were accessing the worldwide web, and almost 200,000 devices were being added daily. Web pages totaled 1.5 billion with almost 2 million pages being added each day. E-commerce, or business conducted over the Internet, totaled US $ 45 billion as recently as 1998. An estimate in January 2000 projected it could explode to over US $ 7 trillion as early as 2004. These are astonishing figures, unprecedented by any measure, but they reflect the activity of less than 5% of the world’s population. The gross disparity in the spread of the Internet and of the economic and social benefits derived from it is a matter of profound concern. There are more hosts in New York than in confinental Africa; there are more hosts in Finland than in Latin America and the Caribbean. Notwithstanding the remarkable progress in the application of ICT in India, many of its villages still lack a working telephone.

International audience; Jets with complex shock-cell structures appear in numerous technological applications. Most supersonic jets used in aeronautics will be imperfectly expanded in flight, even those from carefully designed convergent-divergent nozzles. The adaption to the ambient pressure takes place in a sequence of oblique shocks which interact with the free shear layers and produce noise. The shock/shear-layer interaction emanates a broadband noise component. This may trigger the young shear layer at the nozzle, forming a feedback loop which results in a discrete noise component called screech. Both components are undesirable from structural and environmental (cabin noise) points of view. Screech tones are known to produce sound pressure levels of 160 dB and beyond. The focus of this research project lies in the numerical simulation of jet screech. Different numerical methods are shown with LES and DNS applications of a planar rectangular and three-dimensional jet with overset grid techniques to include complex geometries for the jet nozzle. Furthermore, a shock-capturing method is developed for high-order aeroacoustic computations. It consists in applying an adaptive second-order conservative filtering to handle discontinuities, in combination with a background selective filtering to remove grid-to-grid oscillations. The magnitude of the shock-capturing filtering is determined dynamically from the flow solutions using a procedure based on a Jameson-like shock detector. Results obtained for a shock-propagation problem are shown to validate the method, which will be now used for the simulations of supersonic jets. © 2009 Springer-Verlag Berlin Heidelberg.