Numerical analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid

We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface captured by a level set method. The solid velocity is computed by averaging at avery time the flow velocity in the solid phase. This velocity is used to penalize the flow velocity at the fluid-solid interface and to move the interface. Numerical illustrations are provided to illustrate our convergence result. A discussion of our result in the light of existing existence results is also given. [1] Ph. Angot, C.-H. Bruneau and P. Fabrie, A penalization method to take into account obstacles in incompressible viscous flows, Numer. Math. 81: 497--520 (1999)Comment: 23 page

Mathematics, Hybrid computing and HPC

International audienceHPC appears more and more as a key player in the field of numerical simulation and data processing. This trend comes of course with the desire to perform simulations that are closer and closer to real world situations, and with the development of clusters and platforms that provide access to hundreds to thousands CPU/GPU nodes. The application domains encompass many fields, from fluid mechanics to biology and nano-sciences, in academic research as well as for industrial applications. Concerning industrial applications, major groups have often already a good practice of HPC, with dedicated manpower and available in-house platforms. The access of SMEs to HPC is more problematic as they do not have the appropriate resources in hardware and manpower, and it is sometimes hard for them to have a clear idea of the gain they will obtain through HPC. In the first part of the talk, I will talk about a national initiative led by INRIA, GENCI and BPI, to promote the access of SMEs to HPC. This initiative provides support both in terms of market analysis, access to hardware and technical environment. It now involves middle-size HPC platforms that are distributed in French universities. This initiative will therefore give new opportunities to researchers, in particular mathematicians, to be connected to industrial collaborations. HPC is actually not only a question of accessing hardware and adapting existing codes to massively parallel platforms. It also raises questions about mathematical and numerical models that optimize the emerging hardware and analyze the huge amount of data associated with these simulations, and software engineering to distribute algorithms on heterogeneous clusters. Mathematicians therefore can use HPC as a mean to access challenging industrial collaborations in which they can contribute through new methods and algorithms, in both scientific computing and statistics

The Paris Conference of 1919 Between the Traditions of European Congresses and the “New Diplomacy”

The conflicting combination of Old and New Diplomacy imparted to the Versailles treaty, through numerous compromises, a flexibility which tends to be overlooked and which was meant also to gain time in face of quite rabid Allied public opinion in 1919. Many provisions could be modified (reparations for instance), many delays could be shortened (as the occupation of the Rhineland). The treaty could be implemented harshly, as in 1921–1923, or more leniently, as after Locarno (1925). It was one of the few great international treaties which contained the means for its revision. It is not true that all the disasters of the 1930s were implied by the treaties, even if their legacy was much more short-lived and less successful than that of the Vienna Congress

A Vortex Method for Bi-phasic Fluids Interacting with Rigid Bodies

We present an accurate Lagrangian method based on vortex particles, level-sets, and immersed boundary methods, for animating the interplay between two fluids and rigid solids. We show that a vortex method is a good choice for simulating bi-phase flow, such as liquid and gas, with a good level of realism. Vortex particles are localized at the interfaces between the two fluids and within the regions of high turbulence. We gain local precision and efficiency from the stable advection permitted by the vorticity formulation. Moreover, our numerical method straightforwardly solves the two-way coupling problem between the fluids and animated rigid solids. This new approach is validated through numerical comparisons with reference experiments from the computational fluid community. We also show that the visually appealing results obtained in the CG community can be reproduced with increased efficiency and an easier implementation