This volume collects the contributions of a conference held in June 2005, at the laboratoire Paul PainlevA(c) (UMR CNRS 8524) in Lille, France. The meeting was intended to review hot topics and future trends in fluid dynamics, with the objective to foster exchanges of theoretical and numerical viewpoints. The content of the volume can be split into three categories: A first set of contributions is devoted to the description of the connection between different models of fluid dynamics. An important part of these papers relies on the discussion of the modeling issues, the identification of the relevant dimensionless coefficients, and on the physical interpretation of the models. A second set of contributions considers the question of the stability of particular structures in fluid mechanics equations. The third set of contributions is concerned with numerical issues; it is indeed a crucial challenge to design numerical schemes that are able to capture the complex features generated by fluid flows.
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