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This volume collects the contributions of a Conference held in June 2005 at the laboratoire Paul Painleve (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 various viewpoints (e.g. theoretical, and numerical) on the addressed questions.
Some Recent Asymptotic Results in Fluid Mechanics.- Recent Mathematical Results and Open Problems about Shallow Water Equations.- Direct Numerical Simulation and Analysis of 2D Turbulent Flows.- Numerical Capture of Shock Solutions of Nonconservative Hyperbolic Systems via Kinetic Functions.- Domain Decomposition Algorithms for the Compressible Euler Equations.- The Two-Jacobian Scheme for Systems of Conservation Laws.- Do Navier-Stokes Equations Enable to Predict Contact Between Immersed Solid Particles?.- The Reduced Basis Element Method for Fluid Flows.- Asymptotic Stability of Steady-states for Saint-Venant Equations with Real Viscosity.- Numerical Simulations of the Inviscid Primitive Equations in a Limited Domain.- Some Recent Results about the Sixth Problem of Hilbert.- On Compressible and Incompressible Vortex Sheets.- Existence and Stability of Compressible and Incompressible Current-Vortex Sheets.