Analysis and Simulation of Fluid Dynamics
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. It comprises a collection of research articles on recent advances in the analysis and simulation of fluid dynamics.
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This volume collects the contributions of a conference held in June 2005, at the laboratoire Paul Painlevé (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.
Foreword viiSome Recent Asymptotic Results in Fluid Mechanics 1Recent Mathematical Results and Open Problems about Shallow Water Equations 15Direct Numerical Simulation and Analysis of 2D Turbulent Flows 33 C. Chalons F. Coquel Numerical Capture of Shock Solutions of Nonconservative Hyperbolic Systems via Kinetic Functions 45Domain Decomposition Algorithms for the Compressible Euler Equations 69The Two-Jacobian Scheme for Systems of Conservation Laws 89Do Navier-Stokes Equations Enable to Predict Contact Between Immersed Solid Particles? 109The Reduced Basis Element Method for Fluid Flows 129Asymptotic Stability of Steady-states for Saint-Venant Equations with Real Viscosity 155Numerical Simulations of the Inviscid Primitive Equations in a Limited Domain 163Some Recent Results about the Sixth Problem of Hilbert 183On Compressible and Incompressible Vortex Sheets 201Existence and Stability of Compressible and Incompressible Current-Vortex Sheets 229
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