Analysis and Simulation of Fluid Dynamics / edited by Caterina Calgaro, Jean-François Coulombel, Thierry Goudon.

Springer eBooks

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.

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.

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