By Caterina Calgaro, Jean-François Coulombel, Thierry Goudon
This quantity collects the contributions of a convention held in June 2005 on the laboratoire Paul Painleve (UMR CNRS 8524) in Lille, France. The assembly was once meant to study scorching subject matters and destiny tendencies in fluid dynamics, with the target to foster exchanges of varied viewpoints (e.g. theoretical, and numerical) at the addressed questions. It contains a set of study articles on fresh advances within the research and simulation of fluid dynamics.
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Extra resources for Analysis and Simulation of Fluid Dynamics (Advances in Mathematical Fluid Mechanics)
An existence result for a model of granular material with non-constant density. Asymptotic Analysis, 30,  D. Hoff, D. Serre. The failure of continuous dependence on initial data for the Navier-Stokes equations of compressible ﬂow. SIAM J. Appl. , 51(4):887–898, (1991). 30 D. Bresch, B. Desjardins and G. V. Kazhikhov, Initial-boundary value problems for the Euler equations of an ideal incompressible ﬂuid. Moscow Univ. Math. Bull. 46 (1991), no. 5, 10–14. V. Kazhikhov, A. Veigant. Global solutions of equations of potential ﬂuids for small Reynolds number.
Partial Diﬀ. , 23, 5-6, (1998), 985–1006. L. -J. Chatelon, P. Orenga. On a bi-layer shallow-water problem. Nonlinear Anal. Real World Appl. 4 (2003), no. 1, 139–171.  A. Novotny, I. Straskraba. Introduction to the mathematical theory of compressible ﬂow. Oxford lecture series in Mathematics and its applications, (2004).  M. Oliver, Justiﬁcation of the shallow water limit for a rigid lid ﬂow with bottom topography, Theoretical and Computational Fluid Dynamics 9 (1997), 311–324.  P. Orenga.
The method is constructive, being based on successive approximations, and it brings out clearly the physical basis for the additional condition. To understand it in a better way, open sea boundary conditions could be helpful for shallow-water equations for instance with an application to strait of Gibraltar modelling. 8. Multi-level models We now give an example where it could be important to write multi-level shallow water equations: it concerns the modelling of the dynamics of water in the Alboran sea and the strait of Gibraltar.