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 sizzling themes and destiny traits 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 contemporary 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)
It would be interesting to prove mathematically such formal derivations. We make here a few remarks concerning the hypothesis which have been used to derive formally these viscous shallow water equations with damping terms. First hypothesis. The viscosity is of order ε, meaning that the viscosity is of the same order than the depth, and the asymptotic analysis is performed at order 1. Second hypothesis. The boundary condition at the bottom for the Navier–Stokes equations is taken using wall laws.
Submitted (2005).  L. Min, A. Kazhikhov, S. Ukai. Global solutions to the Cauchy problem of the Stokes approximation equations for two-dimensional compressible ﬂows. Comm. 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).
Numerical approximation of compressible ﬂuid models with density dependent viscosity. In preparation (2005).  D. Bresch, B. -M. Ghidaglia. On bi-ﬂuid compressible models. In preparation (2005). Results and Open Problems about Shallow Water Equations 29  D. Bresch, B. Desjardins. Existence globale de solutions pour les ´equations de Navier–Stokes compressibles compl`etes avec conduction thermique. C. R. Acad. , Paris, Section math´ematiques. Submitted (2005).  D. Bresch, B. Desjardins.