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 check scorching subject matters and destiny developments in fluid dynamics, with the target to foster exchanges of varied viewpoints (e.g. theoretical, and numerical) at the addressed questions. It includes a set of analysis articles on fresh advances within the research and simulation of fluid dynamics.
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Extra info for Analysis and Simulation of Fluid Dynamics (Advances in Mathematical Fluid Mechanics)
2003): “A novel fully-implicit ﬁnite volume method applied to the lid-driven cavity problem. Part I and II”, Int. J. Numer. Methods Fluids Vol. 42 n◦ 1. fr Analysis and Simulation of Fluid Dynamics Advances in Mathematical Fluid Mechanics, 45–68 c 2006 Birkh¨ auser Verlag Basel/Switzerland Numerical Capture of Shock Solutions of Nonconservative Hyperbolic Systems via Kinetic Functions Christophe Chalons and Fr´ed´eric Coquel Abstract. This paper reviews recent contributions to the numerical approximation of solutions of nonconservative hyperbolic systems with singular viscous perturbations.
17, (1964), 35–92.  C. Bernardi, O. Pironneau. On the shallow water equations at low Reynolds number. Commun. Partial Diﬀ. Eqs. 16, 59–104 (1991). L. J. Majda. Vorticity and incompressible ﬂows. Cambridge University Press, (2001). ´tivier, Estimations de Schauder et r´egularit´e  P. Bolley, J. Camus, G. Me H¨ olderienne pour une classe de probl`emes aux limites singuliers, Comm. Partial Diﬀ. Equ. 11 (1986), 1135–1203.  F. Bouchut, A. Mangeney-Castelnau, B. P. Vilotte. A new model of Saint-Venant and Savage-Hutter type for gravity driven shallow water ﬂows.
Here, small scales sensitiveness is encoded thanks to the notion of kinetic functions so as to consider a set of generalized jump conditions. To enforce for validity these jump conditions at the discrete level, we describe a systematic and eﬀective correction procedure. Numerical experiments assess the relevance of the proposed method. 1. Introduction We survey some of the recent numerical methods for approximating the solutions of nonlinear hyperbolic systems with viscous perturbations, in the form: A0 (v )∂t v + A1 (v )∂x v = ∂x (D(v )∂x v ), x ∈ R, t > 0.
Analysis and Simulation of Fluid Dynamics (Advances in Mathematical Fluid Mechanics) by Caterina Calgaro, Jean-François Coulombel, Thierry Goudon