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 used to be meant to study sizzling issues 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 includes a suite of analysis 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)
With these boundary conditions we have a well-posed problem and we do not need to add a sponge domain to get realistic results. In numerous applications it is also necessary to handle obstacles with a no-slip boundary condition imposed on their boundary. Instead of using a body ﬁtting mesh, we prefer here to use the penalisation method that allows to keep a Cartesian mesh on a rectangular box. U = 0 in ]0, T [×Ω = 0 in ]0, T [×Ω (3) where K is the adimensional coeﬃcient of permeability of the medium for the obstacles.
Oxford Science Publication, Oxford, (2004). R. Gent. The energetically consistent shallow water equations. J. Atmos. , 50, 1323–1325, (1993). F. Gerbeau, B. Perthame. Derivation of Viscous Saint-Venant System for Laminar Shallow Water; Numerical Validation, Discrete and Continuous Dynamical Systems, Ser. B, Vol. 1, Num. 1, 89–102, (2001).  C. Goulaouic, N. Shimakura, R´egularit´e H¨ old´erienne de certains probl`emes aux limites d´eg´en´er´es, Ann. Scuola Norm. Sup. Pisa, 10, (1983), 79–108.
01 0 0 50 100 time 150 200 100 0 50 100 time 150 200 Figure 5. Comparison of the energy (left) and the enstrophy (right) histories at Re = 100, 000 with the two initialisations. cut we can isolate the vortices directly on the vorticity ﬁeld. Then the remaining is essentially made of the vorticity ﬁlaments in between. Now we can analyse each part separately as it is shown on Figure 9 computing the 2D Fourier spectrum. -H. 5 2 Figure 6. Zoom of vertical velocity component history (left) and corresponding power spectrum (right) at monitoring point (14/16,1/16) for Re = 100, 000.