Analysis and Simulation of Fluid Dynamics (Advances in Mathematical Fluid Mechanics)
Contributors: Caterina Calgaro (Editor); Jean-François Coulombel (Editor); Thierry Goudon (Editor)
Edition: 1 edition
Publisher: Birkhäuser Basel
Published: December 28, 2006
Language: eng
Format: Hardcover
Number of pages: 246
ISBN-13: 9783764377410
Subjects: Mathematics; Science/Mathematics; Differential Equations; Mechanics - General; Number Systems; Mach number; Mathematics / Differential Equations; compressible models; coriolis force; critical thresholds; incompressible models; multiphase flows; phase transitions; vortex sheets; Computer simulation; Congresses; Fluid dynamics
Description: This volume collects the contributions of a Conference held in June 2005, at the laboratoire Paul Painlev´ e (UMR CNRS 8524) in Lille, France. The meeting was intended to review hot topics and future trends in ?uid dynamics, with the obj- tive to foster exchanges of various viewpoints (e. g. theoretical, and numerical) on the addressed questions. The content of the volume can be split into three categories: –A?rstsetofcontributionsisdevotedtothedescriptionoftheconnectionbetween di?erent models of ?uid dynamics. An important part of these papers relies on the discussion of the modeling issues, the identi?cation of the relevant dimensionless coe?cients, and on the physical interpretation of the models. Then, making r- orous the connection between the di?erent levels of modeling and justifying the validity of some simpli?cations become an asymptotics question, and an overview ofthemoderntoolsofmathematicalanalysisthatallowto treatsuchkindofpr- lems is given. Thepaper by L. Saint-Raymonddescribeshowthe equationsof?uid dynamics (Euler or Navier-Stokes equations) can be derived from the Boltzamnn equation. In the latter, the gas is described statistically through the evolution of the particles density function assuming that particles are subject to a binary col- sion dynamics. This derivation of the ?uid dynamics equations is actually part of the programaddressed at the International Congressof Mathematics, Paris, 1900, and it is often referred to as the 6th Hilbert’s problem. T.