Description

The goal of this is book to give a detailed presentation of multicomponent flow models and to investigate the mathematical structure and properties of the resulting system of partial differential equations. These developments are also illustrated by simulating numerically a typical laminar flame. Our aim in the chapters is to treat the general situation of multicomponent flows, taking into account complex chemistry and detailed transport phe- nomena. In this book, we have adopted an interdisciplinary approach that en- compasses a physical, mathematical, and numerical point of view. In par- ticular, the links between molecular models, macroscopic models, mathe- matical structure, and mathematical properties are emphasized. We also often mention flame models since combustion is an excellent prototype of multicomponent flow. This book still does not pretend to be a complete survey of existing models and related mathematical results. In particular, many subjects like multi phase-flows, turbulence modeling, specific applications, porous me- dia, biological models, or magneto-hydrodynamics are not covered. We rather emphasize the fundamental modeling of multicomponent gaseous flows and the qualitative properties of the resulting systems of partial dif- ferential equations. Part of this book was taught at the post-graduate level at the Uni- versity of Paris, the University of Versailles, and at Ecole Poly technique in 1998-1999 to students of applied mathematics.