Buch, Englisch, 258 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 860 g
Approximation Methods in Kinetic Theory
Buch, Englisch, 258 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 860 g
Reihe: Interaction of Mechanics and Mathematics
ISBN: 978-3-540-24542-1
Verlag: Springer
The well known transport laws of Navier-Stokes and Fourier fail for the simulation of processes on lengthscales in the order of the mean free path of a particle that is when the Knudsen number is not small enough. Thus, the proper simulation of flows in rarefied gases requires a more detailed description.
This book discusses classical and modern methods to derive macroscopic transport equations for rarefied gases from the Boltzmann equation, for small and moderate Knudsen numbers, i.e. at and above the Navier-Stokes-Fourier level. The main methods discussed are the classical Chapman-Enskog and Grad approaches, as well as the new order of magnitude method, which avoids the short-comings of the classical methods, but retains their benefits. The relations between the various methods are carefully examined, and the resulting equations are compared and tested for a variety of standard problems.
The book develops the topic starting from the basic description of an ideal gas, over the derivation of the Boltzmann equation, towards the various methods for deriving macroscopic transport equations, and the test problems which include stability of the equations, shock waves, and Couette flow.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
- Technische Wissenschaften Technik Allgemein Technik: Allgemeines
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Technische Thermodynamik
- Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
- Technische Wissenschaften Technik Allgemein Physik, Chemie für Ingenieure
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Naturwissenschaften Physik Thermodynamik
Weitere Infos & Material
Basic quantities and definitions.- The Boltzmann equation and its properties.- The Chapman-Enskog method.- Moment equations.- Grad’s moment method.- Regularization of Grad equations.- Order of magnitude approach.- Macroscopic transport equations for rarefied gas flows.- Stability and dispersion.- Shock structures.- Boundary value problems.
