Macroscopic Transport Equations for Rarefied Gas Flows Approximation Methods in Kinetic Theory /

• Κύριος συγγραφέας: Struchtrup, Henning (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.
• Σειρά: Interaction of Mechanics and Mathematics,
• Θέματα: Engineering.; Applied mathematics.; Engineering mathematics.; Thermodynamics.; Statistical physics.; Dynamical systems.; Heat engineering.; Heat transfer.; Mass transfer.; Engineering Thermodynamics, Heat and Mass Transfer.; Applications of Mathematics.; Statistical Physics, Dynamical Systems and Complexity.; Engineering, general.

 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. 

 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.