Macroscopic Transport Equations for Rarefied Gas Flows: Approximation Methods in Kinetic Theory: Interaction of Mechanics and Mathematics
Autor Henning Struchtrupen Limba Engleză Paperback – 15 iun 2005
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.
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Specificații
ISBN-13: 9783540245421
ISBN-10: 3540245421
Pagini: 274
Ilustrații: XIV, 258 p. 35 illus.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.39 kg
Ediția:2005
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Interaction of Mechanics and Mathematics
Locul publicării:Berlin, Heidelberg, Germany
ISBN-10: 3540245421
Pagini: 274
Ilustrații: XIV, 258 p. 35 illus.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.39 kg
Ediția:2005
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Interaction of Mechanics and Mathematics
Locul publicării:Berlin, Heidelberg, Germany
Public țintă
GraduateCuprins
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.
Textul de pe ultima copertă
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.
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.
Caracteristici
Introductory textbook presenting the development of continuum models for microscale effects in a concise form – mathematically sound, but as simple as possible Includes supplementary material: sn.pub/extras