Fluid Dynamic Applications of the Discrete Boltzmann Equation

by Monaco, Roberto; Preziosi, Luigi

• ISBN13: 9789810204662
• ISBN10: 9810204663
• Format: Hardcover
• Copyright: 1992-02-01
• Publisher: World Scientific Pub Co Inc

Table of Contents

Preface	vii
The Discrete Boltzmann Equation Modelling and Thermodynamics
The Discrete Boltzmann Equation	3	(1)
On the Mathematical Modelling	4	(10)
The Discrete Boltzmann Equation for a One-Component Gas	5	(5)
The Discrete Boltzmann Equation for Gas Mixtures	10	(4)
Macroscopic Observables	14	(5)
Thermodynamic Equilibrium and Conservation Equations	19	(11)
Analysis for a One-Component Gas	19	(8)
Analysis for Gas Mixtures	27	(3)
Plan of the Book	30	(10)
References	33	(7)
Some Discrete Velocity Models
Planar 2n-Velocity Models	40	(20)
The 4--Velocity Model	42	(4)
The 4--Velocity Model for Binary Gas Mixtures	46	(4)
The 6--Velocity Model	50	(3)
The 6--Velocity Model with Triple Collisions	53	(3)
The 2 x 6-Velocity Model with Triple Collisions	56	(4)
Spatial Models	60	(22)
The Broadwell Model for a One-Component Gas	60	(4)
The Broadwell Model for Binary Gas Mixtures	64	(3)
Cabannes-Type Models	67	(9)
Shizuta-Type Models	76	(3)
References	79	(3)
On the Discrete Boltzmann Equation in Unbounded Domains
The Cauchy Problem for the Discrete Boltzmann Equation	82	(10)
Mathematical Formulation and Local Existence	83	(6)
Existence of Solutions in the Whole Space Rd, d≥2	89	(1)
The Initial Value Problem in One-Space Dimension	90	(2)
On the Solution of the Discrete Boltzmann Equation	92	(23)
References	109	(6)
Shock Waves
Statement of the Mathematical Problem	115	(3)
Determination of the Velocity of Sound	118	(4)
Existence and Stability of Shock Waves	122	(7)
Propagation and Structure of Shock Waves	129	(18)
Shock Waves by the 2 x 6- Broadwell Model for a Binary Gas Mixture	129	(15)
Shock Waves by the Planar 6-Velocity Model with Triple Collisions	144	(3)
Discussion and Open Problems	147	(8)
References	149	(6)
Internal and External Flows
Mathematical Formulation of Boundary Conditions	155	(11)
Applications of the Discrete Boltzmann Equation in Bounded Domains	166	(3)
Flow between Two Walls at Different Temperatures	169	(11)
Couette Flow	180	(10)
Rayleigh Flow	190	(3)
Flow over Convex Bodies	193	(10)
References	199	(4)
The Discrete Boltzmann Equation for Chemically Reacting Gases
Gases with Chemical Reactions	203	(4)
A Mathematical Model for Gases with Bi-Molecular Chemical Reactions	207	(13)
Kinetic Equations of the Discrete Model with Bi-Molecular Chemical Reactions	211	(5)
Thermodynamic Equilibrium in Presence of Bi-Molecular Reactions	216	(4)
A Mathematical Model for a Gas with Chemical Dissociation and Recombination	220	(16)
Kinetic Equations of the Discrete Model with Chemical Dissociation and Recombination	225	(10)
Thermodynamic Equilibrium in Presence of Chemical Dissociation and Recombination	235	(1)
A Discrete Model for a Dissociating Gas	236	(5)
Shock Waves for a Dissociating Gas	241	(8)
Discussion and Open Problems	249	(6)
References	252	(3)
Author Index	255	(4)
Subject Index	259