05361nam 22007694a 450 991097197090332120251116231609.097866119479279781281947925128194792X97898127969059812796908(CKB)1000000000537921(EBL)1679508(OCoLC)879023694(SSID)ssj0000190847(PQKBManifestationID)11177787(PQKBTitleCode)TC0000190847(PQKBWorkID)10183579(PQKB)10070384(MiAaPQ)EBC1679508(WSP)00005155(Au-PeEL)EBL1679508(CaPaEBR)ebr10255755(CaONFJC)MIL194792(PPN)164381899(Perlego)849265(EXLCZ)99100000000053792120021029d2003 uy 0engur|n|---|||||txtccrLecture notes on the discretization of the Boltzmann equation /editors Nicola Bellomo, Renee Gatignol1st ed.River Edge, NJ World Scientificc20031 online resource (317 p.)Series on advances in mathematics for applied sciences ;v. 63Description based upon print version of record.9789812382252 9812382259 Includes bibliographical references.CONTENTS ; Preface ; Chapter 1. From the Boltzmann Equation to Discretized Kinetic Models ; 1.1 Introduction ; 1.2 The Nonlinear Boltzmann Equation ; 1.3 The Discrete and Semicontinuous Boltzmann Equation ; 1.4 Plan of the Lecture Notes ; 1.5 ReferencesChapter 2. Discrete Velocity Models for Gas Mixtures 2.1 Introduction ; 2.2 DVM for mixtures ; 2.3 Models with a finite number of velocities and the problem of spurious invariants ; 2.4 Constructing DVM with arbitrarily many velocities ; 2.5 Concluding remarks ; 2.6 ReferencesChapter 3. Discrete Velocity Models with Multiple Collisions 3.1 Introduction ; 3.2 Discrete Models with Multiple Collisions ; 3.3 Macroscopic Description ; 3.4 Boundary Conditions for Discrete Models ; 3.5 Conclusion ; 3.6 ReferencesChapter 4. Discretization of the Boltzmann Equation and the Semicontinuous Model 4.1 Introduction ; 4.2 Splitting and Energy Formulation ; 4.3 Working in a Finite Energy Interval ; 4.4 Energy Discretization and Kinetic Model4.5 Conservation and Euler Equations for the Discretized Model 4.6 Energy Formulation of the Collision Dynamics ; 4.7 Concluding Remarks ; 4.8 References ; Chapter 5. Semi-continuous Extended Kinetic Theory ; 5.1 Introduction ; 5.2 Continuous Kinetic Equations5.3 Semi-continuous Kinetic EquationsThis book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community. <br><i>Contents:</i><ul><li>From the Boltzmann Equation to Discretized Kinetic Models <i>(N Bellomo & R Gatignol)</i>Series on advances in mathematics for applied sciences ;v. 63.Transport theoryFinite element methodDifferential equationsAsymptotic theoryTransport theory.Finite element method.Differential equationsAsymptotic theory.530.13/8Bellomo N31305Gatignol Renée346331MiAaPQMiAaPQMiAaPQBOOK9910971970903321Lecture notes on the discretization of the Boltzmann equation4535318UNINA