05286nam 22007214a 450 991045408510332120200520144314.01-281-94792-X9786611947927981-279-690-8(CKB)1000000000537921(EBL)1679508(OCoLC)879023694(SSID)ssj0000190847(PQKBManifestationID)11177787(PQKBTitleCode)TC0000190847(PQKBWorkID)10183579(PQKB)10070384(MiAaPQ)EBC1679508(WSP)00005155(PPN)164381899(Au-PeEL)EBL1679508(CaPaEBR)ebr10255755(CaONFJC)MIL194792(EXLCZ)99100000000053792120021029d2003 uy 0engur|n|---|||||txtccrLecture notes on the discretization of the Boltzmann equation[electronic resource] /editors Nicola Bellomo, Renée GatignolRiver Edge, NJ World Scientificc20031 online resource (317 p.)Series on advances in mathematics for applied sciences ;v. 63Description based upon print version of record.981-238-225-9 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 theoryElectronic books.Transport theory.Finite element method.Differential equationsAsymptotic theory.530.13/8Bellomo N31305Gatignol Renée346331MiAaPQMiAaPQMiAaPQBOOK9910454085103321Lecture notes on the discretization of the Boltzmann equation1950901UNINA