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Rarefied gas dynamics : kinetic modeling and multi-scale simulation / / Lei Wu
Rarefied gas dynamics : kinetic modeling and multi-scale simulation / / Lei Wu
Autore Wu Lei
Pubbl/distr/stampa Singapore : , : Springer, , [2022]
Descrizione fisica 1 online resource (293 pages) : illustrations (black and white, and colour)
Disciplina 533.2
Soggetto topico Rarefied gas dynamics - Mathematical models
Rarefied gas dynamics
ISBN 9789811928727
9789811928710
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Navier-Stokes-Fourier Equations -- 1.2 Continuum Breakdown -- 1.2.1 Reentry of Space Vehicle -- 1.2.2 Microelectromechanical Systems -- 1.2.3 Shale Gas Extraction -- 1.2.4 Global Wind Profiling -- 1.3 Simple Gas Kinetic Theory -- 1.4 Knudsen Number -- 1.4.1 Spatial Knudsen Number -- 1.4.2 Temporal Knudsen Number -- 1.5 Molecular Dynamics Simulations -- References -- 2 Gas Kinetic Theory -- 2.1 Velocity Distribution Function -- 2.2 Binary Collision -- 2.2.1 Deflection Angle -- 2.2.2 Differential Cross Section -- 2.2.3 Grazing Collision -- 2.3 Boltzmann Equation -- 2.3.1 H-Theorem -- 2.3.2 Equilibrium Collision Frequency -- 2.3.3 Linearized Boltzmann Equation -- 2.4 Wang-Chang and Uhlenbeck Equation -- 2.5 Enskog Equation -- 2.5.1 Liquid-Vapor Flow -- 2.5.2 Granular Gas -- 2.6 Gas-Surface Boundary Condition -- 2.6.1 Maxwell Boundary Condition -- 2.6.2 Epstein Boundary Condition -- 2.6.3 Cercignani-Lampis Boundary Condition -- 2.7 Numerical Methods -- 2.7.1 Direct Simulation Monte Carlo -- 2.7.2 Discrete Velocity Methods -- 2.7.3 Multi-scale Simulation -- References -- 3 Fluid-Dynamic Equation -- 3.1 Hilbert Expansion -- 3.2 Chapman-Enskog Expansion -- 3.2.1 Expansion in Sonine Polynomials -- 3.2.2 Expansion to the First Order -- 3.2.3 Expansion to Higher Orders -- 3.3 Moment Methods -- 3.4 Accuracy of Macroscopic Equations -- 3.4.1 Equations from Chapman-Enskog Expansion -- 3.4.2 Moment Equations -- 3.5 Convergence of Moment Equations -- 3.5.1 Rayleigh-Brillouin Scattering -- 3.5.2 Sound Propagation -- References -- 4 Fast Spectral Method for Monatomic Gas Flow -- 4.1 Inverse Design of Collision Kernel -- 4.1.1 Power-Law Potential -- 4.1.2 Lennard-Jones Potential -- 4.2 Normalization -- 4.3 Fast Spectral Method -- 4.3.1 Carleman Representation -- 4.3.2 Fourier-Galerkin Spectral Method.
4.3.3 Detailed Implementation -- 4.3.4 Non-uniform Discretization of Velocity Space -- 4.4 Homogeneous Relaxation -- 4.4.1 Bobylev-Krook-Wu Solution -- 4.4.2 Discontinuous Velocity Distribution -- 4.5 Accuracy in Inhomogeneous Problems -- 4.5.1 Normal Shock Waves -- 4.5.2 Force-Driven Poiseuille Flows -- 4.5.3 Thermal Transpiration in a Cavity -- 4.6 Concluding Remarks -- References -- 5 Fast Spectral Method for Linear Gas Flow -- 5.1 Linearization -- 5.2 Poiseuille Flow -- 5.2.1 Poiseuille Flow Between Parallel Plates -- 5.2.2 Poiseuille Flow Through a Long Duct -- 5.3 Thermal Transpiration -- 5.4 Onsager-Casimir Relation -- 5.5 Influence of Intermolecular Potential -- 5.5.1 Lennard-Jones Potential -- 5.5.2 Accurate Transport Coefficients -- 5.5.3 Poiseuille Flow -- 5.5.4 Planar Fourier Flow -- 5.5.5 Planar Couette Flow -- 5.6 Cercignani-Lampis Boundary Condition -- 5.6.1 Poiseuille Flow Through Parallel Plates -- 5.6.2 Poiseuille Flow Through Long Tube -- References -- 6 Kinetic Modeling of Monatomic Gas Flow -- 6.1 Basic Rules -- 6.2 Velocity-Independent Collision Frequency -- 6.2.1 BGK Model -- 6.2.2 Ellipsoidal-Statistical BGK Model -- 6.2.3 Shakhov Model -- 6.2.4 Gross-Jackson Model -- 6.2.5 Nonlinearization -- 6.3 Velocity-Dependent Collision Frequency -- 6.4 Fokker-Planck Model -- 6.5 Accuracy of Kinetic Models -- 6.5.1 Normal Shock Wave -- 6.5.2 Thermal Transpiration -- References -- 7 Kinetic Modeling of Molecular Gas Flow -- 7.1 Bulk Viscosity -- 7.2 Thermal Conductivity -- 7.3 Thermal Relaxation Rates in DSMC -- 7.4 Kinetic Models -- 7.4.1 Hanson-Morse Model -- 7.4.2 Rykov Model -- 7.4.3 ESBGK Model -- 7.4.4 Wu Model -- 7.5 Accuracy of Kinetic Models -- 7.5.1 Normal Shock Wave -- 7.5.2 Couette Flow -- 7.5.3 Maxwell's Demon -- 7.6 Uncertainty Quantification -- 7.6.1 Normal Shock Wave -- 7.6.2 Flow Driven by Maxwell's Demon.
7.6.3 Thermal Transpiration in Cavity -- 7.7 Conclusions and Discussions -- References -- 8 General Synthetic Iterative Scheme -- 8.1 Problems of CIS -- 8.1.1 Slow Convergence -- 8.1.2 False Convergence -- 8.2 General Synthetic Iterative Scheme -- 8.2.1 Scheme-I GSIS -- 8.2.2 Scheme-II GSIS -- 8.3 Properties of GSIS -- 8.3.1 Super Convergence -- 8.3.2 Asymptotic Preserving -- 8.4 Numerical Tests -- 8.4.1 Coherent Rayleigh-Brillouin Scattering -- 8.4.2 Planar Fourier Flow -- 8.4.3 Couette Flow Between Eccentric Cylinders -- 8.5 Concluding Remarks and Outlooks -- References -- 9 Acoustics in Rarefied Gas -- 9.1 Formulation of the Problem -- 9.2 Oscillatory Couette Flow -- 9.3 Oscillating Lid-Driven Cavity Flow -- 9.3.1 Scaling Law for Anti-resonant Frequency -- 9.4 Planar Sound Propagation -- 9.5 Sound Propagation in Cavity -- 9.5.1 Two Types of Resonances -- 9.5.2 Sound Speed -- References -- 10 Slip and Jump Coefficients -- 10.1 State of the Problem -- 10.2 Viscous Slip -- 10.2.1 Viscous Slip Coefficient -- 10.2.2 Knudsen Layer Function -- 10.3 Thermal Slip -- 10.3.1 Thermal Slip Coefficient -- 10.3.2 Knudsen Layer Function -- 10.3.3 Molecular Gases -- 10.4 Temperature Jump -- References -- 11 Accuracy of Kinetic Boundary Condition -- 11.1 Reynolds Lubrication Equation -- 11.2 Experiments and Upscaling -- 11.3 Approximate Velocity Slip Coefficients -- 11.4 Comparison with Experiment -- 11.4.1 Poiseuille Flow Through a Rectangular Duct -- 11.4.2 Thermal Transpiration in a Rectangular Duct -- 11.4.3 Thermal Transpiration Through a Long Tube -- 11.5 Implication in Hypersonic Flows -- References -- 12 Porous Media Flow -- 12.1 Apparent Gas Permeability -- 12.2 Kinetic Formulation -- 12.3 Accuracy of Navier-Stokes Equations -- 12.4 Interpretation of Experiment -- 12.5 Asymptotic Behavior at Large KnKn -- References -- 13 Gas Mixture.
13.1 Boltzmann Equation for Gas Mixture -- 13.2 Fast Spectral Method -- 13.2.1 Accuracy Analysis -- 13.2.2 Efficient Algorithm for Large Mass Ratio -- 13.3 Accuracy in Inhomogeneous Problems -- 13.4 Linearization and GSIS -- 13.5 McCormack Model -- References -- 14 Dense Gas Flow -- 14.1 Fast Spectral Method -- 14.2 Heated Granular Gas -- 14.3 Force-Driven Poiseuille Flow -- 14.3.1 Mass Flow Rate of Dense Gas -- 14.3.2 Influence of Restitution Coefficient -- 14.4 Heat Transfer -- 14.5 Kinetic Model for Dense Gas -- References -- 15 Fluctuation and Light Scattering -- 15.1 Rayleigh-Brillouin Scattering -- 15.1.1 Spontaneous RBS -- 15.1.2 Coherent RBS -- 15.2 Numerical Methods -- 15.2.1 Monatomic Gas -- 15.2.2 Molecular Gas -- 15.3 Accuracy of the Tenti Model -- 15.3.1 Temperature Retrieval Error -- 15.4 Extraction of Gas Property -- References -- Appendix A Special Functions -- Appendix B Relaxation Rates of Maxwellian Molecules -- Appendix C Numerical Quadratures -- C.1 Gauss-Legendre Quadrature -- C.2 Gauss-Hermite Quadrature -- Appendix D Implementation of Fast Spectral Method -- D.1 Algorithm 1: Zero-Padding -- D.2 Algorithm 2: No Zero-Padding -- D.3 Algorithm 3: Collision Frequency -- Appendix E MATLAB Code for Normal Shock Wave -- Appendix F MATLAB Code for Poiseuille Flow and Thermal Transpiration -- Index.
Record Nr. UNINA-9910592981803321
Wu Lei  
Singapore : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Rarefied gas dynamics : kinetic modeling and multi-scale simulation / / Lei Wu
Rarefied gas dynamics : kinetic modeling and multi-scale simulation / / Lei Wu
Autore Wu Lei
Pubbl/distr/stampa Singapore : , : Springer, , [2022]
Descrizione fisica 1 online resource (293 pages) : illustrations (black and white, and colour)
Disciplina 533.2
Soggetto topico Rarefied gas dynamics - Mathematical models
Rarefied gas dynamics
ISBN 9789811928727
9789811928710
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Navier-Stokes-Fourier Equations -- 1.2 Continuum Breakdown -- 1.2.1 Reentry of Space Vehicle -- 1.2.2 Microelectromechanical Systems -- 1.2.3 Shale Gas Extraction -- 1.2.4 Global Wind Profiling -- 1.3 Simple Gas Kinetic Theory -- 1.4 Knudsen Number -- 1.4.1 Spatial Knudsen Number -- 1.4.2 Temporal Knudsen Number -- 1.5 Molecular Dynamics Simulations -- References -- 2 Gas Kinetic Theory -- 2.1 Velocity Distribution Function -- 2.2 Binary Collision -- 2.2.1 Deflection Angle -- 2.2.2 Differential Cross Section -- 2.2.3 Grazing Collision -- 2.3 Boltzmann Equation -- 2.3.1 H-Theorem -- 2.3.2 Equilibrium Collision Frequency -- 2.3.3 Linearized Boltzmann Equation -- 2.4 Wang-Chang and Uhlenbeck Equation -- 2.5 Enskog Equation -- 2.5.1 Liquid-Vapor Flow -- 2.5.2 Granular Gas -- 2.6 Gas-Surface Boundary Condition -- 2.6.1 Maxwell Boundary Condition -- 2.6.2 Epstein Boundary Condition -- 2.6.3 Cercignani-Lampis Boundary Condition -- 2.7 Numerical Methods -- 2.7.1 Direct Simulation Monte Carlo -- 2.7.2 Discrete Velocity Methods -- 2.7.3 Multi-scale Simulation -- References -- 3 Fluid-Dynamic Equation -- 3.1 Hilbert Expansion -- 3.2 Chapman-Enskog Expansion -- 3.2.1 Expansion in Sonine Polynomials -- 3.2.2 Expansion to the First Order -- 3.2.3 Expansion to Higher Orders -- 3.3 Moment Methods -- 3.4 Accuracy of Macroscopic Equations -- 3.4.1 Equations from Chapman-Enskog Expansion -- 3.4.2 Moment Equations -- 3.5 Convergence of Moment Equations -- 3.5.1 Rayleigh-Brillouin Scattering -- 3.5.2 Sound Propagation -- References -- 4 Fast Spectral Method for Monatomic Gas Flow -- 4.1 Inverse Design of Collision Kernel -- 4.1.1 Power-Law Potential -- 4.1.2 Lennard-Jones Potential -- 4.2 Normalization -- 4.3 Fast Spectral Method -- 4.3.1 Carleman Representation -- 4.3.2 Fourier-Galerkin Spectral Method.
4.3.3 Detailed Implementation -- 4.3.4 Non-uniform Discretization of Velocity Space -- 4.4 Homogeneous Relaxation -- 4.4.1 Bobylev-Krook-Wu Solution -- 4.4.2 Discontinuous Velocity Distribution -- 4.5 Accuracy in Inhomogeneous Problems -- 4.5.1 Normal Shock Waves -- 4.5.2 Force-Driven Poiseuille Flows -- 4.5.3 Thermal Transpiration in a Cavity -- 4.6 Concluding Remarks -- References -- 5 Fast Spectral Method for Linear Gas Flow -- 5.1 Linearization -- 5.2 Poiseuille Flow -- 5.2.1 Poiseuille Flow Between Parallel Plates -- 5.2.2 Poiseuille Flow Through a Long Duct -- 5.3 Thermal Transpiration -- 5.4 Onsager-Casimir Relation -- 5.5 Influence of Intermolecular Potential -- 5.5.1 Lennard-Jones Potential -- 5.5.2 Accurate Transport Coefficients -- 5.5.3 Poiseuille Flow -- 5.5.4 Planar Fourier Flow -- 5.5.5 Planar Couette Flow -- 5.6 Cercignani-Lampis Boundary Condition -- 5.6.1 Poiseuille Flow Through Parallel Plates -- 5.6.2 Poiseuille Flow Through Long Tube -- References -- 6 Kinetic Modeling of Monatomic Gas Flow -- 6.1 Basic Rules -- 6.2 Velocity-Independent Collision Frequency -- 6.2.1 BGK Model -- 6.2.2 Ellipsoidal-Statistical BGK Model -- 6.2.3 Shakhov Model -- 6.2.4 Gross-Jackson Model -- 6.2.5 Nonlinearization -- 6.3 Velocity-Dependent Collision Frequency -- 6.4 Fokker-Planck Model -- 6.5 Accuracy of Kinetic Models -- 6.5.1 Normal Shock Wave -- 6.5.2 Thermal Transpiration -- References -- 7 Kinetic Modeling of Molecular Gas Flow -- 7.1 Bulk Viscosity -- 7.2 Thermal Conductivity -- 7.3 Thermal Relaxation Rates in DSMC -- 7.4 Kinetic Models -- 7.4.1 Hanson-Morse Model -- 7.4.2 Rykov Model -- 7.4.3 ESBGK Model -- 7.4.4 Wu Model -- 7.5 Accuracy of Kinetic Models -- 7.5.1 Normal Shock Wave -- 7.5.2 Couette Flow -- 7.5.3 Maxwell's Demon -- 7.6 Uncertainty Quantification -- 7.6.1 Normal Shock Wave -- 7.6.2 Flow Driven by Maxwell's Demon.
7.6.3 Thermal Transpiration in Cavity -- 7.7 Conclusions and Discussions -- References -- 8 General Synthetic Iterative Scheme -- 8.1 Problems of CIS -- 8.1.1 Slow Convergence -- 8.1.2 False Convergence -- 8.2 General Synthetic Iterative Scheme -- 8.2.1 Scheme-I GSIS -- 8.2.2 Scheme-II GSIS -- 8.3 Properties of GSIS -- 8.3.1 Super Convergence -- 8.3.2 Asymptotic Preserving -- 8.4 Numerical Tests -- 8.4.1 Coherent Rayleigh-Brillouin Scattering -- 8.4.2 Planar Fourier Flow -- 8.4.3 Couette Flow Between Eccentric Cylinders -- 8.5 Concluding Remarks and Outlooks -- References -- 9 Acoustics in Rarefied Gas -- 9.1 Formulation of the Problem -- 9.2 Oscillatory Couette Flow -- 9.3 Oscillating Lid-Driven Cavity Flow -- 9.3.1 Scaling Law for Anti-resonant Frequency -- 9.4 Planar Sound Propagation -- 9.5 Sound Propagation in Cavity -- 9.5.1 Two Types of Resonances -- 9.5.2 Sound Speed -- References -- 10 Slip and Jump Coefficients -- 10.1 State of the Problem -- 10.2 Viscous Slip -- 10.2.1 Viscous Slip Coefficient -- 10.2.2 Knudsen Layer Function -- 10.3 Thermal Slip -- 10.3.1 Thermal Slip Coefficient -- 10.3.2 Knudsen Layer Function -- 10.3.3 Molecular Gases -- 10.4 Temperature Jump -- References -- 11 Accuracy of Kinetic Boundary Condition -- 11.1 Reynolds Lubrication Equation -- 11.2 Experiments and Upscaling -- 11.3 Approximate Velocity Slip Coefficients -- 11.4 Comparison with Experiment -- 11.4.1 Poiseuille Flow Through a Rectangular Duct -- 11.4.2 Thermal Transpiration in a Rectangular Duct -- 11.4.3 Thermal Transpiration Through a Long Tube -- 11.5 Implication in Hypersonic Flows -- References -- 12 Porous Media Flow -- 12.1 Apparent Gas Permeability -- 12.2 Kinetic Formulation -- 12.3 Accuracy of Navier-Stokes Equations -- 12.4 Interpretation of Experiment -- 12.5 Asymptotic Behavior at Large KnKn -- References -- 13 Gas Mixture.
13.1 Boltzmann Equation for Gas Mixture -- 13.2 Fast Spectral Method -- 13.2.1 Accuracy Analysis -- 13.2.2 Efficient Algorithm for Large Mass Ratio -- 13.3 Accuracy in Inhomogeneous Problems -- 13.4 Linearization and GSIS -- 13.5 McCormack Model -- References -- 14 Dense Gas Flow -- 14.1 Fast Spectral Method -- 14.2 Heated Granular Gas -- 14.3 Force-Driven Poiseuille Flow -- 14.3.1 Mass Flow Rate of Dense Gas -- 14.3.2 Influence of Restitution Coefficient -- 14.4 Heat Transfer -- 14.5 Kinetic Model for Dense Gas -- References -- 15 Fluctuation and Light Scattering -- 15.1 Rayleigh-Brillouin Scattering -- 15.1.1 Spontaneous RBS -- 15.1.2 Coherent RBS -- 15.2 Numerical Methods -- 15.2.1 Monatomic Gas -- 15.2.2 Molecular Gas -- 15.3 Accuracy of the Tenti Model -- 15.3.1 Temperature Retrieval Error -- 15.4 Extraction of Gas Property -- References -- Appendix A Special Functions -- Appendix B Relaxation Rates of Maxwellian Molecules -- Appendix C Numerical Quadratures -- C.1 Gauss-Legendre Quadrature -- C.2 Gauss-Hermite Quadrature -- Appendix D Implementation of Fast Spectral Method -- D.1 Algorithm 1: Zero-Padding -- D.2 Algorithm 2: No Zero-Padding -- D.3 Algorithm 3: Collision Frequency -- Appendix E MATLAB Code for Normal Shock Wave -- Appendix F MATLAB Code for Poiseuille Flow and Thermal Transpiration -- Index.
Record Nr. UNISA-996490352303316
Wu Lei  
Singapore : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui