Generalized Hydrodynamics Beyond Navier–Stokes

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Special Reference ◽  
Transport Coefficients ◽  
Navier Stokes ◽  
Intermolecular Potentials ◽  
Long Period ◽  
Generalized Hydrodynamics ◽  
Sharp Turn ◽  
Different Types

The work of Chapman and Enskog opened a long period, lasting about three decades, in which most of the activity in kinetic theory was directed to the computation of the transport coefficients for different types of intermolecular potentials. Seeking the solution of the full Boltzmann equation itself was not much in focus, mostly on account of its daunting complexity. This situation took a sharp turn in 1949, with the publication of Harold Grad’s thesis. This Chapter presents the derivation of generalized hydrodynamics beyond the realm of the Navier-Stokes description, with special reference to Grad’s thirteen-moment formulation.

On the Pressure Dependence of the Transport Properties of Dilute Polyatomic Gases

1969 ◽  
Vol 24 (11) ◽  
pp. 1687-1693 ◽  
Author(s):  
F. R. Mccourt ◽  
H. Moraal
Keyword(s):  
Pressure Dependence ◽  
Internal State ◽  
Transport Coefficients ◽  
Navier Stokes ◽  
Nonequilibrium Distribution ◽  
Polyatomic Gases ◽  
Different Types ◽  
Nonequilibrium Distribution Function ◽  
Dependent Transport ◽  
Function Density

Abstract It is shown that the transport coefficients of dilute polyatomic gases in the ordinary Navier-Stokes regime contain an extra pressure dependence when the internal state Hamiltonian does not commute with the nonequilibrium distribution function-density matrix for the gas. As a specific example, the pressure dependence of the shear viscosity of a gas of paramagnetic 2Σ molecules is considered. Furthermore, the pressure dependence of the Senftleben and Senftleben-Beenakker effects is discussed and examples are given of the different types of molecules for which pressure dependence in the field-free as well as in the field-dependent transport coefficients may be expected.

scholarly journals KINETIC THEORY OF PLASMAS: TRANSLATIONAL ENERGY

2009 ◽  
Vol 19 (04) ◽  
pp. 527-599 ◽  
Author(s):  
BENJAMIN GRAILLE ◽  
THIERRY E. MAGIN ◽  
MARC MASSOT
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Transport Coefficients ◽  
Heavy Particle ◽  
Perturbation Parameter ◽  
Convective System ◽  
Translational Energy ◽  
Electron Mass ◽  
Heavy Particles ◽  
The Boltzmann Equation

In the present study, we derive from kinetic theory a unified fluid model for multicomponent plasmas by accounting for the electromagnetic field influence. We deal with a possible thermal nonequilibrium of the translational energy of the particles, neglecting their internal energy and reactive collisions. Given the strong disparity of mass between the electrons and heavy particles, such as molecules, atoms, and ions, we conduct a dimensional analysis of the Boltzmann equation and introduce a scaling based on a multiscale perturbation parameter equal to the square root of the ratio of the electron mass to a characteristic heavy-particle mass. We then generalize the Chapman–Enskog method, emphasizing the role of the perturbation parameter on the collisional operator, the streaming operator, and the collisional invariants of the Boltzmann equation. The system is examined at successive orders of approximation, each corresponding to a physical timescale. At the highest approximation order investigated, the multicomponent Navier–Stokes regime is reached for the heavy particles and is coupled to first-order drift-diffusion equations for the electrons. The transport coefficients are then calculated in terms of bracket operators whose mathematical structure allows for positivity properties to be determined and Onsager's reciprocal relations to hold. The transport coefficients exhibit an anisotropic behavior when the magnetic field is strong enough. We also give a complete description of the Kolesnikov effect, i.e. the crossed contributions to the mass and energy transport fluxes coupling the electrons and heavy particles. Finally, the first and second laws of thermodynamics are proved to be satisfied by deriving a total energy equation and an entropy equation. Moreover, the purely convective system of equations is shown to be hyperbolic.

Boltzmann’s Kinetic Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Statistical Physics ◽  
Neutron Transport ◽  
Condensed Matter ◽  
Relativistic Fluids ◽  
Classical Statistical Mechanics ◽  
Dilute Gas ◽  
Equilibrium Processes ◽  
The Boltzmann Equation

Kinetic theory is the branch of statistical physics dealing with the dynamics of non-equilibrium processes and their relaxation to thermodynamic equilibrium. Established by Ludwig Boltzmann (1844–1906) in 1872, his eponymous equation stands as its mathematical cornerstone. Originally developed in the framework of dilute gas systems, the Boltzmann equation has spread its wings across many areas of modern statistical physics, including electron transport in semiconductors, neutron transport, quantum-relativistic fluids in condensed matter and even subnuclear plasmas. In this Chapter, a basic introduction to the Boltzmann equation in the context of classical statistical mechanics shall be provided.

Prediction and Analysis of the Bubble Formation in Film Boiling

2004 ◽  
Author(s):  
A. Agrawal ◽  
G. Biswas ◽  
S. W. J. Welch ◽  
F. Durst
Keyword(s):  
Complete Solution ◽  
Bubble Formation ◽  
Transport Coefficients ◽  
Quantitative Information ◽  
Horizontal Surface ◽  
Film Boiling ◽  
Navier Stokes ◽  
Interface Tracking ◽  
Energy Equations ◽  
Interface Mass Transfer

The bubble formation and heat transfer on a horizontal surface have been numerically analyzed using a volume of fluid (VOF) based interface tracking method incorporated into a complete solution of the Navier-Stokes and the thermal energy equations. The numerical method took into account the effects of surface tension, the interface mass transfer and the corresponding latent heat. The computations demonstrated capability of the algorithm in generating quantitative information on unsteady periodic bubble release patterns and on the spatially and temporally varying film thickness. The computations also predict the transport coefficients on the horizontal surface.

Sloshing Response of Floating Roofed Liquid Storage Tanks Subjected to Earthquakes of Different Types

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
F. G. Golzar ◽  
R. Shabani ◽  
S. Tariverdilo ◽  
G. Rezazadeh
Keyword(s):  
Ground Motions ◽  
Far Field ◽  
Storage Tanks ◽  
Natural Period ◽  
Design Spectrum ◽  
Long Period ◽  
Lateral Forces ◽  
Different Types ◽  
Hamiltonian Variational Principle ◽  
Stress Patterns

Using extended Hamiltonian variational principle, the governing equations for sloshing response of floating roofed storage tanks are derived. The response of the floating roofed storage tanks is evaluated for different types of ground motions, including near-source and long-period far-field records. Besides comparing the response of the roofed and unroofed tanks, the effect of different ground motions on the wave elevation, lateral forces, and overturning moments induced on the tank is investigated. It is concluded that the dimensionless sloshing heights for the roofed tanks are solely a function of their first natural period. Also it is shown that while long-period far-field ground motions control the free board height, near-source records give higher values for lateral forces and overturning moments induced on the tank. This means that same design spectrum could not be used to evaluate the free board and lateral forces in the seismic design of storage tanks. Finally, two cases are studied to reveal the stress patterns caused by different earthquakes.

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