A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas

We investigate sound wave propagation in a monatomic gas using a volume-based hydrodynamic model. In Physica A vol 387(24) (2008) pp6079-6094, a microscopic volume-based kinetic approach was proposed by analyzing molecular spatial distributions; this led to a set of hydrodynamic equations incorporating a mass-density diffusion component. Here we find that these new mass-density diffusive flux and volume terms mean that our hydrodynamic model, uniquely, reproduces sound wave phase speed and damping measurements with excellent agreement over the full range of Knudsen number. In the high Knudsen number (high frequency) regime, our volume-based model predictions agree with the plane standing waves observed in the experiments, which existing kinetic and continuum models have great difficulty in capturing. In that regime, our results indicate that the "sound waves" presumed in the experiments may be better thought of as "mass-density waves", rather than the pressure waves of the continuum regime.Comment: Revised to aid clarification (no changes to presented model); typos corrected, figures added, paper title change

A continuum model of gas flows with localized density variations

We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows

A fully relativistic lattice Boltzmann algorithm

Starting from the Maxwell-Juettner equilibrium distribution, we develop a relativistic lattice Boltzmann (LB) algorithm capable of handling ultrarelativistic systems with flat, but expanding, spacetimes. The algorithm is validated through simulations of quark-gluon plasma, yielding excellent agreement with hydrodynamic simulations. The present scheme opens the possibility of transferring the recognized computational advantages of lattice kinetic theory to the context of both weakly and ultra-relativistic systems.Comment: 12 pages, 8 figure

Lattice Boltzmann scheme for relativistic fluids

A Lattice Boltzmann formulation for relativistic fluids is presented and numerically verified through quantitative comparison with recent hydrodynamic simulations of relativistic shock-wave propagation in viscous quark-gluon plasmas. This formulation opens up the possibility of exporting the main advantages of Lattice Boltzmann methods to the relativistic context, which seems particularly useful for the simulation of relativistic fluids in complicated geometries.Comment: Submitted to PR

Quantum Kinetic Evolution of Marginal Observables

We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution of marginal observables and the evolution of quantum states described in terms of a one-particle marginal density operator are established. Such approach gives the alternative description of the kinetic evolution of quantum many-particle systems to generally accepted approach on basis of kinetic equations.Comment: 18 page

Continuum description of finite-size particles advected by external flows. The effect of collisions

The equation of the density field of an assembly of macroscopic particles advected by a hydrodynamic flow is derived from the microscopic description of the system. This equation allows to recognize the role and the relative importance of the different microscopic processes implicit in the model: the driving of the external flow, the inertia of the particles, and the collisions among them. The validity of the density description is confirmed by comparisons of numerical studies of the continuum equation with Direct Simulation Monte Carlo (DSMC) simulations of hard disks advected by a chaotic flow. We show that the collisions have two competing roles: a dispersing-like effect and a clustering effect (even for elastic collisions). An unexpected feature is also observed in the system: the presence of collisions can reverse the effect of inertia, so that grains with lower inertia are more clusterized.Comment: Final (strongly modified) version accepted in PRE; 6 pages, 3 figure

Derivation of the Lattice Boltzmann Model for Relativistic Hydrodynamics

A detailed derivation of the Lattice Boltzmann (LB) scheme for relativistic fluids recently proposed in Ref. [1], is presented. The method is numerically validated and applied to the case of two quite different relativistic fluid dynamic problems, namely shock-wave propagation in quark-gluon plasmas and the impact of a supernova blast-wave on massive interstellar clouds. Close to second order convergence with the grid resolution, as well as linear dependence of computational time on the number of grid points and time-steps, are reported

Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains

The formation and propagation of singularities for Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. Consider the nonlinear Boltzmann solution near Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We demonstrate that discontinuity is created at the non-convex part of the grazing boundary, then propagates only along the forward characteristics inside the domain before it hits on the boundary again.Comment: 39 pages, 5 Figure