Stochastic Hard-Sphere Dynamics for Hydrodynamics of Non-Ideal Fluids

A novel stochastic fluid model is proposed with non-ideal structure factor consistent with compressibility, and adjustable transport coefficients. This Stochastic Hard Sphere Dynamics (SHSD) algorithm is a modification of the Direct Simulation Monte Carlo (DSMC) algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nano-particle suspended in a compressible solvent.Comment: This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-JRNL-401745). To appear in Phys. Rev. Lett. 200

Fluctuating hydrodynamics of multi-species, non-reactive mixtures

In this paper we discuss the formulation of the fuctuating Navier-Stokes (FNS) equations for multi-species, non-reactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of non-equilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well as reverse diffusion in a ternary mixture. Good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multi-species fluids. The extension to include chemical reactions will be treated in a sequel paper

A new kinetic equation for dense gases

This paper establishes a theoretical foundation for the Consistent Boltzmann Algorithm by deriving the limiting kinetic equation. Besides its relation to the algorithm, this new equation serves as a useful alternative to the Enskog equation in the kinetic theory of dense gases. For a simplified model, the limiting equation is solved numerically, and very good agreement with the predictions of the theory is found

Time step truncation error in direct simulation Monte Carlo

The time step truncation error in direct simulation Monte Carlo calculations is found to be O(Δt2) for a variety of simple flows, both transient and steady state. The measured errors in the transport coefficients (viscosity, thermal conductivity, and self-diffusion) are in good agreement with predictions from Green-Kubo analysis (N. Hadjiconstantinou, Phys. Fluids, submitted 1999)

Generation of the Maxwellian inflow distribution

This paper presents several efficient, exact methods for generating the Maxwellian inflow distribution, the velocity distribution of gas molecules crossing a plane. The new methods are demonstrated to be computationally faster and more accurate than the schemes commonly used for open boundary conditions in particle simulations

Some new properties of the kinetic equation for the consistent Boltzmann algorithm

We study properties of the consistent Boltzmann algorithm for dense gases, using its limiting kinetic equation. First we derive an H-theorem for this equation. Then, following the classical derivation by Chapman and Cowling, we find approximations to the equations of continuity, momentum and energy. The first order correction terms with respect to the particle diameter turn out to be the same as for the Enskog equation. These results confirm previous derivations, based on the virial, of the corresponding equation of state

A direct simulation Monte Carlo method for the Uehling-Uhlenbeck-Boltzmann equation

In this paper we describe a DSMC algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady state distribution