Digital Commons Network^™

Inferring The Global Cosmic Dust Influx To The Earth’S Atmosphere From Lidar Observations Of The Vertical Flux Of Mesospheric Na, Chester S. Gardner, Alan Z. Liu, Dan Marsh, Wuhu Feng, John Plane

Alan Z Liu

Low Mach Number Fluctuating Hydrodynamics Of Diffusively Mixing Fluids, Aleksandar Donev, Andy J. Nonaka, Yifei Sun, Thomas Fai, Alejandro Garcia, John B. Bell

Alejandro Garcia

We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fast isentropic fluctuations in pressure associated with the propagation of sound waves by replacing the equation of state with a local thermodynamic constraint. We demonstrate that the low Mach number model preserves the spatio-temporal spectrum of the slower diffusive fluctuations. We develop a strictly conservative finite-volume spatial discretization of the low Mach number fluctuating equations in both two and three dimensions. We construct several explicit Runge-Kutta temporal integrators that strictly maintain the …

Diffusive Transport Enhanced By Thermal Velocity Fluctuations, Alejandro Garcia, A. Donev, A. De La Fuente, J. B. Bell

Faculty Publications

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. We find good agreement between a simple fluctuating hydrodynamics theory and particle and finite-volume simulations. The enhancement of the diffusive transport depends on the system size L and grows as ln⁡(L/L0) in quasi-two-dimensional systems, while in three dimensions it scales as L0-1-L-1, where L0 is a reference length. Our results demonstrate that fluctuations play an important role in the hydrodynamics of small-scale systems.

Diffusive Transport Enhanced By Thermal Velocity Fluctuations, Alejandro Garcia, Aleksandar Donev, Anton De La Fuente, John B. Bell

Alejandro Garcia

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. We find good agreement between a simple fluctuating hydrodynamics theory and particle and finite-volume simulations. The enhancement of the diffusive transport depends on the system size L and grows as ln⁡(L/L0) in quasi-two-dimensional systems, while in three dimensions it scales as L0-1-L-1, where L0 is a reference length. Our results demonstrate that fluctuations play an important role in the hydrodynamics of small-scale systems.

A Hybrid Particle-Continuum Method For Hydrodynamics Of Complex Fluids, Alejandro Garcia, A. Donev, J. B. Bell, B. Alder

Faculty Publications

A previously developed hybrid particle-continuum method [J. B. Bell, A. Garcia, and S. A. Williams, Multiscale Model. Simul., 6 (2008), pp. 1256–1280] is generalized to dense fluids and two- and three-dimensional flows. The scheme couples an explicit fluctuating compressible Navier–Stokes solver with the isotropic direct simulation Monte Carlo (DSMC) particle method [A. Donev, A. L. Garcia, and B. J. Alder, J. Stat. Mech. Theory Exp., 2009 (2009), article P11008]. To achieve bidirectional dynamic coupling between the particle (microscale) and continuum (macroscale) regions, the continuum solver provides state-based boundary conditions to the particle subdomain, while the particle solver provides flux-based boundary …

Computational Fluctuating Fluid Dynamics, Alejandro Garcia, J. B. Bell, S. Williams

Faculty Publications

This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret effect). We present various numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate good agreement with theoretical results and molecular simulation

Computational Fluctuating Fluid Dynamics, Alejandro Garcia, John B. Bell, Sarah Williams

Alejandro Garcia

This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret effect). We present various numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate good agreement with theoretical results and molecular simulation

On The Accuracy Of Explicit Finite-Volume Schemes For Fluctuating Hydrodynamics, Aleksandar Donev, Eric Vanden-Eijnden, Alejandro Garcia, John B. Bell

Alejandro Garcia

This paper describes the development and analysis of finite-volume methods for the Landau–Lifshitz Navier–Stokes (LLNS) equations and related stochastic partial differential equations in fluid dynamics. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by the addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation relation. Originally derived for equilibrium fluctuations, the LLNS equations have also been shown to be accurate for nonequilibrium systems. Previous studies of numerical methods for the LLNS equations focused primarily on measuring variances and correlations computed at equilibrium and for selected nonequilibrium flows. In this paper, we introduce a more systematic approach …

A Hybrid Particle-Continuum Method For Hydrodynamics Of Complex Fluids, Alejandro Garcia, Aleksandar Donev, John B. Bell, Berni Alder

Alejandro Garcia

A previously developed hybrid particle-continuum method [J. B. Bell, A. Garcia, and S. A. Williams, Multiscale Model. Simul., 6 (2008), pp. 1256–1280] is generalized to dense fluids and two- and three-dimensional flows. The scheme couples an explicit fluctuating compressible Navier–Stokes solver with the isotropic direct simulation Monte Carlo (DSMC) particle method [A. Donev, A. L. Garcia, and B. J. Alder, J. Stat. Mech. Theory Exp., 2009 (2009), article P11008]. To achieve bidirectional dynamic coupling between the particle (microscale) and continuum (macroscale) regions, the continuum solver provides state-based boundary conditions to the particle subdomain, while the particle solver provides flux-based boundary …

Stochastic Hard-Sphere Dynamics For Hydrodynamics Of Non-Ideal Fluids, Alejandro Garcia, A. Donev, B. J. Alder

Faculty Publications

A novel stochastic fluid model is proposed with a nonideal 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 algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a 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 nanoparticle suspended in a compressible solvent.

Stochastic Hard-Sphere Dynamics For Hydrodynamics Of Non-Ideal Fluids, Alejandro Garcia, Aleksandar Donev, Berni J. Alder

Alejandro Garcia

A novel stochastic fluid model is proposed with a nonideal 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 algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a 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 nanoparticle suspended in a compressible solvent.

Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, S. Williams, J. B. Bell

Faculty Publications

This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau–Lifshitz Navier–Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently developed solver for the LLNS equations based on third-order Runge–Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the …

Numerical Methods For The Stochastic Landau-Lifshitz Navier-Stokes Equations, Alejandro Garcia, J. B. Bell, S. Williams

Faculty Publications

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack’s two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk …

Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, Sarah Williams, John B. Bell

Alejandro Garcia

This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau–Lifshitz Navier–Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently developed solver for the LLNS equations based on third-order Runge–Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the …

Numerical Methods For The Stochastic Landau-Lifshitz Navier-Stokes Equations, Alejandro Garcia, John B. Bell, Sarah Williams

Alejandro Garcia

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack’s two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk …

Hydrodynamic Description Of The Adiabatic Piston, Alejandro Garcia, M. M. Mansour

Faculty Publications

A closed macroscopic equation for the motion of the two-dimensional adiabatic piston is derived from standard hydrodynamics. It predicts a damped oscillatory motion of the piston towards a final rest position, which depends on the initial state. In the limit of large piston mass, the solution of this equation is in quantitative agreement with the results obtained from both hard disk molecular dynamics and hydrodynamics. The explicit forms of the basic characteristics of the piston’s dynamics, such as the period of oscillations and the relaxation time, are derived. The limitations of the theory’s validity, in terms of the main system …

Estimating Hydrodynamic Quantities In The Presence Of Microscopic Fluctuations, Alejandro Garcia

Faculty Publications

This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical …

Estimating Hydrodynamic Quantities In The Presence Of Microscopic Fluctuations, Alejandro Garcia

Alejandro Garcia

This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical …

Hydrodynamic Description Of The Adiabatic Piston, Alejandro Garcia, Malek M. Mansour

Alejandro Garcia

A closed macroscopic equation for the motion of the two-dimensional adiabatic piston is derived from standard hydrodynamics. It predicts a damped oscillatory motion of the piston towards a final rest position, which depends on the initial state. In the limit of large piston mass, the solution of this equation is in quantitative agreement with the results obtained from both hard disk molecular dynamics and hydrodynamics. The explicit forms of the basic characteristics of the piston’s dynamics, such as the period of oscillations and the relaxation time, are derived. The limitations of the theory’s validity, in terms of the main system …

Rectification Of Thermal Fluctuations In Ideal Gases, Alejandro Garcia, P. Meurs, C. Van De Broeck

Faculty Publications

We calculate the systematic average speed of the adiabatic piston and a thermal Brownian motor, introduced by C. Van den Broeck, R. Kawai and P. Meurs [Phys. Rev. Lett. 93, 090601 (2004)], by an expansion of the Boltzmann equation and compare with the exact numerical solution.

Rectification Of Thermal Fluctuations In Ideal Gases, Alejandro Garcia, P. Meurs, C. Van De Broeck

Alejandro Garcia

We calculate the systematic average speed of the adiabatic piston and a thermal Brownian motor, introduced by C. Van den Broeck, R. Kawai and P. Meurs [Phys. Rev. Lett. 93, 090601 (2004)], by an expansion of the Boltzmann equation and compare with the exact numerical solution.

Inverted Velocity Profile In The Cylindrical Couette Flow Of A Rarefied Gas, Alejandro Garcia, K. Aoki, H. Yoshida, T. Nakanishi

Faculty Publications

The cylindrical Couette flow of a rarefied gas is investigated, under the diffuse-specular reflection condition of Maxwell’s type on the cylinders, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest. The inverted velocity profile for small accommodation coefficients, pointed out by Tibbs, Baras, and Garcia [Phys. Rev. E 56, 2282 (1997)] on the basis of a Monte Carlo simulation, is investigated extensively by means of a systematic asymptotic analysis for small Knudsen numbers as well as the direct numerical analysis of the Boltzmann equation, and the parameter range in which the phenomenon appears …

A Direct Simulation Monte Carlo Method For The Uehling-Uhlenbeck-Boltzmann Equation, Alejandro Garcia, W. Wagner

Faculty Publications

In this paper we describe a direct simulation Monte Carlo 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.

A Direct Simulation Monte Carlo Method For The Uehling-Uhlenbeck-Boltzmann Equation, Alejandro Garcia, Wolfgang Wagner

Alejandro Garcia

In this paper we describe a direct simulation Monte Carlo 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.

Inverted Velocity Profile In The Cylindrical Couette Flow Of A Rarefied Gas, Alejandro Garcia, K. Aoki, H. Yoshida, T. Nakanishi

Alejandro Garcia

The cylindrical Couette flow of a rarefied gas is investigated, under the diffuse-specular reflection condition of Maxwell’s type on the cylinders, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest. The inverted velocity profile for small accommodation coefficients, pointed out by Tibbs, Baras, and Garcia [Phys. Rev. E 56, 2282 (1997)] on the basis of a Monte Carlo simulation, is investigated extensively by means of a systematic asymptotic analysis for small Knudsen numbers as well as the direct numerical analysis of the Boltzmann equation, and the parameter range in which the phenomenon appears …

Comment On ‘‘Stress-Density Ratio Slip-Corrected Reynolds Equation For Ultra-Thin Film Gas Bearing Lubrication’’, Alejandro Garcia

Alejandro Garcia

No abstract provided.

Comment On ‘‘Stress-Density Ratio Slip-Corrected Reynolds Equation For Ultra-Thin Film Gas Bearing Lubrication’’, Alejandro Garcia

Faculty Publications

No abstract provided.

Molecular Simulations Of Sound Wave Propagation In Simple Gases, Alejandro Garcia, N. Hadjiconstantinou

Alejandro Garcia

Molecular simulations of sound waves propagating in a dilute hard sphere gas have been performed using the direct simulation Monte Carlo method. A wide range of frequencies is investigated, including very high frequencies for which the period is much shorter than the mean collision time. The simulation results are compared to experimental data and approximate solutions of the Boltzmann equation. It is shown that free molecular flow is important at distances smaller than one mean free path from the excitation point.

Molecular Simulations Of Sound Wave Propagation In Simple Gases, Alejandro Garcia, N. Hadjiconstantinou

Faculty Publications

Molecular simulations of sound waves propagating in a dilute hard sphere gas have been performed using the direct simulation Monte Carlo method. A wide range of frequencies is investigated, including very high frequencies for which the period is much shorter than the mean collision time. The simulation results are compared to experimental data and approximate solutions of the Boltzmann equation. It is shown that free molecular flow is important at distances smaller than one mean free path from the excitation point.

Erratum: "Cell Size Dependence Of Transport Coefficients In Stochastic Particle Algorithms", Alejandro Garcia, F. Alexander, B. Alder

Faculty Publications

No abstract provided.