Estimating hydrodynamic quantities in the presence of microscopic fluctuations

Garcia, Alejandro L.

doi:10.2140/camcos.2006.1.53

Cited by 15 publications

(12 citation statements)

References 19 publications

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“…We also define the mesoscopic velocity and concentrations to be the ensemble averages of the instantaneous values, where the subscript zero will be used to simplify the cumbersome notation. It is important to point out that for non-conserved quantities such as v and c the mesoscopic mean can be different from the macroscopic mean due to fluctuations [42,43],v 1 = v (1) 0 andc = c 0 . For conserved quantities (e.g.,j 1 and j (1) 0 ), however, the mesoscopic and macroscopic ensemble means are equal and in fact independent of ∆x and ∆z (but not necessarily ∆y).…”

Section: B Fluctuation-enhanced Diffusion Coefficientmentioning

confidence: 99%

Enhancement of diffusive transport by non-equilibrium thermal fluctuations

Donev¹,

Bell²,

Fuente³

et al. 2011

J. Stat. Mech.

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We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is enhanced because of long-range correlations between concentration fluctuations and fluctuations of the velocity parallel to the concentration gradient. The enhancement of the diffusive transport depends on the system size L and grows as ln(L/L 0 ) in quasi-two dimensional systems, while in three dimensions it grows as L −1 0 − L −1 , where L 0 is a reference length. The predictions of a simple fluctuating hydrodynamics theory, closely related to second-order mode-mode coupling analysis, are compared to results from particle simulations and a finite-volume solver and excellent agreement is observed. We elucidate the direct connection to the long-time tail of the velocity autocorrelation function in finite systems, as well as finite-size corrections employed in molecular dynamics calculations. Our results conclusively demonstrate that the nonlinear advective terms need to be retained in the equations of fluctuating hydrodynamics when modeling transport in small-scale finite systems.

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Section: B Fluctuation-enhanced Diffusion Coefficientmentioning

confidence: 99%

Enhancement of diffusive transport by non-equilibrium thermal fluctuations

Donev¹,

Bell²,

Fuente³

et al. 2011

J. Stat. Mech.

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“…3 and 5;the statistics for z-momentum are similar to those for y-momentum, and are omitted here. We only consider these conserved mechanical variables because the continuum scheme is based on them, they are easily measured in molecular simulations, and hydrodynamic variables, such as pressure and temperature, are directly obtained from these mechanical variables [36]. Figure 3: Mean, variance, and center point correlation of x-momentum versus spatial location for a system at equilibrium.…”

Section: Equilibrium System: State Variablesmentioning

confidence: 99%

“…(This variance can be found using the ideal gas law and expressions derived in [36].) Note that using a wide stencil limits the variation even when N c is small (and, consequently, fluctuations are large).We select cells j for refinement where D(P ) j exceeds the equilibrium value, namely zero, by three standard deviations.…”

Section: Adaptive Refinementmentioning

confidence: 99%

Algorithm Refinement for Fluctuating Hydrodynamics

Williams¹,

Bell²,

Garcia³

2008

Multiscale Model. Simul.

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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 al-1 gorithm 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 LLNS, based on third-order Runge-Kutta. We present numerical tests of systems in and out of equilibrium, including timedependent systems, and demonstrate dynamic adaptive refinement by the computation of a moving shock wave. Mean system behavior and second moment statistics of our simulations match theoretical values and benchmarks well. We find that particular attention should be paid to the spectrum of the flux at the interface between the particle and continuum methods, specifically for the non-hydrodynamic (kinetic) time scales.

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“…Hence, we have used the instantaneous temperature when computing the reaction rates. All final (output) results were obtained by combining those from multiple independent DSMC simulations using the appropriate summation techniques as discussed by Garcia [10].…”

Section: Discussionmentioning

confidence: 99%

Simulation of unsteady flows by the DSMC macroscopic chemistry method

Goldsworthy¹,

Macrossan²,

Abdel–jawad³

2009

Journal of Computational Physics

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In the Direct Simulation Monte Carlo (DSMC) method, a combination of statistical and deterministic procedures applied to a finite number of 'simulator' particles are used to model rarefied gas-kinetic processes. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reactions are decoupled from the specific particle pairs selected for collisions. Information from all of the particles within a cell, not just those selected for collisions, is used to determine a reaction rate coefficient for that cell. Unlike particle-based methods, MCM can be used with any viscosity or nonreacting collision models and any non-reacting energy exchange models. It can be used to implement any reaction rate formulations, whether these be from experimental or theoretical studies. MCM has been previously validated for steady flow DSMC simulations. Here we show how MCM can be used to model chemical kinetics in DSMC simulations of unsteady flow. Results are compared with a collision-based chemistry procedure for two binary reactions in a 1-D unsteady shock-expansion tube simulation. Close agreement is demonstrated between the two methods for instantaneous, ensemble-averaged profiles of temperature, density and species mole fractions, as well as for the accumulated number of net reactions per cell.

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Estimating hydrodynamic quantities in the presence of microscopic fluctuations

Cited by 15 publications

References 19 publications

Enhancement of diffusive transport by non-equilibrium thermal fluctuations

Enhancement of diffusive transport by non-equilibrium thermal fluctuations

Algorithm Refinement for Fluctuating Hydrodynamics

Simulation of unsteady flows by the DSMC macroscopic chemistry method

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