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Coarse-grained hydrodynamics from correlation functions
Phys. Rev. E 97, 022106 – Published 6 February, 2018
DOI: https://doi.org/10.1103/PhysRevE.97.022106
Abstract
This paper will describe a formalism for using correlation functions between different grid cells as the basis for determining coarse-grained hydrodynamic equations for modeling the behavior of mesoscopic fluid systems. Configurations from a molecular dynamics simulation or other atomistic simulation are projected onto basis functions representing grid cells in a continuum hydrodynamic simulation. Equilibrium correlation functions between different grid cells are evaluated from the molecular simulation and used to determine the evolution operator for the coarse-grained hydrodynamic system. The formalism is demonstrated on a discrete particle simulation of diffusion with a spatially dependent diffusion coefficient. Correlation functions are calculated from the particle simulation and the spatially varying diffusion coefficient is recovered using a fitting procedure.
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References (24)
- D. Kim and E. Darve, Molecular dynamics simulation of electro-osmotic flows in rough wall nanochannels, Phys. Rev. E 73, 051203 (2006).
- Y. Li, J. Xu, and D. Li, Molecular dynamics simulation of nanoscale liquid flows, Microfluid. Nanofluid. 9, 1011 (2010).
- A. Prakash, J. Pfaendtner, J. Chun, and C. Mundy, Quantifying the molecular-scale aqueous response to the mica surface, J. Phys. Chem. C 121, 18496 (2017).
- B. Palmer, Direct simulation of hydrodynamic relaxation in microchannels, J. Chem. Phys. 109, 196 (1998).
- M. S. Green, Markoff random processes and the statistical mechanics of time-dependent phenomena, J. Chem. Phys. 20, 1281 (1952).
- M. S. Green, Markoff random processes and the statistical mechanics of time-dependent phenomena. II. Irreversible processes in fluids, J. Chem. Phys. 22, 398 (1954).
- D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions (The Benjamin/Cummings Publishing Company, Inc., Reading, MA, 1975).
- C. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer-Verlag, New York, 1985).
- S. Isvekov and G. Voth, Multiscale coarse graining of liquid-state systems, J. Chem. Phys. 123, 134105 (2005).
- W. Noid, J.-W. Chu, G. Ayton, V. Krishna, S. Isvekov, G. Voth, A. Das, and H. Andersen, The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models, J. Chem. Phys. 128, 244114 (2008).
- P. Español and P. Warren, Statistical mechanics of dissipative particle dynamics, Europhys. Lett. 30, 191 (1995).
- J. Monaghan, Smoothed particle hydrodynamics, Rep. Prog. Phys. 68, 1703 (2005).
- R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems, J. Phys. Soc. Jpn. 12, 570 (1957).
- R. Zwanzig, Time-correlation functions and transport coefficients in statistical mechanics, Annu. Rev. Phys. Chem. 16, 67 (1965).
- J.-P. Boon and S. Yip, Molecular hydrodynamics (Dover, New York, 1980).
- C. Hoheisel and R. Vogelsang, Thermal transport coefficients for one- and two-component liquids for time correlation functions computed by molecular dynamics, Comput. Phys. Rep. 8, 1 (1988).
- B. Palmer, Transverse-current autocorrelation-function calculations of the shear viscosity for molecular liquids, Phys. Rev. E 49, 359 (1994).
- B. Palmer, Calculation of thermal-diffusion coefficients from plane-wave fluctuations in the heat-energy density, Phys. Rev. E 49, 2049 (1994).
- B. Hess, Determining the shear viscosity of model liquids from molecular dynamics simulations, J. Chem. Phys. 116, 209 (2002).
- B. Shang, N. Voulgarakis, and J.-W. Chu, Fluctuating hydrodynamics for multiscale modeling and simulation: Energy and heat transfer in molecular fluids, J. Chem. Phys. 137, 044117 (2012).
- P. Español and I. Zúñiga, On the definition of discrete hydrodynamic variables, J. Chem. Phys. 131, 164106 (2009).
- P. Español, J. Anero, and I. Zúñiga, Microscopic derivation of discrete hydrodynamics, J. Chem. Phys. 131, 244117 (2009).
- P. Español and A. Donev, Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics, J. Chem. Phys. 143, 234104 (2015).
- M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).
