Nonreflecting boundaries for ultrasound in fluctuating hydrodynamics of open systems.

We present a formulation for nonreflecting boundaries in fluctuating hydrodynamics. Nonreflecting boundary conditions are designed to evacuate sound waves out of the computational domain, thus allowing one to deal with open systems and to avoid finite size effects associated with periodic boundaries. Thermodynamic consistency for the fluctuation of the total mass and momentum of the open system is ensured by a fluctuation-dissipation balance which controls the amplitude of the sound waves generated by stress fluctuations near the boundary. We consider equilibrium and out-of-equilibrium situations (forced sound) in liquid water at ambient conditions and argon ranging from gas to liquid densities. Nonreflecting boundaries for fluctuating hydrodynamics make feasible simulations of ultrasound in microfluidic devices.

[1]  Franck Nicoud,et al.  Actual impedance of nonreflecting Boundary conditions: Implications for computation of resonators , 2004 .

[2]  J. Oliger,et al.  Theoretical and practical aspects of some initial-boundary value problems in fluid dynamics , 1976 .

[3]  Tim Colonius,et al.  MODELING ARTIFICIAL BOUNDARY CONDITIONS FOR COMPRESSIBLE FLOW , 2004 .

[4]  R. Koch,et al.  Compressible large eddy simulation of turbulent combustion in complex geometry on unstructured meshes , 2004 .

[5]  John B Bell,et al.  Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  R. Delgado‐Buscalioni,et al.  Cyclic motion of a grafted polymer under shear flow. , 2006, Physical review letters.

[7]  G De Fabritiis,et al.  Towards multi-scale modelling of complex liquids using hybrid particle—continuum schemes , 2008 .

[8]  G. W. Hedstrom,et al.  Nonreflecting Boundary Conditions for Nonlinear Hyperbolic Systems , 1979 .

[9]  John B. Bell,et al.  Algorithm Refinement for Fluctuating Hydrodynamics , 2008, Multiscale Model. Simul..

[10]  P Español,et al.  Thermodynamically consistent mesoscopic fluid particle model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Parviz Moin,et al.  Partially reflecting and non-reflecting boundary conditions for simulation of compressible viscous flow , 2006, J. Comput. Phys..

[12]  Jurg Dual,et al.  Contactless micromanipulation of small particles by an ultrasound field excited by a vibrating body. , 2005, The Journal of the Acoustical Society of America.

[13]  G De Fabritiis,et al.  Embedding molecular dynamics within fluctuating hydrodynamics in multiscale simulations of liquids. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  P. Coveney,et al.  Fluctuating hydrodynamic modeling of fluids at the nanoscale. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  G De Fabritiis,et al.  Multiscale modeling of liquids with molecular specificity. , 2006, Physical review letters.

[16]  P. Coveney,et al.  Hybrid method coupling fluctuating hydrodynamics and molecular dynamics for the simulation of macromolecules. , 2007, The Journal of chemical physics.

[17]  A. Ladd,et al.  Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries. , 2005, The Journal of chemical physics.

[18]  Aleksandar Donev,et al.  Stochastic Event-Driven Molecular Dynamics , 2008, J. Comput. Phys..

[19]  D. M. Campbell,et al.  Numerical simulation of particle motion in an ultrasound field using the lattice Boltzmann model. , 2004, Ultrasonics.

[20]  F. García-Vidal,et al.  Collimation of sound assisted by acoustic surface waves , 2007 .

[21]  John A. Zollweg,et al.  The Lennard-Jones equation of state revisited , 1993 .

[22]  T. Poinsot.  Boundary conditions for direct simulations of compressible viscous flows , 1992 .

[23]  D. Heyes.  Simple expressions for the self-diffusion coefficient, shear viscosity and thermal conductivity of Lennard-Jones fluids , 1988 .

[24]  Alejandro L. Garcia,et al.  Numerical integration of the fluctuating hydrodynamic equations , 1987 .

[25]  M. Cates,et al.  Fluctuating lattice Boltzmann , 2004, cond-mat/0402598.

[26]  F. Schlögl,et al.  J. Keizer: “Statistical Thermodynamics of Nonequilibrium Processes”, Springer‐Verlag, New York, Berlin, Heidelberg, London, Paris, Tokyo 1987. 506 Seiten, Preis: DM 128,–. , 1989 .

[27]  David H. Rudy,et al.  A nonreflecting outflow boundary condition for subsonic navier-stokes calculations , 1980 .