Hybrid Particle–Continuum Method for Hydrodynamics of Complex Fluids

Aleksandar Donev, Lawrence Berkeley Laboratory
February 4th, 2010 at 2PM–3PM in 740 Evans Hall [Map]

We generalize a previously-developed hybrid particle–continuum method [1] 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 [2]. To achieve bidirectional dynamic coupling between the particle (microscale) and continuum (macroscale) regions, the continuum solver provides state-based boundary conditions to the particle domain, while the particle domain provides flux-based boundary conditions for the continuum solver, thus ensuring both state and flux continuity across the particle–continuum interface. A small mismatch is observed between the mean density and temperature in the particle and continuum regions that comes from the finite size of the hydrodynamic cells used to estimate mean hydrodynamic values. By calculating the dynamic structure factor for both a 'bulk' (periodic) and a finite system, we verify that the hybrid algorithm is capable of accurately capturing the propagation of spontaneous thermal fluctuations across the particle–continuum interface. We then study the equilibrium diffusive motion of a large spherical bead suspended in a particle solvent and find that the hybrid method correctly reproduces the velocity autocorrelation function of the bead only if thermal fluctuations are included in the continuum solver. Finally, we apply the hybrid to the well-known adiabatic piston problem and find that the hybrid correctly reproduces the slow non-equilibrium relaxation of the piston toward thermodynamic equilibrium when fluctuations are included in the continuum solver. These examples clearly demonstrate the need to include fluctuations in continuum solvers employed in hybrid multiscale methods.


  1. J. B. Bell, A. Garcia and S. A. Williams, SIAM Multiscale Modeling and Simulation, 6:1256–1280, 2008.
  2. A. Donev and A. L. Garcia and B. J. Alder, ArXiv preprint 0908.0510.