## UC Berkeley / Lawrence Berkeley Laboratory

#### 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.

#### References

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