A Hybrid Particle-Continuum Method for Hydrodynamics of Complex Fluids

Abstract

Abstract. A previously developed hybrid particle-continuum method [J. B. Bell, A. Garcia, and S. A. Williams, Multiscale Model. Simul., 6 (2008), pp. 1256-1280] is generalized to dense fluids and two-and three-dimensional flows. The scheme couples an explicit fluctuating compressible NavierStokes solver with the isotropic direct simulation Monte Carlo (DSMC) particle method B. J. Alder, J. Stat. Mech. Theory Exp., 2009 (2009), article P11008]. To achieve bidirectional dynamic coupling between the particle (microscale) and continuum (macroscale) regions, the continuum solver provides state-based boundary conditions to the particle subdomain, while the particle solver provides flux-based boundary conditions for the continuum subdomain. This type of coupling ensures both state and flux continuity across the particle-continuum interface analogous to coupling approaches for deterministic parabolic partial differential equations; here, when fluctuations are included, a small (< 1%) mismatch is expected and observed in the mean density and temperature across the interface. By calculating the dynamic structure factor for both a "bulk" (periodic) and a finite system, it is verified that the hybrid algorithm accurately captures the propagation of spontaneous thermal fluctuations across the particle-continuum interface. The equilibrium diffusive (Brownian) motion of a large spherical bead suspended in a particle fluid is examined, demonstrating that the hybrid method correctly reproduces the velocity autocorrelation function of the bead but only if thermal fluctuations are included in the continuum solver. Finally, the hybrid is applied to the well-known adiabatic piston problem, and it is found that the hybrid correctly reproduces the slow nonequilibrium relaxation of the piston toward thermodynamic equilibrium but, again, only if the continuum solver includes stochastic (white-noise) flux terms. These examples clearly demonstrate the need to include fluctuations in continuum solvers employed in hybrid multiscale methods.

Simulation of Osmotic Swelling by the Stochastic Immersed Boundary Method

“…Later, this approach was substantially developed and extended by many authors [13,14,15,16,20,21,48,49]. Computational methods for fluctuating hydrodynamics were developed in [22,30,45,44,46,47,50].…”

Coupled Mesoscopic and Microscopic Simulation of Stochastic Reaction-Diffusion Processes in Mixed Dimensions

“…with initial condition p z (z, t n |r n , t n ) = δ(z − z n ) and boundary condition (15). The analytical solution is derived in [10, p. 358].…”

“…Then the no-slip condition at solid surfaces is no longer valid. Another example is when the geometry in nanoscale and microscale devices has to be resolved at a molecular level [15,26,36]. Methods to couple a particle model and discretizations of a continuum model on a mesh are reviewed in [36].…”

“…Methods to couple a particle model and discretizations of a continuum model on a mesh are reviewed in [36]. The computational domain is split into subdomains with either a particle model or a continuum model [13,15]. The difficulty is to handle the interaction at the interface between the subdomains.…”

Adaptive resolution simulation of an atomistic protein in MARTINI water

“…3 Many of the multiscale approaches are concerned with interfacing of atomistic and the continuum models of liquids. [4][5][6][7][8][9][10][11] In these hybrid methods, typically molecular dynamics (MD) or a similar approach is used for simulating dynamics on the atomistic scale, whereas the Navier-Stokes equation governs the fluid dynamics on the continuum scale. Alternatively, multiscale schemes have been introduced usa) s.j.marrink@rug.nl b) praprot@cmm.ki.si ing particle-based models only, e.g., atomistic and physically simplified coarse-grained (CG) molecular models.…”