Hybrid molecular-continuum simulations using smoothed dissipative particle dynamics

Abstract

We present a new multiscale simulation methodology for coupling a region with atomistic detail simulated via molecular dynamics (MD) to a numerical solution of the fluctuating Navier-Stokes equations obtained from smoothed dissipative particle dynamics (SDPD). In this approach, chemical potential gradients emerge due to differences in resolution within the total system and are reduced by introducing a pairwise thermodynamic force inside the buffer region between the two domains where particles change from MD to SDPD types. When combined with a multi-resolution SDPD approach, such as the one proposed by Kulkarni et al. [J. Chem. Phys. 138, 234105 (2013)], this method makes it possible to systematically couple atomistic models to arbitrarily coarse continuum domains modeled as SDPD fluids with varying resolution. We test this technique by showing that it correctly reproduces thermodynamic properties across the entire simulation domain for a simple Lennard-Jones fluid. Furthermore, we demonstrate that this approach is also suitable for non-equilibrium problems by applying it to simulations of the start up of shear flow. The robustness of the method is illustrated with two different flow scenarios in which shear forces act in directions parallel and perpendicular to the interface separating the continuum and atomistic domains. In both cases, we obtain the correct transient velocity profile. We also perform a triple-scale shear flow simulation where we include two SDPD regions with different resolutions in addition to a MD domain, illustrating the feasibility of a three-scale coupling.

FIG. 1.

Adaptive resolution weighting function versus position in the problem domain (dark black curve). A snapshot of the system is superimposed for clarity. The part of the domain where s(z) = 1 is the MD region, the part where it is zero is the SDPD region, and particles within the remaining “buffer” domains interact through a linear combination of both MD and SDPD forces.

FIG. 2.

Effective time-averaged force-versus-separation between particle pairs as a function of position within the buffer. Curves were obtained from simulations where all the particles in the system interact through either pure MD or SDPD forces, or some linear combination of the two that is constant throughout the simulation domain. The red (solid triangle) and blue (solid circle) curves denote the force between pure MD and SDPD particles, respectively. The green (hollow circle) and orange (hollow triangle) curves indicate the hybrid force at two different points within the buffer region. The results show that hybrid particles with λ between 0 and 1 can experience effective repulsions corresponding to a modified particle size.

FIG. 3.

(a) Temperature profile for a LJ system coupled to a SDPD domain at equilibrium with a pairwise correction force. The profile is approximately flat, with deviations less than 2.0% from the target temperature. (b) Density profiles for the system. The red curve (squares) is the density without corrections, while the blue curve (triangles) is with a pairwise correction. The densities within the MD/SDPD domains are within 3.2% of the target value with this correction. The black curve (circles) is the density profile when the strength of the pairwise thermodynamic force is increased by a factor of 10. For the MD and buffer regions, densities are computed by binning the system and counting particles, while for the SDPD part of the system, we use the SPH calculation for density [Eq. (7)] at randomly sampled points.

FIG. 4.

Snapshots of the system for the (a) perpendicular and (b) parallel flow cases. (c) Velocity profiles for the MD, buffer, and SDPD domains for perpendicular start-up shear flow as compared to the analytical solution. (d) Velocity profiles for the parallel case. The velocities are averaged over 20 independent trajectories for both scenarios.

FIG. 5.

(a) Visualization of the system for the parallel flow, triple-scale simulation. The coarse SDPD particles are twice as massive as the finely resolved ones, with half the number density. (b) Velocity profiles across the channel width for different times when the fluid is sheared. The exact solution is shown in black.