Concurrent multiscale modelling of atomistic and hydrodynamic processes in liquids

Abstract

Fluctuations of liquids at the scales where the hydrodynamic and atomistic descriptions overlap are considered. The importance of these fluctuations for atomistic motions is discussed and examples of their accurate modelling with a multi-space-time-scale fluctuating hydrodynamics scheme are provided. To resolve microscopic details of liquid systems, including biomolecular solutions, together with macroscopic fluctuations in space-time, a novel hybrid atomistic-fluctuating hydrodynamics approach is introduced. For a smooth transition between the atomistic and continuum representations, an analogy with two-phase hydrodynamics is used that leads to a strict preservation of macroscopic mass and momentum conservation laws. Examples of numerical implementation of the new hybrid approach for the multiscale simulation of liquid argon in equilibrium conditions are provided.

Keywords: Landau–Lifshitz fluctuating hydrodynamics equations; hybrid atomistic–continuum methods; hydrodynamic analogy; molecular dynamics; multiscale modelling; nanofluidics.

Figure 1.

Simulation results with fluctuating hydrodynamics, comparison with the theory. CS2 corresponds to the small-scale part of the domain and CS1 corresponds to large scales. (Online version in colour.)

Figure 2.

Simulation results for thermal fluctuations in water at equilibrium conditions for a range of control volumes (bins number 1 and 256 correspond to the largest control volumes and bin number 128 corresponds to the smallest ones): instantaneous (a) density and (b) x-velocity component fluctuations.

Figure 3.

Simulation results for thermal fluctuations in water at equilibrium conditions for a range of control volumes: standard deviation of density fluctuations as a function of the system size.

Figure 4.

Water density fluctuations around a dialanine peptide. (a) The peptide molecule and two dihedral angles ϕ and ψ that define the shape of the molecule; (b) the same molecule together with oxygen (red) and hydrogen (blue mesh) densities around it; and (c) the projection of water density on the X–Y plane outlined in (b): right, the total density, left, the density dynamically correlated with the dihedral angles ϕ and ψ.

Figure 5.

Schematic of the hybrid LL-FH/MD model: by entering the hybrid LL-FH/MD zone the MD particles lose some part of their pair potential interaction and become partially driven by the continuum LL-FH force field.

Figure 6.

The convergence of the standard deviation of the velocity x-component with the number of MD time steps for the current hybrid model at s=0.1 and s=0.8 (conservative velocity variable) and the reference pure MD and FH models. (Online version in colour.)

Figure 7.

Velocity convergence for the case of starting the hybrid model with an initial drift specified in the x-component of the continuum (FH) part of the solution while the MD solution is initialized with no drift. The solutions for a single control volume and the solution averaged over all control volumes are shown. Each iteration corresponds to 50 MD time steps.