Rafael Delgado-Buscalioni

Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow.

The aim of hybrid methods in simulations is to communicate regions with disparate time and length scales. Here, a fluid described at the atomistic level within an inner region P is coupled to an outer region C described by continuum fluid dynamics. The matching of both descriptions of matter is made across an overlapping region and, in general, consists of a two-way coupling scheme (C-->P and P-->C) that conveys mass, momentum, and energy fluxes. The contribution of the hybrid scheme hereby presented is twofold. First, it treats unsteady flows and, more importantly, it handles energy exchange between both C and P regions. The implementation of the C-->P coupling is tested here using steady and unsteady flows with different rates of mass, momentum and energy exchange. In particular, relaxing flows described by linear hydrodynamics (transversal and longitudinal waves) are most enlightening as they comprise the whole set of hydrodynamic modes. Applying the hybrid coupling scheme after the onset of an initial perturbation, the cell-averaged Fourier components of the flow variables in the P region (velocity, density, internal energy, temperature, and pressure) evolve in excellent agreement with the hydrodynamic trends. It is also shown that the scheme preserves the correct rate of entropy production. We discuss some general requirements on the coarse-grained length and time scales arising from both the characteristic microscopic and hydrodynamic scales.

Mori–Zwanzig formalism as a practical computational tool

An operational procedure is presented to compute explicitly the different terms in the generalized Langevin equation (GLE) for a few relevant variables obtained within Mori-Zwanzig formalism. The procedure amounts to introducing an artificial controlled parameter which can be tuned in such a way that the so-called projected dynamics becomes explicit and the GLE reduces to a Markovian equation. The projected dynamics can be realised in practice by introducing constraints, and it is shown that the Green-Kubo formulae computed with these dynamics do not suffer from the plateau problem. The methodology is illustrated in the example of star polymer molecules in a melt using their center of mass as relevant variables. Through this example, we show that not only the effective potentials, but also the friction forces and the noise play a very important role in the dynamics.

USHER: An algorithm for particle insertion in dense fluids

The insertion of solvent particles in molecular dynamics simulations of complex fluids is required in many situations involving open systems, but this challenging task has been scarcely explored in the literature. We propose a simple and fast algorithm (USHER) that inserts the new solvent particles at locations where the potential energy has the desired prespecified value. For instance, this value may be set equal to the system’s excess energy per particle in such a way that the inserted particles are energetically indistinguishable from the other particles present. During the search for the insertion site, the USHER algorithm uses a steepest-descent iterator with a displacement whose magnitude is adapted to the local features of the energy landscape. The only adjustable parameter in the algorithm is the maximum displacement, and we show that its optimal value can be extracted from an analysis of the structure of the potential energy landscape. We present insertion tests in periodic and nonperiodic system...

Hamiltonian Adaptive Resolution Simulation for Molecular Liquids

Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well-defined statistical ensembles can be generated making use of all standard molecular dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework.

Multiscale modeling of liquids with molecular specificity

The separation between molecular and mesoscopic length and time scales poses a severe limit to molecular simulations of mesoscale phenomena. We describe a hybrid multiscale computational technique which addresses this problem by keeping the full molecular nature of the system where it is of interest and coarse graining it elsewhere. This is made possible by coupling molecular dynamics with a mesoscopic description of realistic liquids based on Landaus fluctuating hydrodynamics. We show that our scheme correctly couples hydrodynamics and that fluctuations, at both the molecular and continuum levels, are thermodynamically consistent. Hybrid simulations of sound waves in bulk water and reflected by a lipid monolayer are presented as illustrations of the scheme.

Concurrent triple-scale simulation of molecular liquids

We present a triple-scale simulation of a molecular liquid, in which the atomistic, coarse-grained, and continuum descriptions of the liquid are concurrently coupled. The presented multiscale approach, which covers the length scales ranging from the micro- to macroscale, is a combination of two dual-scale models: a particle-based adaptive resolution scheme (AdResS), which couples the atomic and mesoscopic scales, and a hybrid continuum-molecular dynamics scheme (HybridMD). The combined AdResS-HybridMD scheme successfully sorts out the problem of large molecule insertion in the hybrid particle-continuum simulations of molecular liquids. The combined model is shown to correctly describe the hydrodynamics within a hybrid particle-continuum framework. The presented approach opens up the possibility to perform efficient grand-canonical molecular dynamics simulations of truly open molecular liquid systems.

Fluctuating hydrodynamic modeling of fluids at the nanoscale

A good representation of mesoscopic fluids is required to combine with molecular simulations at larger length and time scales [De Fabritiis, Phys. Rev. Lett. 97, 134501 (2006)]. However, accurate computational models of the hydrodynamics of nanoscale molecular assemblies are lacking, at least in part because of the stochastic character of the underlying fluctuating hydrodynamic equations. Here we derive a finite volume discretization of the compressible isothermal fluctuating hydrodynamic equations over a regular grid in the Eulerian reference system. We apply it to fluids such as argon at arbitrary densities and water under ambient conditions. To that end, molecular dynamics simulations are used to derive the required fluid properties. The equilibrium state of the model is shown to be thermodynamically consistent and correctly reproduces linear hydrodynamics including relaxation of sound and shear modes. We also consider nonequilibrium states involving diffusion and convection in cavities with no-slip boundary conditions.

Staggered schemes for fluctuating hydrodynamics

We develop numerical schemes for solving the isothermal compressible and incompressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive, advective, and stochastic fluxes that satisfies a discrete fluctuation-dissipation balance and construct temporal discretizations that are at least second-order accurate in time deterministically and in a weak sense. Specifically, the methods reproduce the correct equilibrium covariances of the fluctuating fields to the third (compressible) and second (incompressible) orders in the time step, as we verify numerically. We apply our techniques to model recent experimental measurements of giant fluctuations in diffusively mixing fluids in a microgravity environment [A. Vailati et al., Nat. Comm., 2 (2011), 290]. Numerical results for the static spectrum of nonequilibrium concentration fluctuations are in excellent agreement between the compressible and incompressible simulati...

Coupling atomistic and continuum hydrodynamics through a mesoscopic model: Application to liquid water

We have conducted a triple-scale simulation of liquid water by concurrently coupling atomistic, mesoscopic, and continuum models of the liquid. The presented triple-scale hydrodynamic solver for molecular liquids enables the insertion of large molecules into the atomistic domain through a mesoscopic region. We show that the triple-scale scheme is robust against the details of the mesoscopic model owing to the conservation of linear momentum by the adaptive resolution forces. Our multiscale approach is designed for molecular simulations of open domains with relatively large molecules, either in the grand canonical ensemble or under nonequilibrium conditions.

Hybrid molecular-continuum fluid dynamics

We describe recent developments in the hybrid atomistic/continuum modelling of dense fluids. We discuss the general implementation of mass, momentum and energy transfers between a region described by molecular dynamics and a neighbouring domain described by the Navier–Stokes equations for unsteady continuum fluid flow.