Embedding molecular dynamics within fluctuating hydrodynamics in multiscale simulations of liquids R. Delgado-Buscalioni 1, * and G. De Fabritiis 2,† 1 Departamento de Física Teorica de la Materia Condensada, Universidad Autónoma de Madrid, Campus de Cantoblanco, Madrid E-28049, Spain 2 Computational Biochemistry and Biophysics Laboratory (GRIB-IMIM), Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), C/ Dr. Aiguader 88, 08003 Barcelona, Spain Received 27 April 2007; published 25 September 2007 We present a hybrid protocol designed to couple the dynamics of a nanoscopic region of liquid described at atomistic level with a fluctuating hydrodynamics description of the surrounding liquid. The hybrid technique is based on the exchange of fluxes and it is shown to respect the conservation laws of fluid mechanics. This fact allows us to solve unsteady flows involving shear and sound waves crossing the interface of both domains. In equilibrium we find perfect agreement with the grand-canonical ensemble at low and moderate densities, while within the nanoscopic volumes considered, mass fluctuation both in hybrid and full MD simulations becomes slightly larger than predicted by the thermodynamic limit. Stress fluctuations across the hybrid interface are shown to have a seamless profile. Nonequilibrium scenarios involving shear startup of Couette flow and longitudinal flow sound waves are also illustrated. DOI: 10.1103/PhysRevE.76.036709 PACS numbers: 47.11.Mn, 07.05.Tp, 47.61.Jd I. INTRODUCTION Multiscale modeling has been rapidly evolving during the past decade, and it now constitutes a new paradigm in com- puter simulation to resolve systems and processes compris- ing different length scales. The essence of a multiscale, mul- tiphysics approach consists of using different model descrip- tions for each relevant scale. Importantly, information has to be able to feed backward and forward between different scales and models. In many instances, multiscale simulations can be performed in a hierarchical way, i.e., by extracting information from one scale as input parameters for the higher level model. Relevant examples of this procedure are the coarse-graining techniques which start from atomistic simu- lations to produce simplified coarse-grained representations of complex molecules used for the study of equilibrium properties of complex fluids 1. However, many processes take place as a consequence of the continuous interaction between elements pertaining to different spatiotemporal scales. These sort of processes require another kind of mul- tiscale approach in which the information required for each model needs to be exchanged on-the-fly. In this case one can talk about concurrent coupling 2,3 and hybrid models. Hy- brid models are now deployed in many different disciplines, such as quantum-classical treatment of solid fractures 4, plasma physics 5, rarefied gases 6, complex liquids 7–9, turbulence, and more. A list which cannot be exhaustive. In this work, we focus on hybrid models for the liquid phase coupling two domains described respectively by ato- mistic and continuum descriptions domain decomposition. In general, hybrid models in the liquid phase can be divided in two groups: Either based on an Eulerian-Lagrangian de- composition 8,9 or on domain decomposition 7,10. The Eulerian-Lagrangian approach consists in modeling solute particles as Lagrangian objects moving in a Eulerian fluid description and is useful for phenomena involving the bulk flow of complex fluids. Domain decomposition is meant to provide an accurate atomistic representation of a small rel- evant region of the system, for instance at a molecular inter- face or around a macromolecule, embedded into a coarser mesoscopic description of matter 10. This area has received multiple contributions during the last decade or so for a recent review, we refer to Ref. 7. In general terms, previ- ous works on this subject have focused on how the mean flow profiles at the bulk are affected by the discrete nature of matter near boundary regions e.g., near walls 11 or contact lines 12. Consequently, in these works accurate atomistic representation of the particle system was not considered, and particles were usually described using the standard coarse- grained Lennard-Jones model. In these scenarios, flows are driven by shear stress and the large time separation between the molecular domain and the fluid bulk enables the assump- tion of stationary process. In this sense, some groups have used the Schwartz method variable coupling7 as a fast way to reach the stationary state, by consecutively imposing the mean velocity field at the hybrid border overlapping region toward and from the particle and continuum do- mains. Being interested in mean flow features, fluctuations, naturally arising from the particle system, have been usually considered as a nuisance with the exception, in gases, of the works by Garcia’s group 13. Methods to control the noise- to-signal ratio have been consequently proposed in the litera- ture 14,15. One important objective of the present hybrid model is to enable the study of the effects of external flow in a nano- scopic region and on its molecular structure. Such an objec- tive required the inclusion of important features not readily available in the literature. A coupling protocol for hybrid molecular dynamics simulations, designed to bridge nano- scopic and microscopic molecular scales hybrid MD was *rafael.delgado@uam.es † gianni.defabritiis@upf.edu PHYSICAL REVIEW E 76, 036709 2007 1539-3755/2007/763/03670913 ©2007 The American Physical Society 036709-1