Simulation of a Particle Domain in a Continuum, Fluctuating Hydrodynamics Reservoir

Abbas Gholami, Rupert Klein, and Luigi Delle Site

Phys. Rev. Lett. 129, 230603 – Published 30 November 2022

Abstract

In molecular simulation and fluid mechanics, the coupling of a particle domain with a continuum representation of its embedding environment is an ongoing challenge. In this Letter, we show a novel approach where the latest version of the adaptive resolution scheme (AdResS), with noninteracting tracers as particles’ reservoir, is combined with a fluctuating hydrodynamics (FHD) solver. The resulting algorithm, supported by a solid mathematical model, allows for a physically consistent exchange of matter and energy between the particle domain and its fluctuating continuum reservoir. Numerical tests are performed to show the validity of the algorithm. Differently from previous algorithms of the same kind, the current approach allows for simulations where, in addition to density fluctuations, also thermal fluctuations can be accounted for, thus large complex molecular systems, as, for example, hydrated biological membranes in a thermal field, can now be efficiently treated.

Received 14 June 2022
Revised 4 October 2022
Accepted 24 October 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.230603

Physics Subject Headings (PhySH)

Classical statistical mechanics Compressible flows Continuum mechanics Interparticle interactions Molecular dynamics

Multiscale modeling

Fluid DynamicsStatistical Physics & ThermodynamicsGeneral PhysicsParticles & Fields

Authors & Affiliations

Abbas Gholami ^*, Rupert Klein ^†, and Luigi Delle Site ^‡

Freie Universität Berlin, Institute of Mathematics, Arnimallee 6, 14195 Berlin, Germany

^*agholami@zedat.fu-berlin.de
^†rupert.klein@fu-berlin.de
^‡luigi.dellesite@fu-berlin.de

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Issue

Vol. 129, Iss. 23 — 2 December 2022

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Images

Figure 1
Illustration of the AdResS (or open system model) and its coupling to the continuum (a), the technical setup of AdResS only (b), and its inclusion into a continuum solver as particle domain (c). The particles of the $Δ$ region and the tracers of the TR region of AdResS overlap with the continuum description and exchange information (green and red arrows) in a way that boundary conditions from the continuum to the AT region and vice versa are defined.
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Figure 2
The definitions of boundaries of Fig. 1 are considered. The simulation starts with an initial state of a given density, velocity, and temperature for the whole domain as if it was a pure continuum domain. Next, according to the density and temperature of the neighboring macrocells of the continuum, the thermodynamic forces for the left and right sides of the AdResS domain are calculated by interpolation from the dictionary and the particle simulation is executed. The temperature on the left and right sides of the particle domain is set according to the temperature of the neighboring macrocells. Average values of physical quantities of interest and the related interface fluxes are calculated from the particle simulation in the AT region and imposed in the continuum macrocells corresponding to the AT region and in the neighboring or interface cells to ensure that such imposing preserves the conservation laws. Finally, the fluctuating hydrodynamic solver will advance for a certain number of continuum time steps, considered as a single coupling time step, and a new state with updated density, velocities, and temperature is defined and the procedure repeated.
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Figure 3
Profiles of density (a),(c),(e),(g) and temperature (b),(d),(f),(h) evolved from initial step functions ( $ϱ_{left} = 1010 [kg / m^{3}]$ , $T_{left} = 279.3 [K]$ , $ϱ_{right} = 919.6 [kg / m^{3}]$ , and $T_{right} = 322.3 [K]$ ) with constant pressure ( $P = 100 [MPa]$ ) over time at $t = 0.05 [ns]$ (a) and (b), $t = 0.25 [ns]$ (c) and (d), $t = 1.2 [ns]$ (e) and (f), and $t = 3.5 [ns]$ (g) and (h). The colored regions in the middle of the box show the AdResS domain with the atomistic region (red) in contact with the TR region (blue) through a narrow transition region (gray). Results from FHD, MD, and coupled AdResS-FHD simulations are shown as black solid, dashed, and red lines, respectively.
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Figure 4
The profile of density (a) and temperature (b) in the AdResS domain and in the full atomistic simulation over time, for the initial step function for the density and temperature. The red and blue regions represent the hot and cold reservoirs, respectively. The time slices are the same as for Fig. 3.
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