Inertial coupling for point particle fluctuating hydrodynamics

Usabiaga, Florencio Balboa; Pagonabarraga, Ignacio; Delgado‐Buscalioni, Rafael

doi:10.1016/j.jcp.2012.10.045

Cited by 37 publications

(38 citation statements)

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“…In the majority of the simulations we use the three-point discrete kernel function of Roma and Peskin 30,31 to discretize the kernel δ a . By using the Peskin four-point kernel 27 instead of the three-point discrete kernel function the translational invariance of the spatial discretization can be improved, however, at a potentially significant increase in computational cost, particularly in three dimensions.…”

Section: Resultsmentioning

confidence: 99%

“…The deterministic mobility tensor can be obtained by turning off fluctuations, applying a unit force along each of the coordinate directions in turn, solving the spatially discretized steady Stokes equation, and then calculating the resulting velocity of the particle. After accounting for finite-size effects due to the finite length of the periodic box, in three dimensions we numerically estimate 17,30 the effective hydrodynamic radius to be R 3pt H = (0.91 ± 0.01) h the three-point kernel, 53 where h is the grid spacing, and R 4pt H = (1.255 ± 0.005) h for the 4pt kernel. 46 In two dimensions, the effective (rigid disk) hydrodynamic radii are estimated to be R 3pt H = (0.72 ± 0.01) h and R 4pt H = (1.04 ± 0.005) h. Note that the spatial discretization we use is not perfectly translationally invariant and there is a small variation of R H (quoted above as an error bar) as the particle moves relative to the underlying fixed fluid grid.…”

Section: Resultsmentioning

confidence: 99%

“…There are well-known finite-size corrections to the mobility for periodic systems with a unit cell of volume L d that scale like L −1 in three dimensions. 14,29,30 The hydrodynamic radius of the blobs that we employ in our numerical implementation has been measured computationally in Refs. 17 and 30.…”

Section: Brownian Particle Modelmentioning

confidence: 99%

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The Stokes-Einstein relation at moderate Schmidt number

Usabiaga

Xie

Delgado‐Buscalioni

et al. 2013

The Journal of Chemical Physics

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The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently developed minimally resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The mismatch arises because thermal fluctuations affect the drag coefficient for a particle due to the nonlinear nature of the fluid-particle coupling. The numerical data are in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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The Stokes-Einstein relation at moderate Schmidt number

Usabiaga

Xie

Delgado‐Buscalioni

et al. 2013

The Journal of Chemical Physics

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“…The particle kernel, originally designed by Peskin and Roma [25] for the immersed boundary (IB) method, is used to interpolate local fluid properties and to spread the particle forces to the surrounding fluid. The third important issue in our method, which we refer to as the "inertial coupling" (IC) method [26], resides in imposing an instantaneous "no-slip" constraint (the particle velocity equals the interpolated fluid velocity) to couple the dynamics of the particle and the fluid. Such coupling is instantaneous and, as shown in our previous work [26], it captures the fast ultrasound-particle interaction.…”

Section: Introductionmentioning

confidence: 99%

“…The third important issue in our method, which we refer to as the "inertial coupling" (IC) method [26], resides in imposing an instantaneous "no-slip" constraint (the particle velocity equals the interpolated fluid velocity) to couple the dynamics of the particle and the fluid. Such coupling is instantaneous and, as shown in our previous work [26], it captures the fast ultrasound-particle interaction. Here we further explore this line of minimally resolved particle modeling which is based on the idea that the particle kernel (originally designed for interpolation purposes [23]) can be used to embed all the relevant physical properties of the particle, such as its hydrodynamic radius R H [22], its volume V , and its mass (m p = m e + ρ V ).…”

Section: Introductionmentioning

confidence: 99%

Minimal model for acoustic forces on Brownian particles

Usabiaga

Delgado‐Buscalioni

2013

Phys. Rev. E

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We present a generalization of inertial coupling (IC) [Balboa Usabiaga et al., J. Comput. Phys. 235, 701 (2013)], which permits the resolution of radiation forces on small particles with arbitrary acoustic contrast factor. The IC method is based on a Eulerian-Lagrangian approach: particles move in continuum space while the fluid equations are solved in a regular mesh (here we use the finite volume method). Thermal fluctuations in the fluid stress, important below the micron scale, are also taken into account following the Landau-Lifshitz fluid description. Each particle is described by a minimal cost resolution which consists of a single small kernel (bell-shaped function) concomitant to the particle. The main role of the particle kernel is to interpolate fluid properties and spread particle forces. Here, we extend the kernel functionality to allow for an arbitrary particle compressibility. The particle-fluid force is obtained from an imposed "no-slip" constraint which enforces similar particle and kernel fluid velocities. This coupling is instantaneous and permits the capture of the fast, nonlinear effects underlying the radiation forces on particles. Acoustic forces arise because of an excess either in particle compressibility (monopolar term) or in mass (dipolar contribution) over the fluid values. Comparison with theoretical expressions shows that the present generalization of the IC method correctly reproduces both contributions. Due to its low computational cost, the present method allows for simulations with many [O(10 4 )] particles using a standard graphical processor unit.

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Particle–Continuum Coupling and its Scaling Regimes: Theory and Applications

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Praprotnik

Bell

et al. 2020

Advcd Theory and Sims

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This work is motivated by the goal of designing simulation software for technical devices that, at their functional core, rely on atomistic-scale processes embedded in a larger-scale fluid environment. The core of the problem is the conceptual and technical approach for coupling particle and continuum representations of a fluid. The state of the art for key aspects including physical modeling, mathematical formalization, computational implementation, and applications, is discussed and organized in a consistent picture across the relevant physical regimes.Key building blocks of the related developments that we will summarize and appraise in some detail below are i) finite volume FHD solvers following Bell, Donev, Garcia, Nonaka and colleagues [4] (see Section 2), ii) the "adaptive resolution simulation" (AdResS) approach that enables molecular dynamics simulations on limited size domains [5][6][7] (see Section 3), and iii) the recent mathematical formalization of open molecular systems by two of the authors [8] (see Section 4). In Section 5, we discuss scaling regimes and the rationale behind possible MD-FHD coupling strategies, finally, Section 6 is dedicated to the description of some representative examples, while Section 7 outlines future perspectives and summarizes our conclusions.

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Inertial coupling for point particle fluctuating hydrodynamics

Cited by 37 publications

References 37 publications

The Stokes-Einstein relation at moderate Schmidt number

The Stokes-Einstein relation at moderate Schmidt number

Minimal model for acoustic forces on Brownian particles

Particle–Continuum Coupling and its Scaling Regimes: Theory and Applications

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