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Fluid simulations with atomistic resolution : a hybrid multiscale method with field-wise coupling
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Borg, Matthew K., Lockerby, Duncan A. and Reese, Jason M. (2013) Fluid simulations with atomistic resolution : a hybrid multiscale method with field-wise coupling. Journal of Computational Physics, Volume 255 . pp. 149-165. doi:10.1016/j.jcp.2013.08.022 ISSN 0021-9991.
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Official URL: http://dx.doi.org/10.1016/j.jcp.2013.08.022
Abstract
We present a new hybrid method for simulating dense fluid systems that exhibit multiscale behaviour, in particular, systems in which a Navier–Stokes model may not be valid in parts of the computational domain. We apply molecular dynamics as a local microscopic refinement for correcting the Navier–Stokes constitutive approximation in the bulk of the domain, as well as providing a direct measurement of velocity slip at bounding surfaces. Our hybrid approach differs from existing techniques, such as the heterogeneous multiscale method (HMM), in some fundamental respects. In our method, the individual molecular solvers, which provide information to the macro model, are not coupled with the continuum grid at nodes (i.e. point-wise coupling), instead coupling occurs over distributed heterogeneous fields (here referred to as field-wise coupling). This affords two major advantages. Whereas point-wise coupled HMM is limited to regions of flow that are highly scale-separated in all spatial directions (i.e. where the state of non-equilibrium in the fluid can be adequately described by a single strain tensor and temperature gradient vector), our field-wise coupled HMM has no such limitations and so can be applied to flows with arbitrarily-varying degrees of scale separation (e.g. flow from a large reservoir into a nano-channel). The second major advantage is that the position of molecular elements does not need to be collocated with nodes of the continuum grid, which means that the resolution of the microscopic correction can be adjusted independently of the resolution of the continuum model. This in turn means the computational cost and accuracy of the molecular correction can be independently controlled and optimised. The macroscopic constraints on the individual molecular solvers are artificial body-force distributions, used in conjunction with standard periodicity. We test our hybrid method on the Poiseuille flow problem for both Newtonian (Lennard-Jones) and non-Newtonian (FENE) fluids. The multiscale results are validated with expensive full-scale molecular dynamics simulations of the same case. Very close agreement is obtained for all cases, with as few as two micro elements required to accurately capture both the Newtonian and non-Newtonian flowfields. Our multiscale method converges very quickly (within 3–4 iterations) and is an order of magnitude more computationally efficient than the full-scale simulation.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QC Physics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||
Library of Congress Subject Headings (LCSH): | Molecular dynamics, Newtonian fluids, Non-Newtonian fluids, Fluid dynamics | ||||
Journal or Publication Title: | Journal of Computational Physics | ||||
Publisher: | Academic Press Inc. Elsevier Science | ||||
ISSN: | 0021-9991 | ||||
Official Date: | 15 December 2013 | ||||
Dates: |
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Volume: | Volume 255 | ||||
Page Range: | pp. 149-165 | ||||
DOI: | 10.1016/j.jcp.2013.08.022 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 26 December 2015 | ||||
Date of first compliant Open Access: | 26 December 2015 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
Grant number: | EP/I011927/1, EP/K000586/1 (EPSRC) |
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