Fluid simulations with atomistic resolution: a hybrid multiscale method with field-wise coupling

Matthew K. Borg, Duncan A. Lockerby, Jason M. Reese

Research output: Contribution to journalArticle

20 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)149-165
Number of pages17
JournalJournal of Computational Physics
Volume255
DOIs
Publication statusPublished - 15 Dec 2013

Fingerprint

Fluids
Molecular dynamics
fluids
continuums
simulation
grids
molecular dynamics
force distribution
Thermal gradients
flow separation
Tensors
Macros
laminar flow
iteration
periodic variations
temperature gradients
slip
Computer simulation
tensors
costs

Keywords

  • coupled solvers
  • fluid dynamics
  • hybrid method
  • molecular dynamics
  • multiscale simulations
  • Newtonian and non-Newtonian flows
  • scale separation

Cite this

Borg, Matthew K. ; Lockerby, Duncan A. ; Reese, Jason M. / Fluid simulations with atomistic resolution : a hybrid multiscale method with field-wise coupling. In: Journal of Computational Physics. 2013 ; Vol. 255. pp. 149-165.
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Fluid simulations with atomistic resolution : a hybrid multiscale method with field-wise coupling. / Borg, Matthew K.; Lockerby, Duncan A.; Reese, Jason M.

In: Journal of Computational Physics, Vol. 255, 15.12.2013, p. 149-165.

Research output: Contribution to journalArticle

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AU - Borg, Matthew K.

AU - Lockerby, Duncan A.

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AB - 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.

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