Projects per year
Abstract
We present a new hybrid method for simulating dense fluid systems that exhibit multiscale behaviour, in particular, systems in which a NavierStokes model may not be valid in parts of the computational domain. We apply molecular dynamics as a local microscopic refinement for correcting the NavierStokes 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. pointwise coupling), instead coupling occurs over distributed heterogeneous fields (here referred to as fieldwise coupling). This affords two major advantages. Whereas pointwise coupled HMM is limited to regions of flow that are highly scaleseparated in all spatial directions (i.e. where the state of nonequilibrium in the fluid can be adequately described by a single strain tensor and temperature gradient vector), our fieldwise coupled HMM has no such limitations and so can be applied to flows with arbitrarilyvarying degrees of scale separation (e.g. flow from a large reservoir into a nanochannel). 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 bodyforce distributions, used in conjunction with standard periodicity. We test our hybrid method on the Poiseuille flow problem for both Newtonian (LennardJones) and nonNewtonian (FENE) fluids. The multiscale results are validated with expensive fullscale 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 nonNewtonian flowfields. Our multiscale method converges very quickly (within 34 iterations) and is an order of magnitude more computationally efficient than the fullscale simulation.
Original language  English 

Pages (fromto)  149165 
Number of pages  17 
Journal  Journal of Computational Physics 
Volume  255 
DOIs  
Publication status  Published  15 Dec 2013 
Keywords
 coupled solvers
 fluid dynamics
 hybrid method
 molecular dynamics
 multiscale simulations
 Newtonian and nonNewtonian flows
 scale separation
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Projects
 3 Finished

E Infrastructure Bid  Recurrent Costs Bid
Littlejohn, D., Fedorov, M., Mulheran, P. & Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/04/12 → 31/03/13
Project: Research

E Infrastructure Bid  Capital Equipment Bid
Littlejohn, D., Fedorov, M., Mulheran, P. & Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
20/01/12 → 31/03/12
Project: Research

NonEquilibrium Fluid Dynamics for Micro/Nano Engineering Systems
Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/01/11 → 16/02/16
Project: Research