The Basic Research Questions:

What is thermodynamic non-equilibrium in fluids?

The traditional model of transport in fluids — the set of Navier-Stokes-Fourier (NSF) equations — requires a large degree of separation between effects occurring on a microscopic scale and those on a macroscopic scale. If this is the case in a flow, then heat and momentum are locally equilibrated rapidly in comparison to the timescale for evolution of the bulk flow. However, thermodynamic non-equilibrium can enter even a conventionally-Newtonian fluid flowfield in two main ways. First, through the influence of bounding surfaces or interfaces (which act, typically, to re-set the local fluid molecular distribution); second, through high-gradient (spatial, temporal) processes in the bulk. In the applications targetted in this Programme, thermodynamic non-equilibrium in the flow is likely to have a profound effect on the overall system performance.

How can we deal with non-equilibrium?

As it stems from the microscopic nature of matter, non-equilibrium can be accounted for by employing a suitable microscopic model (e.g. a kinetic model for gases, or Molecular Dynamics (MD) for liquids) over the entire flow domain. While this is possible when studying the dynamics of a carbon nanotube, a small group of proteins, or other very small-scale systems, in engineering problems the simulation domain is often much larger and more complex, making this approach computationally impractical. Also, in many cases, the degree of scale separation may vary across the flowfield, as well as with time, and using a model of microscopic interactions in close-to-equilibrium regions is unnecessary because perfectly adequate macroscale models exist (i.e. the NSF equations). With the focus on computability as well as accuracy, the modelling approach pursued in our partnership is one that couples a macroscale model to a microscale model; a hybrid strategy.

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Recent Publications

MJ Zimon, R Prosser, DR Emerson, MK Borg, D Bray, L Grinberg, JM Reese (2016) An evaluation of noise reduction algorithms for particle-based fluid simulations in multi-scale applications. Journal of Computational Physics, 325: 380-394 (full paper here)

BS Collyer, C Connaughton, DA Lockerby (2016) Importance sampling variance reduction for the Fokker–Planck rarefied gas particle method. Journal of Computational Physics, 325: 116-128 (full paper here)

MJ Zimon, JM Reese, DR Emerson (2016) A novel coupling of noise reduction algorithms for particle flow simulationsJournal of Computational Physics, 321: 169-190 (full paper here)