Multiscale and Multiphysics Scientific Computations

Modelling fluid dynamics has long been a task considered in the framework of the Euler and Navier-Stokes equations, whose success in computer simulations aiming at understanding the physics of fluid dynamics and heat transfer, as well as in assisting with the design and optimisation of macroscopic structures and devices has established it as the most effective method for studying fluid flow. This approach, however, is based on the assumption of a continuum fluid which is in equilibrium at any point or infinitesimal volume, a premise reasonable at larger scales. As the fluid is restricted spatially to nano-metre sized characteristic dimensions, phenomena at interfaces, which occupy a significant percentage of the overall system, influence the homogeneous structure of the liquid particles and introduce dynamics that cannot be captured by continuum mechanics

Atomic scale simulation techniques such as Molecular Dynamics (MD) and Monte Carlo (MC) methods have proven effective in delineating, from first principles, the physical apparatus, which governs the dynamics of such systems, assisting in the resolution of discrepancies between experimental results and macroscopic computational models. However, the main disadvantage of atomic-scale simulation methods is their computational expense, which increases exponentially with the size of the simulation domain. This blend of difficulties in such systems makes the independent use of either continuum or atomistic methods insufficient or practically impossible. To account for this, we have developed mesoscale and hybrid molecular-continuum methods (HMCM) methods. These methods attempt to couple the two types of models, thus allowing for an accurate calculation of the properties of the system at reduced computational cost. Mesoscale models comprise a single solver, which attempts to give a more efficient solution based on atomistic observations, while HMCM utilises both molecular and continuum solvers exchanging information.

Time and length scales in which atomistic,
continuum and hybrid methods are used.
Multiscale method based on the coupling of CFD
and Molecular Dynamics
Unsteady microjet flows using coupled CFD and MD methods

Furthermore, we have developed an artificial neural network (ANN) multiscale method for coupling continuum and molecular simulations. Molecular dynamics modelling is employed as a local high resolution refinement of computational data required by the continuum computational fluid dynamics solver. The coupling between atomistic and continuum simulations is obtained by an ANN. The ANN aims to optimise the transfer of information through minimization of the computational cost by avoiding repetitive atomistic simulations of nearly identical states, as well as the fluctuation strength of the atomistic outputs that are fed back to the continuum solver. We have tested the above methods for different fluid flow and heat transfer problems. More information is provided in the published papers


  • D. Drikakis, M. Frank, N. Asproulis, Advances and Challenges in Computational Research of Micro and Nano Flows, Microfluidics Conference, UCL London, 2014
  • N. Asproulis, M. Kalweit, D. Drikakis, A Hybrid Molecular Continuum Method using Point Wise Coupling, Advances in Engineering Software, Vol. 46, Issue 1, 85-92, 2012
  • M. Kalweit, D. Drikakis, Multiscale simulation strategies and mesoscale modelling of gas and liquid flows, IMA Journal of Applied Mathematics, 1 - 11, 201
  • M. Kalweit, D. Drikakis, On the behavior of fluidic material at molecular dynamics boundary conditions used in hybrid molecular-continuum simulations, Molecular Simulation, Vol. 36, Issue 9, 657-662, 2010
  • N. Asproulis, M. Kalweit, E. Shapiro, D. Drikakis, Mesoscale flow and heat transfer modelling and its application to liquid and gas flows, Journal of Nanophotonics, 3(01), 031960-031975, 2009.
  • M. Kalweit, D. Drikakis, Multiscale Methods for Micro/Nano Flows and Materials, Journal of Computational and Theoretical Nanoscience, 5, 1923-1938, 2008.
  • M. Kalweit, D. Drikakis, Coupling strategies for hybrid molecular-continuum simulation methods, Proc. IMechE, Vol. 222, Part C: J. Mechanical Engineering
  • D. Drikakis, M. Kalweit, Computational Modelling of Flow and Mass Transport Processes in Nanotechnology, Invited Chapter in the First Handbook in Theoretical and Computational Nanotechnology, eds. M. Rieth, W.Schommers, American Scientific Publishers, Chapter 11, 470-545, 2006.
  • D. Drikakis, N. Asproulis, Multiscale Computational Modelling of Flow and Heat Transfer, International Journal for Numerical Methods for Heat and Fluid Flow, 5(20), 2010
  • D. Drikakis, N. Asproulis, Quantification of Computational Uncertainty in Science and Engineering, ASME Applied Mechanics Review, 64(4), 2011
  • N. Asproulis and D. Drikakis, An Artificial Neural Network based Multiscale Method for Hybrid Atomistic-Continuum Simulations, Microfluidics and Nanofluidics, 15(4), 559-574, 2013.