In a number of multiscale problems, a variable resolution approach is beneficial when a fine-scale model is used in a limited part of the solution domain and a simpler ‘coarse-grain’ model is applied as an effective boundary condition. Such boundary condition is aimed to truncate the size of the computational domain in order to reduce the cost associated with the fine-scale calculation. 

In this presentation, a novel multiscale state-variable coupling scheme between the Molecular Dynamics and the Fluctuating Hydrodynamics representations of the same liquid, which has been developed by the authors, is considered. In comparison with many multiscale schemes in the literature, the current method uses the framework of a physical analogy to specify the coupling terms in the ‘buffer’ zone between the atomistic and hydrodynamic regions. Physical analogy methods for coupling models of different resolution have been used in continuum fluid dynamics for several decades; for example, in aeroacoustics research to exactly rearrange the governing Navier-Stokes equations to the form of non-homogeneous linear equations to nominally separate large-size acoustic scales and small-size turbulence scales. Following a similar line of thought, an analogy with two-phase modelling is introduced where one “phase” is atomistic/Lagrangian based on Molecular Dynamics and the other one is a continuum/Eulerian representation of the same liquid based on Fluctuating Hydrodynamics. The “phases” interact in accordance with macroscopic conservation laws and the user-defined partial concentration function, which determines how much of the liquid is modelled atomistically and how much is modelled as the continuum in each part of the solution domain.

Validation examples of the current approach will be provided for “simple” liquids such as argon at high pressure and water at equilibrium conditions as well as for the problems where equilibrium is held only locally such as in case of a hydrodynamic wave travelling through a hybrid atomistic/continuum fluid dynamics region. Possible extensions of the current method for applications with large space-time-scale variations will be also discussed.