(361a) Talking about Multi-Scale Simulations

Many industrial multi-phase flows inherently are multi-scale systems in which several time and length scales interact in a complex way: particle (or bubble or drop) size, the spectrum of turbulent eddies, the scale of the equipment. Diffusion, heat conduction, and chemical reactions may complicate the scene even further at the higher end of the spectrum.  And simulating these systems computationally adds another scale, viz. that of the computational cell size.
Various options are available for such simulations, each with their own pros and cons. Most of the options heavily rely on such divergent issues as the concept of interpenetrating continua, particle size distribution kernels, sub-grid scale models, models for the interaction force(s) between the phases, models for turbulence under two-phase flow conditions, micro-mixing models, et cetera. For the simulation of industrially relevant systems, clever choices should be made, with due regard to the size of the computational effort affordable.
An essential question is: Does the set of particle differential equations really reflect the actual physics of the system of interest? Some dilemmas in answering this key question are discussed: how realistic is it to track many (point) particles in an Euler-Lagrangian approach? What are the limitations of the Euler-Euler method? How should we take sub-grid scale effects into account?
Current computational resources may make it possible to invoke the promise of Direct Numerical Simulations carried out in periodic boxes. DNSs refrain from models and are capable of resolving the real physics. Carrying out a number of such DNSs for conditions spanning the spatial distribution of governing parameters might reproduce the actual processes of interest much better. Most computational time should be devoted to mimicking the detailed processes, while much less efforts is spent in the coarse-grained reactor-scale simulation. Feeding back the results of the localized DNSs back into the coarse-grained simulation and interpolating between the results of the set of localized DNSs is part of the challenge of this truly multi-scale approach.