Multi-scale CFD approach—a compromise of

3 Multi-scale CFD approach—a compromise of predictability and scalability 

To meet the industrial demand for both large-scale computation and good predictability, the reasonable way out is not to simulate from the beginning of the micro-scale, but to use coarse-grid simulation with meso-scale modeling for the effects of structure. This kind of approach can be termed the multi-scale CFD. It is entitled multi-scale, not because the problem it solves is multi-scale, but because its meso-scale model contains multi-scale structure parameters. 

According to the choice of meso-scale models, we may divide the multi-scale CFD into two branches the correlative and the variational, as named in Li and Kwauk (2003) and will be discussed in the following sections. 

The correlative multi-scale CFD, here, refers to CFD with meso-scale models derived from DNS, which is the way that we normally follow when modeling turbulent single-phase flows. That is, to start from the Navier-Stokes equations and perform DNS to provide the closure relations of eddy viscosity for LES, and thereon, to obtain the larger scale stress for RANS simulations (Pope, 2000). There are a lot of reports about this correlative multi-scale CFD for single-phase turbulent flows. Normally, clear scale separation should first be distinguished for the correlative approach, since the finer scale simulation need clear specification of its boundary. In this regard, the correlative multi-scale CFD may be viewed as a multilevel approach, in the sense that each span of modeled scales is at comparatively independent level and the finer level output is interlinked with the coarser level input in succession. 

These subparticle simulations also allow in-depth understanding of the applicability of their closure laws for higher scale simulations. For example, Ma et al. (2009) found that the typical drafting-kissing- 

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