Multiscale Simulation Approaches

In most liquid- and solid-phase systems, the dilute approximation is typically invalid, and, as a result, many body effects play a significant role. Many body effects are manifested through the effect of solvent or catalyst on reactivity and through concentration-dependent reaction rate parameters. Under these conditions, the one-way coupling is inadequate, and fully coupled models across scales are needed, i.e., two-way information traffic exists. This type of modeling is the most common in chemical sciences and will be of primary interest hereafter. In recent papers the terms multiscale integration hybrid, parallel, dynamic, 

Parameterize lower scale with a reduced model and pass this to the next scale model surface response methods 

Types of multiscale modeling and solution strategies. Hybrid models (one model at each scale) apply well when there is separation of scales (onion or nested-type models). When there is lack of separation of scales, mesoscale models need to be developed where the same technique (e.g., MD or MC) is accelerated. Alternatively, multigrid (heterogeneous) hybrid models can be employed where the unresolved degrees of freedom are determined from a finer scale model and passed to a coarser scale model. 

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In general, previous experimental values and computational data can be used to estimate the kinetic parameters needed for a KMC-based simulation. These parameters may be improved and adjusted after KMC simulation, if an initially identified reaction mechanism is shown to be insufficient to capture the experimental behavior. Most importantly, the DFT+KMC multiscale simulation approach establishes a well-defined pathway for taking atomistic-level details and reaching lab-level experimental results, which can be used to accelerate the discovery process and enhance engineering design. 

This contribution outlines a multiscale simulation approach for analysis of a Wurster coating process occurring in a fluidized bed. The processes occurring in the apparatus are described on four different time and length scales The Discrete Element Method coupled with Computational Fluid Dynamics, where each particle is considered as a separate entity and its motion in fluid field is calculated, play a central role in the modeling framework. On the macroscale, the Population Balance Model describes the particle... 

Another class of methods, which is not listed in the classification proposed by Toschkoff and Khinast (2013) and which can be effectively appUed for modeling of industrial scale FBs, is a multiscale simulation approach. This methodology implies a combination of submodels and computational methods applied for process simulation on different time and length scales. According to Werther et al. (2011), the models of different apparatuses and processes in the solids industry can be distinguished by detailing levels and application purposes, whereby each level can only be applied to some specific application of modeling Fig. 1. 

Goldenfeld, N., B.P. Athreya, and J.A. Dantzig. 2005. Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model. Phys. Rev. E 72 1-4. 

In molecular models, a surface site is modeled using an analogous molecular reaction. This is the simplest approach, which requires the least amount of computational resources. The selection of a molecule that can more or less adequately reproduce the properties of the surface site under study determines the success or failure of the approach. This approach was used in Ref. [20] in the multiscale simulation of zirconium and hafnium oxide film growth. 

A hierarchy of models can often be derived from a more detailed model under certain assumptions. This approach was discussed above in the case of deterministic, continuum models (see Fig. 3a). Such hierarchical models can be valuable in multiscale modeling. Let us just mention two cases. First, one could use different models from a hierarchy of models for different situations or length scales. This approach plays a key role in hybrid multiscale simulation discussed extensively below. Second, one could easily apply systems tasks to a simpler model to obtain an approximate solution that is then refined by employing a more sophisticated, accurate, and expensive model from the hierarchy. 

Systems approach borrowed from the optimization and control communities can be used to achieve various other tasks of interest in multiscale simulation. For example, Hurst and Wen (2005) have recently considered shear viscosity as a scalar input/output map from shear stress to shear strain rate, and estimated the viscosity from the frequency response of the system by performing short, non-equilibrium MD. Multiscale model reduction, along with optimal control and design strategies, offers substantial promise for engineering systems. Intensive work on this topic is therefore expected in the near future. 

More recently, techniques have been developed for utilizing multiscale simulation models to perform systems engineering tasks, such as parameter estimation, optimization and control (e.g. see reviews by [9, 10] and [11], and references cited therein). This incorporation of models that couple molecular through macroscopic length scales within systems engineering tools enables a systematic approach to the simultaneous optimization of all of the length scales of the process. 

A widely used type of multiscale simulation combines quantum mechanical and molecular mechanical (QM/MM) simulations. In this approach, the functional core of the molecular system, for example, the catalytic sites of an enzyme, is described at the electronic level (QM region), whereas the surrounding macromolecular system is treated using a classical description (MM region). Some of the biological applications for which QM/MM calculations have been widely utilized are chemical reactions in enzymes, proton transfer in proteins and optical excitations. In QM/MM... 

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