Heterogeneous multiscale methods

Heterogeneous Multiscale Method The heterogeneous multiscale method provides a general framework for dealing with multiscale phenomena and can be easily applied to the coupling of continuum and atomistic (molecular dynamics) simulations at finite temperature. 

Weinan E, Engquist B, Li X, Ren W, Vanden-Eijnden E Heterogeneous multiscale methods a review, Comput Phys Commun 2 367—450, 2007. 

To account for the effect of a sufficiently broad, statistical distribution of heterogeneities on the overall transport, we can consider a probabilistic approach that will generate a probability density function in space (5) and time (t), /(i, t), describing key features of the transport. The effects of multiscale heterogeneities on contaminant transport patterns are significant, and consideration only of the mean transport behavior, such as the spatial moments of the concentration distribution, is not sufficient. The continuous time random walk (CTRW) approach is a physically based method that has been advanced recently as an effective means to quantify contaminant transport. The interested reader is referred to a detailed review of this approach (Berkowitz et al. 2006). 

The heterogeneous reactors with supported porous catalysts are one of the driving forces of experimental research and simulations of chemically reactive systems in porous media. It is believed that the combination of theoretical methods and surface science approaches can shorten the time required for the development of a new catalyst and optimization of reaction conditions (Keil, 1996). The multiscale picture of heterogeneous catalytic processes has to be considered, with hydrodynamics and heat transfer playing an important role on the reactor (macro-)scale, significant mass transport resistances on the catalyst particle (meso-)scale and with reaction events restricted within the (micro-)scale on nanometer and sub-nanometer level (Lakatos, 2001 Mann, 1993 Tian et al., 2004). 

Existing quantum mechanics and molecular dynamics methods have not yet advanced to the stage where water can be reliably modeled by itself [148-151], much less when involved in electrochemical reactions at a surface [152]. An important requirement ofany general multiscale systems framework is that it must be able to enable the resolution of the unknowns in complex heterogeneous mechanisms. 

Kell FJ (2012) Multiscale modelling in computational heterogeneous catalysis. In Kirchner B, Vrabec J (eds) Multiscale molecular methods in applied chemistry. Topics in current chemistry, vol 307. Springer, Berlin, pp 69-107... 

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