Multiscale dynamically coupled

Figure 4.7 Schematic of the dynamically coupled multiscale simulation of the electrodeposition of copper into a trench to form a copper wire. A finite volume code that simulates the potential field and concentration fields of all chemical species in aqueous solution sends the solution concentrations and potential at the solid-liquid interface to a KMC code, which simulates adsorption, desorption and chemical and electrochemical reactions that occur on the surface. The KMC code...

Rusli, E., Drews, T.O. and Braatz, R.D. (2004) Systems Analysis and Design of Dynamically Coupled Multiscale Reactor Simulation Codes. Chem. Eng. Sci., 59, 5607-5613. 

There have been many hybrid multiscale simulations published recently in other diverse areas. It appears that the first onion-type hybrid multiscale simulation that dynamically coupled a spatially distributed 2D KMC for a surface reaction with a deterministic, continuum ODE CSTR model for the fluid phase was presented in Vlachos et al. (1990). Extension to 2D KMC coupled with ID PDE flow model was described in Vlachos (1997) and for complex reaction networks studied using 2D KMC coupled with a CSTR ODEs model in Raimondeau and Vlachos (2002a, b, 2003). Other examples from catalytic applications include Tammaro et al. (1995), Kissel-Osterrieder et al. (1998), Qin et al. (1998), and Monine et al. (2004). For reviews, see Raimondeau and Vlachos (2002a) on surface-fluid interactions and chemical reactions, and Li et al. (2004) for chemical reactors. 

Recently, there has been strong interest in multigrid-type hybrid multiscale simulation. As depicted in Fig. 6, a coarse mesh is employed to advance the macroscopic, continuum variable over macroscopic length and time scales. At each node of the coarse mesh, a microscopic simulation is performed on a finer mesh in a simulation box that is much smaller than the coarse mesh discretization size. The microscopic simulation information is averaged (model reduction or restriction or contraction) to provide information to the coarser mesh by interpolation. On the other hand, the coarse mesh determines the macroscopic variable evolution that can be imposed as a constraint on microscopic simulations. Passing of information between the two meshes enables dynamic coupling. 

He, Y., Braatz, R. and Alkire, R. (2007) Effect of Additives on Shape Evolution during Electrodeposition. I. Multiscale Simulation with Dynamically Coupled Kinetic Monte Carlo and Moving-Boundary Finite-Volume Codes. /. Electrochem. Soc., 154, D230-D240. 

Baig, C. and Mavrantzas, V.G. (2009) Multiscale simulation of polymer melt viscoelasticity guided from nonequilibrium statistical thermodynamics atomistic nonequilibrium molecular dynamics coupled with Monte Carlo in an expanded statistical ensemble. Phys. Rev. B, 79, 144302. 

Impressive, highly ordered centimetre-sized fibres are obtained whose synergistic growth mechanism based on the kinetic cross-coupling of a dynamical supramolecular self-assembly and a stabilizing silica mineralization may well be the basis of the synthetic paths used by Nature to obtain its materials with well-defined multiscale architectures in biological systems. 

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,... 

Wavelets and multiscale description of surfaces and interfaces MULTISCALE SIMULATION METHODS FOR SOLIDS Large-scale molecular dynamics methods Coupling methods... 

Abstract We here treat a diffusion problem coupled with water flow in bentonite. The remarkable behavior originates from molecular characteristics of its constituent clay mineral, namely montmorillonite, and we show the behavior based on a unified simulation procedure starting with the molecular dynamic (MD) method and extending the obtained local characteristics to a macroscale behavior by the multiscale homogenization analysis (HA Sanchez-Palencia. 1980). Not only the macroscale effective diffusion property but also the adsorption behavior is well defined based on this method. 

For characterizing the microstructure we use a confocal laser scanning microscope (CLSM). By CLSM we can specify a 3-D configuration under atmospheric condition. Smectite minerals are extremely fine and poorly crystallized, so it is difficult to determine the properties by experiment. We inquire into the physicochemical properties by a molecular dynamics (MD) simulation method. Then, we develop a multiscale homogenization analysis (HA) method to extend the microscopic characteristics to the macroscopic behavior. We show numerical examples of a coupled water-flow and diffusion problem. 

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