Dynamically coupled multiscale simulation

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. 

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

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. 

Coupling Atomistic and Continuum Length Scales in Heteroepitaxial Systems Multiscale Molecular-Dynamics/Finite-Element Simulations of Strain Relaxation in Si/Si3N4 Nanopixels. 

Multiscale Simulation from Atomistic to Continuum-Coupling Molecular Dynamics (MD) with the Material Point Method (MPM). 

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. 

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... 

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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