Bridging scales in fluids and materials science

Many problems arising in science, engineering, and technology share the common need to deal with phenomena interacting on a wide range of scales. The thesis focuses on developing coarse-graining methodologies to understand how physical principles or models in a given discipline change across scales. We present coarse-graining methods for two major problems: (1) the passage from Molecular Dynamics (MD) models of fluids to the Navier-Stokes equations, and (2) modeling and simulation of grain growth in polycrystalline materials at different scales.; The goal of the first problem is to construct an intermediate scale model that connects MD simulation of fluids to the Navier-Stokes equations describing its large scale dynamics. The microscopic and macroscopic descriptions of fluids are bridged by taking spatial and temporal averages of atomic quantities. A formal counting method can be applied that transforms evolution of these local averages into surface fluxes and force-related terms. Combining analysis with computer simulation results, the deterministic as well as random parts of these are characterized in terms of local averages, and the spatial and temporal scales. The result is a set of discrete stochastic equations governing the evolution of coarse-grained mass, momentum, and energy, which can be shown to converge to a finite-difference representation of the Navier-Stokes equations in the large scale limit.; The second problem aims at understanding relations and differences between grain growth models at different physical scales or different levels of modeling details, and at constructing accurate and efficient algorithms that benefit from such understandings. In particular, we examine Boundary Tracking and Monte-Carlo simulation of grain growth at the mesoscale, Vertex Models with coarse-grained representation of grain boundaries, Molecular Dynamics modeling of microstructural evolution at the atomic scale. We show that the boundary tracking model of curvature driven growth can be viewed as the large scale limit of the Monte-Carlo model as the underlying lattice of Monte-Carlo is refined, or equivalently as the Monte-Carlo microstructure is coarsened. We propose a new vertex model that offers computational efficiency and produces almost identical statistical properties concerning grain size and interfacial curvature as the boundary tracking model. We also observe some unique features of NO simulation of microstructural evolution and discuss challenges in modeling and simulation of texture and grain boundary character.