Coupling atomistic and continuum hydrodynamics through a mesoscopic model: application to liquid water

We have conducted a triple-scale simulation of liquid water by concurrently coupling atomistic, mesoscopic, and continuum models of the liquid. The presented triple-scale hydrodynamic solver for molecular liquids enables the insertion of large molecules into the atomistic domain through a mesoscopic region. We show that the triple-scale scheme is robust against the details of the mesoscopic model owing to the conservation of linear momentum by the adaptive resolution forces. Our multiscale approach is designed for molecular simulations of open domains with relatively large molecules, either in the grand canonical ensemble or under non-equilibrium conditions.Comment: triple-scale simulation, molecular dynamics, continuum, wate

Algorithms for propagating uncertainty across heterogeneous domains

We address an important research area in stochastic multiscale modeling, namely, the propagation of uncertainty across heterogeneous domains characterized by partially correlated processes with vastly different correlation lengths. This class of problems arises very often when computing stochastic PDEs and particle models with stochastic/stochastic domain interaction but also with stochastic/deterministic coupling. The domains may be fully embedded, adjacent, or partially overlapping. The fundamental open question we address is the construction of proper transmission boundary conditions that preserve global statistical properties of the solution across different subdomains. Often, the codes that model different parts of the domains are black box and hence a domain decomposition technique is required. No rigorous theory or even effective empirical algorithms have yet been developed for this purpose, although interfaces defined in terms of functionals of random fields (e.g., multipoint cumulants) can overcome the computationally prohibitive problem of preserving sample-path continuity across domains. The key idea of the different methods we propose relies on combining local reduced-order representations of random fields with multilevel domain decomposition. Specifically, we propose two new algorithms: The first one enforces the continuity of the conditional mean and variance of the solution across adjacent subdomains by using Schwarz iterations. The second algorithm is based on PDE-constrained multiobjective optimization, and it allows us to set more general interface conditions. The effectiveness of these new algorithms is demonstrated in numerical examples involving elliptic problems with random diffusion coefficients, stochastically advected scalar fields, and nonlinear advection-reaction problems with random reaction rates

Mechanics of Materials

All up-to-date engineering applications of advanced multi-phase materials necessitate a concurrent design of materials (including composition, processing routes, microstructures and properties) with structural components. Simulation-based material design requires an intensive interaction of solid state physics, material physics and chemistry, mathematics and information technology. Since mechanics of materials fuses many of the above fields, there is a pressing need for well founded quantitative analytical and numerical approaches to predict microstructure-process-property relationships taking into account hierarchical stationary or evolving microstructures. Owing to this hierarchy of length and time scales, novel approaches for describing/ modelling non-equilibrium material evolution with various degrees of resolution are crucial to linking solid mechanics with realistic material behavior. For example, approaches such as atomistic to continuum transitions (scale coupling), multiresolution numerics, and handshaking algorithms that pass information to models with different degrees of freedom are highly relevant in this context. Many of the topics addressed were dealt with in depth in this workshop