An Introduction to Multiscale Modeling with Applications

This book collects the slides prepared for the course of Advanced Engineering Thermodynamics (Master of Science in Mechanical Engineering) and those for the course of Multiscale Modelling and Simulation of Molecular and Mesoscopic Dynamics (PhD Program in Energetics), taught in English at Turin Polytechnic. Here, we provide a broad overview on the different topics taught in our classes. Even though not all topics are presented in the same class, students should be able to more easily reconstruct the connections among different phenomena (and scales), build their own mind map and, eventually, find their own way of deepening the subjects they are more interested in. Several engineering applications have been included. This helps in stressing that very different phenomena are described by transport theory and obey the same underlying fundamental laws of engineering thermodynamics. Detailed tutorials are reported, based on open-source codes for the laboratories (Gromacs, Palabos, OpenFoam and Cantera

Fast computation of multi-scale combustion systems

In the present work, we illustrate the process of constructing a simplified model for complex multi-scale combustion systems. To this end, reduced models of homogeneous ideal gas mixtures of methane and air are first obtained by the novel Relaxation Redistribution Method (RRM) and thereafter used for the extraction of all the missing variables in a reactive flow simulation with a global reaction mode

Approximation of slow and fast dynamics in multiscale dynamical systems by the linearized Relaxation Redistribution Method

In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold - SIM). As a result, the demanding problem of constructing SIM of any dimensions is recast into the remarkably simpler task of solving a properly devised ODE system by stiff numerical schemes available in the literature. In the same spirit, a set of equations is elaborated for local construction of the fast subspace, and possible initialization procedures for the above equations are discussed. The implementation to a detailed mechanism for combustion of hydrogen and air has been carried out, while a model with the exact Chapman-Enskog solution of the invariance equation is utilized as a benchmark.Comment: accepted in J. Comp. Phy

Looking for massive carbon capture

Afforestation on drylands can help mitigate climate change through carbon sequestration, but the water and energy implications can hinder implementation. A study now investigates the environmental and economic potential of afforestation enabled by desalination plants powered by renewable electricity

Critical aspects to enable viable solar-driven evaporative technologies for water treatment

Recent studies in passive solar-driven evaporative technologies have introduced a plethora of new materials and devices which promise higher economic and environmental sustainability in water treatment. However, many challenges remain for the effective adoption of such technologies. Here, we identify three main pillars and the corresponding issues which future research activities should focus on to bring the proposed solutions to the next maturity level. Specifically, our analysis focuses on standards for comparing productivity, strategies to overcome the single stage limit, scalability and robustness

The global relaxation redistribution method for reduction of combustion kinetics

An algorithm based on the Relaxation Redistribution Method (RRM) is proposed for constructing the Slow Invariant Manifold (SIM) of a chosen dimension to cover a large fraction of the admissible composition space that includes the equilibrium and the initial state. The manifold boundaries are determined with the help of the Rate Controlled Constrained Equilibrium (RCCE) method, which also provides the initial guess for the SIM. The latter is iteratively refined until convergence and the converged manifold is tabulated. A criterion based on the departure from invariance is proposed to find the region over which the reduced description is valid. The global realization of the RRM algorithm is applied to constant pressure auto-ignition and adiabatic premixed laminar flames of hydrogen-air mixture

The notion of energy through multiple scales: From a molecular level to fluid flows and beyond

In the present paper, we review the consistent definition of macroscopic total energy in classical fluid mechanics, as a function of the microscopic canonical Hamiltonian field, based on a Lennard-Jones model with some spatially varying external field. The macroscopic total energy (sum of mechanical and internal energy) is proved to be equal to the equilibrium ensemble-averaged Hamiltonian. In particular, the conditions for including the effects of the external field both in the macroscopic potential energy and in the internal energy are discussed. {We present the notion of energy as defined in different scientific communities, starting from the standard macroscopic systems all the way down to small ones, which are gaining an increasing popularity

Realizing Symmetry-Breaking Architectures in Soap Films

We show here that soap films—typically expected to host symmetric molecular arrangements—can be constructed with differing opposite surfaces, breaking their symmetry, and making them reminiscent of functional biological motifs found in nature. Using fluorescent molecular probes as dopants on different sides of the film, resonance energy transfer could be employed to confirm the lack of symmetry, which was found to persist on timescales of several minutes. Further, a theoretical analysis of the main transport phenomena involved yielded good agreement with the experimental observations