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

Viscous coupling based lattice Boltzmann model for binary mixtures

A new lattice Boltzmann model for binary mixtures, which can naturally include both the two-fluid approach and the single-fluid approach, is developed. The model is derived from the continuous kinetic model proposed by Hamel, which independently takes into account self-collisions and cross collisions. The original kinetic model is discussed in order to appreciate that cross collisions realize an internal coupling force, proportional to the diffusion velocity, and an additional coupling effect in the effective stress tensor, proportional to the deformation of the barycentric velocity field. For this reason, Hamel’s model is the natural forerunner of all linearized models based on the two-fluid approach and allows us to describe binary mixtures at different limiting regimes consistently. A discrete lattice Boltzmann model, which recovers the original Hamel’s model with second-order accuracy in both time and space, is proposed. This discrete model can analyze ordinary diffusion, pressure diffusion, and forced diffusion

Link-wise Artificial Compressibility Method

The Artificial Compressibility Method (ACM) for the incompressible Navier-Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the Lattice Boltzmann Method (LBM). The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical computational fluid dynamics, with special emphasis on finite differences (at least in the present paper), at the cost of minor changes. For instance, wall boundaries not aligned with the background Cartesian mesh can be taken into account by tracing the intersections of each link with the wall (analogously to LBM technology). LW-ACM requires no high-order moments beyond hydrodynamics (often referred to as ghost moments) and no kinetic expansion. Like finite difference schemes, only standard Taylor expansion is needed for analyzing consistency. Preliminary efforts towards optimal implementations have shown that LW-ACM is capable of similar computational speed as optimized (BGK-) LBM. In addition, the memory demand is significantly smaller than (BGK-) LBM. Importantly, with an efficient implementation, this algorithm may be one of the few which is compute-bound and not memory-bound. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between the present approach and state of the art methods from the literature is carried out. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accuracy.Comment: 62 pages, 20 figure

Multiple wh-quantifier float in dialectal English

This paper focuses on a dialect of English called Philadelphian Irish English (PhIrE) which allows quantifier float under wh-movement. This dialect also allows multiple quantifiers to be stranded at various stages of intermediate movement, a novel pattern not observed before. Here I focus on the patterns of multiple quantifier float and their restrictions. I propose that single and multiple quantifier float are derived through two different mechanisms: stranding and copying, respectively. Single quantifier float is derived through the standard stranding mechanisms, while wh-phrases in multiple quantifier constructions leave multiple copies which then undergo scattered deletion (See Bošković 2001; Nunes 2004)