The course aims at introducing the main ideas associated to numerical computing for energy-related problems, where heat and mass transfer play a significant role. The different scales, from nano- to macro-, are considered. For each scale, examples of the respective models, methods and tools are provided and simple applications are presented. The ubiquitous question of the quality assurance (verification&validation) of the solution is addressed.

Foundations of Mathematics and Physics, Fluid dynamics and Thermodynamics

Introduction to computing. Identification of suitable model, method, tool, platform. Verification&validation of the solution. The nano-scale: fundamentals of energy transport by principal energy carriers: electron; phonon; fluid particle; photon. Phonons: molecular dynamics (MD) simulations; Kapitza resistance. Fluid particles: statistical thermodynamics; fluid dynamic continuum limit. Photons: radiative transfer equation. The main tools: GROMACS, LAMMPS. The meso-scale (Computational Fluid Dynamics, CFD): Convection/Diffusion. The theory of the conservation laws and the Navier-Stokes equations. Incompressible vs. compressible flow problems. Laminar flows and theory of instability of laminar flows. Modeling of turbulence with advanced CFD. Mesh generation. Main features of the numerical schemes. Method of the characteristics for the Euler equations and numerical treatment of shocks. The main tools: ANSYS Fluent, StarCCM+, OpenFoam. The macro-scale: System-level models. Object-oriented programming. The main tools: Modelica, Amesim, GT-POWER. Approach to multi-scale problems.

Mixed mode

Written report presentation

P.D.2-2 - June