Review of the key notions in transport phenomena. Classification of numerical methods for the solution of heat, mass and momentum transfer. Review of modeling and classical numerical methods (finite difference/volume/element). Lattice Boltzmann method (LBM). Smoothed particle hydrodynamics (SPH). Discrete element method (DEM) for the simulation of granular flows. Development, principles and implementation of specialized methods, algorithmic considerations and applications. Advantages and disadvantages of the various methods. CFD-DEM coupling for solid-fluid applications. Introduction to high performance scientific computing. Principles of verification and validation. Project applied to heat, mass and momentum transfer problems.