Presents basic techniques and recent progress in numerical combustion while establishing important connections with the underlying combustion basics. Fully updated to reflect the latest advances in combustion research. Mirrors evolution of unsteady simulation methods such as LES codes for partially premixed flames and complex geometry burners. Includes extended descriptions of wave equations in reacting flows, physics of combustion instabilities, acoustic/combustion coupling; and a new chapter devoted to LES in real combustors, including comparisons with experimental data.