Introduction Governing Equations: Compressible and Incompressible Formulations Turbulence and Direct Numerical Simulation (DNS) Large-Eddy Simulation (LES) Numerical Treatment of Boundary Conditions Inflow and Outflow Boundary Conditions Wall Boundary Conditions Other Boundary Conditions Discrete Time Integration Methods High-Order Runge¿Kutta (RK) Methods Linear Multistep Methods: Adams¿Bashforth and Adams¿Moulton Methods Other Time Integration Methods DNS of Incompressible Flows Sample Results: DNS of Channel Flows Numerical Features: DNS of Incompressible Flows DNS of Compressible Flows Sample Results: DNS of Compressible Jet Flows Numerical Features: High-Order Schemes for Spatial Discretization LES of Incompressible Flows Sample Results: LES of Incompressible Flows in Complex Geometries Subgrid Scale Modeling of Incompressible Flows Numerical Features: LES on Unstructured Grids and Immersed Boundary Technique for Complex Geometries LES of Compressible Flows Sample Results of LES of Compressible Flows Subgrid-Scale Modeling of Compressible Flows and Implicit Large-Eddy Simulation (ILES) Further Topics and Challenges in DNS and LES Multiscale Flow Simulations Challenges in DNS and LES: Complex Geometry and SGS Modeling Hybridization: Detached Eddy Simulation (DES) Appendix: Supplementary Material: FORTRAN 90 Routines of the Finite Difference Schemes Index References appear at the end of each chapter.