As researchers deal with processes and phenomena that are geometrically complex and phenomenologically coupled the demand for high-performance computational fluid dynamics (CFD) increases continuously. The intrinsic nature of coupled irreversibility requires computational tools that can provide physically meaningful results within a reasonable time. This book collects the state-of-the-art CFD research activities and future R and D directions of advanced fluid dynamics. Topics covered include in-depth fundamentals of the Navier-Stokes equation, advanced multi-phase fluid flow, and coupling algorithms of computational fluid and particle dynamics. In the near future, true multi-physics and multi-scale simulation tools must be developed by combining micro-hydrodynamics, fluid dynamics, and chemical reactions within an umbrella of irreversible statistical physics.