Exploring new variations of classical methods as well as recent approaches appearing in the field Computational Fluid Dynamics demonstrates the extensive use of numerical techniques and mathematical models in fluid mechanics. It presents various numerical methods including finite volume finite difference finite element spectral smoothed particle hydrodynamics (SPH) mixed-element-volume and free surface flow. Taking a unified point of view the book first introduces the basis of finite volume weighted residual and spectral approaches. The contributors present the SPH method a novel approach of computational fluid dynamics based on the mesh-free technique and then improve the method using an arbitrary Lagrange Euler (ALE) formalism. They also explain how to improve the accuracy of the mesh-free integration procedure with special emphasis on the finite volume particle method (FVPM). After describing numerical algorithms for compressible computational fluid dynamics the text discusses the prediction of turbulent complex flows in environmental and engineering problems. The last chapter explores the modeling and numerical simulation of free surface flows including future behaviors of glaciers. The diverse applications discussed in this book illustrate the importance of numerical methods in fluid mechanics. With research continually evolving in the field there is no doubt that new techniques and tools will emerge to offer greater accuracy and speed in solving and analyzing even more fluid flow problems.