Computational fluid dynamics This reference concentrates on advanced techniques of computational fluid dynamics. It offers illustrations of new developments of classical methods as well as recent methods that appear in the field. Each chapter takes a tutorial approach and covers a different method or application. Topics discussed include finite volumes weighted residuals spectral methods smoothed particle hydrodynamics (SPH) application of SPH methods to conservation equations finite volume particle methods (FVPM) and numerical algorithms for unstructured meshes. The authors offer theory algorithms and applications for each topic This book concentrates on the numerical of computational fluid mechanics (including mathematical models in computational fluid mechanics numerical methods in computational fluid mechanics finite volume finite difference finite element spectral methods smoothed particle hydrodynamics methods mixed element volume methods free surface flow) followed by some focus of new development of classical methods and to the recent methods appearing in this field. The topics covered in this book are wide ranging and demonstrate the extensive use in computational fluid mechanics. The book opens with a presentation of the basis of finite volume methods weighted residual methods and spectral methods. These specific approaches are particularly important in the context of fluid mechanics where they cover complementary domains of application. A unified point of view is introduced based on the weighted residuals description. Chapter 1 presents the finite volume method. Chapter 2 describes the principles of weighted residuals methods. Chapter 3 introduces the spectral method. Chapter 4 presents computational fluid dynamics based on the smoothed particle hydrodynamics (SPH) method. Chapter 5 focuses on an improved SPH method based on an arbitrary Lagrange Euler (ALE) formalism. Chapter 6 using the similarity with the finite volumes method introduces high order flux schemes between interacting points. Chapter 7 presents some numerical methods for compressible computational fluid dynamics. Chapter 8 deals with the prediction of turbulent complex flows as occur. Chapter 9 discusses the modeling and numerical simulation of free surface flows