Complex fluid flows are encountered widely in nature, in living beings, and in engineering practice. These flows often involve both geometric and dynamic complexity and present problems that are difficult to analyze because of their wide range of length and time scales, as well as their geometric configuration. This book describes some newly developed computational techniques and modeling strategies for analyzing and predicting complex transport phenomena. It summarizes advances in the context of a pressure-based algorithm. Among methods discussed are discretization schemes for treating convection and pressure, parallel computing, multigrid methods, and composite, multiblock techniques. With respect to physical modeling, the book addresses issues of turbulence closure and multiscale, multiphase transport from an engineering viewpoint. Both fundamental and practical issues are considered, along with the relative merits of competing approaches. The final chapter is devoted to practical applications that illustrate the advantages of various numerical and physical tools. Numerous examples are given throughout the text. Mechanical, aerospace, chemical, and materials engineers can use the techniques presented in this book to tackle important, practical problems more effectively.