Practical applications and examples highlight this treatment of computational modeling for handling complex flowfields. A reference for researchers and graduate students of many different backgrounds, it also functions as a text for learning essential computation elements. Drawing upon his own research, the author addresses both macroscopic and microscopic features. He begins his three-part treatment with a survey of the basic concepts of finite difference schemes for solving parabolic, elliptic, and hyperbolic partial differential equations. The second part concerns issues related to computational modeling for fluid flow and transport phenomena. In addition to a focus on pressure-based methods, this section also discusses practical engineering applications. The third and final part explores the transport processes involving interfacial dynamics, particularly those influenced by phase change, gravity, and capillarity. Case studies, employing previously discussed methods, demonstrate the interplay between the fluid and thermal transport at macroscopic scales and their interaction with the interfacial transport.