This is an introductory course to computational methods for fluid dynamics. Following a preface to numerical simulation and a review of the governing equations for mass, momentum, and energy, the structure and mathematical behaviors of partial differential equations will be discussed, which are classified as hyperbolic, parabolic, and elliptic types. A discretization scheme to approximate the mathematical models, i.e. the finite-difference method, will be described along with the analyses for the resulting errors and stability; they are followed by the strategies of allocation and transformation of grids. Some typical CFD techniques will then be illustrated, in terms of various schemes suited for different categories of PDE’s. With sufficient background of the elementals, we shall work on real problems for solving the Navier-Stokes equations on the basis of pressure correction approaches. The students will have an opportunity to practice coding and simulating flow field. Various methods of discretization other than the finite-difference approach, such as finite-volume method and finite-element method, would be briefly mentioned if time is available.