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, the finite-difference method, is
described along with the analyses for the resulting errors
and stability, followed by strategies of allocation and
transformation of grids. Some simple CFD techniques will
then be illustrated, in terms of various schemes suited
for different categories of PDE’s. Various methods of
discretization other than the finite-difference approach,
such as finite-volume method and finite-element method,
shall be briefly mentioned if time is available.