Simulation of overland flow has significant impact on the economic and
urban development for the nation. Most of the existing simulation
models are based on approximate or greatly simplified forms of the
Saint Venant equations and the subsurface flow equation obtained from
the Darcy's law. An ideal model for the simulation of two dimensional
overland flow is expected to handle fluid bodies and simulating
regions of arbitrary shape. The features that make models useful for
practical applications include the ability to handle wetting and
drying; the ability to simulate fluid flow through structures such as
weirs, gates and culverts; and the ability to handle tributary and
slough inflows.  The modeling system may combine an overland flow
model, a channel flow model, an infiltration model, a sewer flow model
(in urban areas), and a model linking surface flow and sewer flow.

This talk will discuss some of the models and their numerical
treatments by finite element methods. In particular, a numerical
scheme will be presented for the Stokes equation with stability and
convergence analysis.