The aim of this talk is to introduce a flow/flood simulation system
which is designed to simulate coupled surface and subsurface flow
problems arising from flood prediction and control. The mathematical
and computational challenges are: (1) model deveoplement and model
reduction, (2) numerical approximation for shallow water equations
with complex physics, (3) algorithm design, (4) computer
simulation/implementation, and (5) validation. The first four
challenges shall be discussed in this talk, and particularly emphasis
will be given to the model development and algorithm design. The talk
should be accessible to general audience in applied/computational
mathematics and hydraulogy.