The paper presents a two-dimensional unsteady-flow model, RBFVM-2D, ba
sed on the finite-volume method with a combination of unstructured tri
angular and quadrilateral grids in a river-basin system. The attractiv
e feature of this model is that it calculate of the mass and momentum
flux across each side of elements as a Riemann problem, which is solve
d using the Osher scheme. This feature enables this model to deal with
the wetting and drying processes for floodplain and wetland studies,
dam breaking phenomena involving discontinuous flows, subcritical and
supercritical flows, and other cases. The computations of tributary in
flows and regulated flows through gates, weirs, and culverts or bridge
s are also included. Sample applications of this model to two dam-brea
k problems showed fairly satisfactory results. Also, this model was ap
plied to a portion of the Kissimmee River Basin in Florida for flow si
mulations and the results agreed well with the field and laboratory da
ta in a physical-model study of this fiver reach conducted at the Univ
ersity of California, Berkeley.