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This paper presents three approximate Riemann solver schemes, namely: the flux vector splitting (FVS), the flux difference splitting (FDS), and the Osher scheme. Originally used to solve the Euler equations in aerodynamic problems, these Riemann solvers based on the characteristic theory are used in the finite volume method (FVM) for solving the two-dimensional shallow water equations. The three solvers are compared in this paper according to theoretical development, difference schemes, practical applications to shock wave problems, and sensitivity analysis on the computational stability of the methods. The effects of changes in bed elevations on the solutions are also investigated. Comparison of numerical and analytical solutions indicates that very good agreement can be obtained by all three approximate Riemann solvers. Differences in accuracy, computer time, and numerical stability among the three schemes are not significant. For practical purposes, all of them can satisfactorily simulate the hydraulic phenomena in subcritical and supercritical flows as well as in smooth and discontinuous flows, especially shock wave modeling. These solvers are useful for studying levee failure or dam break due to extreme flood events, or the sudden opening or closing of sluice gates in a channel.

The paper presents a two‐dimensional unsteady‐flow model, RBFVM‐2D, based on the finite‐volume method with a combination of unstructured triangular and quadrilateral grids in a river‐basin system. The attractive 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 solved using the Osher scheme. This feature enables this model to deal with the wetting and drying processes for flood‐plain and wetland studies, dam breaking phenomena involving discontinuous flows, subcritical and supercritical flows, and other cases. The computations of tributary inflows and regulated flows through gates, weirs, and culverts or bridges are also included. Sample applications of this model to two dam‐break problems showed fairly satisfactory results. Also, this model was applied to a portion of the Kissimmee River Basin in Florida for flow simulations and the results agreed well with the field and laboratory data in a physical‐model study of this ri...

The use of derived distributions to predict flood frequency is relatively new and requires refinement and improvement. This paper reports another effort to obtain and test a derived flood‐frequency distribution, applicable to small watersheds in which overland flow is considered an important runoff component. Watersheds are conceptualized as first‐order streams with two symmetrical planes. The kinematic wave theory is used to obtain expressions to compute peak discharge and time to peak, as functions of effective precipitation variables and watershed parameters, for four different runoff cases. These cases are formulated according to whether or not there is concentration on the overland flow plane and in the stream. Some of these expressions are subsequently improved using regression analysis and kinematic wave simulated results. The probabilistic model for rainfall characteristics and the infiltration model are taken from results presented previously in the literature for other derived flood‐frequency di...