Raymond W. Schaffranek — Page 2

USGS1985

MODEL FOR SIMULATING FLOODS IN RIVERS.

A one-dimensional model capable of simulating flood wave propagation in a river or network of channels is presented. The computer model is programmed to provide maximum flexibility in the adaptation of channel geometry, the specification of conveyance properties, and the treatment of boundary conditions. An equation transformation procedure is employed in the model to minimize computer storage and execution time requirements by reducing the order of the resultant coefficient matrices. Based on a four-point implicit finite-difference approximation of the governing, nonlinear, flow equations, the model can be used to simulate the wide range of flow conditions typically encountered in various natural waterbody systems. Two particular applications are presented to demonstrate the computational features and capabilities of the model in the simulation of flood wave propagation.

Conference Paper↗

USGS1981

A model for simulation of flow in singular and interconnected channels

A one-dimensional numerical model is presented for simulating the unsteady flow in singular riverine or estuarine reaches and in networks of reaches composed of interconnected channels. The model is both general and flexible in that it can be used to simulate a wide range of flow conditions for various channel configurations. The channel geometry of the network to be modeled should be sufficiently simple so as to lend itself to characterization in one spatial dimension. The flow must be substantially homogenous in density, and hydrostatic pressure must prevail everywhere in the network channels. The slope of each channel bottom ought to be mild and reasonably constant over its length so that the flow remains subcritical. The model accommodates tributary inflows and diversions and includes the effects of wind shear on the water surface as a forcing function in the flow equations. Water-surface elevations and flow discharges are computed at channel junctions, as well as at specified intermediate locations within the network channels. The one-dimensional branch-network flow model uses a four-point, implicit, finite-difference approximation of the unsteady-flow equations. The flow equations are linearized over a time step, and branch transformations are formulated that describe the relationship between the unknowns at the end points of the channels. The resultant matrix of branch-transformation equations and required boundary-condition equations is solved by Gaussian elimination using maximum pivot strategy. Five example applications of the flow model are illustrated. The applications cover such diverse conditions as a singular upland river reach in which unsteady flow results from hydropower regulations, coastal rivers composed of sequentially connected reaches subject to unsteady tide-driven flow, and a multiply connected network of channels whose flow is principally governed by wind tides and seiches in adjoining lakes. The report includes a listing of the FORTRAN IV computer program and a description of the input data requirements. Model supporting programs for the processing and input of initial and boundary-value data are identified, various model output formats are illustrated, and instructions are given to permit the production of graphical output using the line printer, electromechanical pen plotters, cathode-ray-tube display units, or microfilm recorders.

Techniques of Water-Resources Investigations↗