Computer Simulation of Unsteady Flows in Waterways

The set of nonlinear, partial differential equations describing one-dimensional, translatory wave motion provides the mathematical model used in the development of three distinctly different techniques for the digital simulation of unsteady flows in rivers and estuaries. The first technique is based upon power series methods and uses a Maclaurin series expansion of the partial differential equations. The second technique is premised upon the method of characteristics and uses a numerical evaluation process at successive specified time intervals. The third simulation technique relies upon an implicit method of flow simulation wherein the partial differential equations are transformed to finite difference equations. The effects of fluid friction, variable channel geometry, wind, lateral inflow or outflow, the Coriolis celeration, as well as overbank storage, are included. Flows are considered to be of homogenous density. Each of the methods is programmed for high speed digital computer. Comparisons of the simulated flows obtained using each of the simulation techniques with the appropriate field measured transient flows indicate generally good agreement.