On the Use of Explicit Methods of Solution of the Saint Venant Equations for open Channel Flow

Abstract

Explicit methods of solution, of the Saint Venant equations for open channel flow, have not been favoured for use in practice by some engineers. The reason, given for this disfavour, is that the observance of the so called Courant condition for stability imposes a severe restriction on the size of the time step used at each stage of the computation, even though the acceptable accuracy may not warrant the use of such small time steps, and that this in turn results in large computation times. The limitation, on the size of the time steps seems, to the writer, to stem indirectly from an assumption that is implicit in the procedure normally used. This assumption seems to be that in the computation of the dependent variables at a grid point on the new time level, its domain of dependence should lie within the adjoining cells of the grid used. This paper shows how, when this assumption is relaxed, it is possible to use arbitrary time steps without violating the essence of the Courant condition.