Stability of a General Preissmann Scheme

The stability and convergence characteristics of a four‐point implicit finite‐difference scheme due to Preissmann, which has been widely used in open‐channel flow modeling, are examined. The analysis is made for a general linear hyperbolic system of n first‐order equations, but is restricted to the homogeneous or frictionless case. In particular, the effect of a weighting factor in space, as well as in time, is considered. The specific case of unsteady sedimenttransport modeling, which conventionally results in a third‐order system, is discussed with particular reference to its singularly perturbed nature. Recommendations for practical computations are made.