Kinematic wave routing incorporating shock fitting

Abstract

An analytical solution to the kinematic wave approximation for unsteady flow routing is presented. The model allows time‐dependent lateral inflow with piecewise spatial uniformity and can be applied to complex kinematic cascades. Kinematic shocks are considered as manifestations of higher‐order effects such as rnonoclinal flood waves, bores, etc. Within the context of kinematic approximation therefore we retain their dynamic effects by routing the discontinuities as they appear. Certain simplifying assumptions are made which permit closed form solutions and an efficient numerical algorithm, based on the method of characteristics, is employed. The resulting model, called an approximate shock‐fitting scheme, preserves the effect of the shocks without the usual computational complications and compares favorably with an implicit finite difference solution. The efficiency and accuracy of the new method are illustrated by computing a variety of unsteady flows, ranging from simple cascades to complex natural watersheds.

Application of a distributed hydrological model to the design of a road inundation warning system for flash flood prone areas

“…The kinematic wave model, used to transfer the runoff flows on the slopes and in the river system, appears to be often an accurate approximation of the Saint-Venant shallow water equations governing one-dimensional unsteady free surface flows (Borah et al, 1980). An analytical method is used to solve the kinematic wave differential equations (DaluzVieira, 1983) to avoid the disturbing effect of numerical diffusion on the model results.…”

Calibrating a watershed simulation model involving human interference: an application of multi-objective genetic algorithms

“…In this study, the runoff curve number extension is used. The excess rainfall is routed over overland planes and through channel segments using analytical and approximate shock-fitting solutions (Borah et al 1980;Borah 1989) of the kinematic wave Equations (Lighthill & Whitham 1955). Combined subsurface flow, comprised of interflow, tile drain flow and base flow, is computed using a modification to the Sloan et al (1983) kinematic storage equation and using the spatially uniform and temporally varying continuity Equation (Borah et al 2004).…”

Storm Event Flow and Sediment Simulations in Agricultural Watersheds Using DWSM

“…The routing scheme is based on analytical and approximate shock−fitting solutions (Borah et al, 1980) of the continuity and approximate momentum equations. The scheme is robust because of the closed−form solutions.…”

“…It emerged from SEDLAB, the USDA−ARS National Sedimentation Laboratory watershed model (Borah et al, 1980(Borah et al, , 1981, and RUNOFF, the runoff and its constituent simulation model (Borah, 1989a(Borah, , 1989bAshraf and Borah, 1992). In this study, two new schemes were added to the model for routing subsurface and reservoir flows.…”