An algorithm for routing unsteady flows in urban drainage networks

Since flow in an urban drainage network is usually unsteady, the routing of hydrographs through a network is an important aspect of the design and analysis of urban drainage networks. The use of numerical solution of the Saint Venant equations to determine the propagation of unsteady flows through pipes has been validated by many researchers during the previous two decades. Amongst the many numerical techniques which have been developed for the analysis of unsteady flows in open channels is the four-point implicit finite difference scheme, commonly referred to as the Amein scheme. Use ofthe Amein requires the solution of C x Δv = — R where C is a large sparse n x n matrix and Δv and R are nx column vectors. The proposed algorithm uses the properties ofthe drainage network to develop an efficient algorithm for the solution of C x Δv = –l R . This algorithm is based upon partitioning and decomposing the coefficient matrix C . As an additional advantage, the proposed solution algorithm enables the determination ofthe water surface level within a manhole and, hence, the possibility of surcharge at a manhole. An example urban drainage network is analysed showing the use ofthe proposed solution algorithm.