Unsteady Flow Analysis in Large-scale Canal Networks Using the Implicit Finite Difference Model with Computational Ordering Procedures

Abstract

A systematic modeling method and an efficient flow condition analysis algorithm inlarge-scale canal networks using the Preissmann implicit scheme are proposed. The results are shown as follows.
1) The modeling is generally complicated in case of computing unsteady flows in canal networks with the Preissmann scheme. However, this problem can be simplified by means of disconnecting the looped network. This procedure means that the looped network is considered to be a branched one. The branched network is represented by an oriented graph, and the topological sort technique is applied to it in order to decide the order of computation for the efficient sweep algorithm.
2) The large-scale simultaneous linear equations derived from the Preissmann scheme are solved by a sweep algorithm for a branched network and low dimensional simultaneous linear equations. The algorithm is certified with a simple network model, which has 57 grid points for computations. The computational cost depends on the configuration of the canal network, and it decreases according as the grid points' ratio of loops to whole networks and the number of detachedcanals decrease. The proposed method is enough of practical use, because the computational cost for the simple network model is equal to Gauss method for a sparse matrix.
3) The method is applied for flow condition analysis of a large-scale canal network which has 539 grid points for computations, in low-lying paddy field basin, and the calculated values are closely consistent with the observed results. The computational cost is 5.5 times larger than the simple network model's one per the same time steps. It is suppressed, because the grid points ratio of loops to whole networks is low in comparison with the simple network model. Meanwhile, the computational cost using Gauss method increases drastically, namely, it is 90.5 times larger than the simple network model. The reason is that many non-diagonal elements of the coefficient matrix appear by the increase of canal junctions. These results indicate that the proposed method is excellent for flow condition analysis in large-scale networks using the Preissmann scheme.