An Optimized and Scalable Algorithm for the Fast Convergence of Steady 1-D Open-Channel Flows

Abstract

Calculating an open-channel steady flow is of main interest in many situations; this includes defining the initial conditions for the unsteady simulation or the computation of the water level for a given discharge. There are several applications that require a very short computation time in order to envisage a large number of runs, for example, uncertainty analysis or optimization. Here, an optimized algorithm was implemented for the fast and efficient computation of a 1-D steady flow. It merges several techniques: a pseudo-time version of the Saint-Venant equations, an evolutionary domain and the use of a non-linear Krylov accelerator. After validation of this new algorithm, we also showed that it performs well in scalability tests. The computation cost evolves linearly with the number of nodes. This was also corroborated when the execution time was compared to that obtained by the non-linear solver, CasADi. A real-world example using a 9.5 km stretch of river confirmed that the computation times were very short compared to a standard time-dependent computation.

Shallow Water Equations in Hydraulics: Modeling, Numerics and Applications

“…In [9], the authors introduced several innovations, including the use of the non-linear Krylov accelerator in open-channel flows, an evolutionary domain algorithm and the use of CasADi to solve steady 1D flows using the Saint-Venant model equations. These improvements led to an algorithm that is able to quickly solve steady open-channel flows.…”