A multiple grid algorithm for one-dimensional transient open channel ̄ows

Numerical modeling of open channel ̄ows with shocks using explicit ®nite di€erence schemes is constrained by the choice of time step, which is limited by the CFL stability criteria. To overcome this limitation, in this work we introduce the application of a multiple grid algorithm to the ®eld of computational hydraulics. By coupling this algorithm to a second-order accurate MacCormack scheme, we demonstrate that the solution can be accelerated to the desired transient state. The present formulation has been tested to simulate shocks arising from sudden closure of a sluice gate and for ̄ows accompanied with a hydraulic jump. The close agreement between the obtained results and the theoretical ®ndings indicates the reliability of the proposed algorithm. Ó 2000 Elsevier Science Ltd. All rights reserved.