Survey of numerical methods for hydraulic transients

The finite difference methods of Lax, Lax-Wendroff, donor cell type, and finite element method using Galerkin procedure with B-splines as approximating functions were compared with the method of characteristics for the solution of water hammer transients as typified by valve closure problems. From the point of view of accuracy, the two step Lax-Wendroff method and the method of characteristics are comparable and produce the best results. The donor cell type and the Galerkin procedure with quadratic B-spline basis as approximating functions display roughly the same accuracy. From the comparison presented, it appears that Galerkin technique offers no substantial advantage over the other finite difference methods except that of ease in handling boundary conditions as compared to finite difference methods.