Survey of numerical methods for hydraulic transients

The finite difference methods of Lax, Lax-Wendroff (two-step), donor cell type and finite-element method using Galerkin procedure with B-splines as approximating functions are 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 Lax methods fair worst. 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