Time-stepping Padé–Petrov–Galerkin models for hydraulic jump simulation

Four Padé–Petrov–Galerkin models, for numerical computation discontinuous flow in open channels, are proposed in this work. Time discretization, in multi-stage approach of Saint-Venant’s basic equations, is obtained by first- and second-sub-diagonal L-stable Padé approximations in factorized form, whereas the spatial discretization is obtained by the standard Petrov–Galerkin finite element method, with two parameters cubic weight functions. The accuracy of the time-stepping models, formulated in the explicit stages by the unknown mass matrix in lumped form, is investigated by von Neumann’s classical analysis. Then, the adjustment parameter values of the weight functions are obtained in order to give a second-order accuracy to the schemes. Finally, the resulting models produce a clean, sharp jump structure that agrees favorably with the exact solution of the test problems in frictionless and friction channels.