A third-order explicit central scheme for open channel flow simulations

Abstract

A third-order explicit time-stepping model for the simulations in open channels flow is presented. The time discretization of one-dimensional Saint- Venant's basic equations is obtained by Taylor series expansion, formulated in multi-stage approach, whereas the spatial discretization is obtained by finite difference central scheme. First- and second-order models have been obtained by using piecewise constant and piecewise linear MUSCL (monotone upwind scheme for conservation laws) approximations. Afterwards, the third-order model proposed is obtained by a piecewise quadratic polynomial approximation. Using Fourier's linear analysis, the stability and the accuracy of the scheme are investigated. The numerical results, for predicting dam-break in a horizontal and frictionless channel and for the representation of the hydraulic jump in prismatic and non-prismatic channels, with non-uniform bottom slope, are evaluated, and compared with the corresponding analytical and measured solutions.