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The one-dimensional (1D) mathematical models of open channel flow considered crucial to water resources development and environmental protection have been used popularly in engineering practice. This 1D model is often known as the Saint-Venant equation system and it considers only the main flow velocity along the river with the assumption of a hydrostatic pressure. However, in many cases, there is effect of river-bed disturbance, and the flow is considered non-hydrostatic pressure. Therefore, in this paper, the authors developed a mathematical model of 1D open channel flow under the influence of the gravitational field, with velocity w^* along gravity acceleration direction at the channel bed. The received governing equations are the more general form of the classic Saint-Venant equation system with the non-hydrostatic pressure.

To solve the derived system of equations, the Taylor-Galerkin finite element method (FEM) with the third order of accuracy was used. The temporal terms were discretized by Taylor expansion series and then the spatial terms were discretized by the Galerkin FEM. In the temporal discretization, the expansion of depth and flow vectors at the time step (n + 1), i.e. (h, Q)_n+1, is a Taylor series expansion over time t at the right of time t = t_n; next, replacing the spatial terms in to this Taylor series was truncated. In the spatial discretization, the second order interpolation function was used. The simulated results based on the proposed numerical scheme showed a good agreement with the experimental data obtained from the physical model built in the National Laboratory for Coastal and River Dynamics in Vietnam.

Taylor-Galerkin; finite element method; one-dimensional mathematical models of open channel flow; velocity along gravity acceleration direction at the channel bed, non-hydrostatic pressure; physical model experiment.