Moving Finite Element Solution of Discontinuous Open Channel Flow

Abstract

<p>Over the years, rapidly varying channel flow and discontinuities in the solution of fluid mechanics problems have provided stimulation and challenge to numerical modelers. Traditional finite difference and finite element methods produce accurate but oscillatory solutions. Attempts to selectively eliminate these parasitic waves have been only partially successful in that the cost of a smoother profile was a lower accuracy solution. It is common to employ either internal and external dissipation parameters or a provision of dispersive interface.</p> <p>In this thesis, the problem of rapidly varying open channel flow is represented by a pair of nonlinear partial differential equations which are solved by a powerful moving finite element technique. The method developed in this research is based on the linking of a novel Lagrangian mode solution with the convenience of the Eularian grid at each time step. This second order scheme was employed in solving a variety of devised and reported open channel flow problems with near discontinuities.</p> <p>Comparisons with solutions obtained using the finite difference and finite element methods with Crank-Nicholson centred weightings demonstrates the quality improvements which have been achieved by this moving element scheme. The basic scheme was further generalized in both spatial and temporal dimensions. Sensitivity analysis of these generalized parameters established the grid size relaxations for a variety of problems. The moving element technique solved near discontinuous and gradually varied flow problems both in supercritical and subcritical regimes.</p> <p>An alternate form of Petrov-Galerkin weighting function was tested and found to give promising results. Further experimentation and testing are required before implementation.</p> <p>The robustness of the solution procedure is indicated by the adaptation of the model from the numerical and laboratory experiment stage to field problems. The model was successfully applied to the Teton Dam break flood and flood routing problem in the (Ontario) Grand River basin. Sensitivity analysis with very mild sloped channels with topographical features such as sudden expansions and offchannel storage suggest that the Eulerian-Lagrangian mode algorithm provides the missing link between the fluid mechanics of discontinuities and a practical tool for the modelling of rapidly varying open channel flow.</p>