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Higher Order Numerical Methods Evaluation for the Computation of One Dimensional Free Surface Shallow Water Flows

Several explicit high resolution TVD methods and their detailed application to steady and unsteady one-dimensional free surface channel flow problems are presented. Some of these methods are widely presented in the literature. Their evaluation is based on computations performed for steady state benchmark problems with analytical solutions and for a wide range of cases, which include friction, nonuniform bed slopes, hydraulic jumps and non-prismatic channel cross sections. Results for the classical benchmark problem of an idealised dam-break are also presented. The results obtained by the various TVD methods are compared with each other and the exact solutions, providing insight into the limitations of the methods along with their relative performances in robustness and accuracy. Some subtle points of the methods and the effects of selecting different options for certain methods are emphasized.