| In this work the Godunov method, modified by Colella and Woodward for gas-dynamics discontinuous flows, is adapted to discontinuous open-channel flow problems, in particular to instantaneous dambreaks. Some of the most commonly used numerical methods for discontinuous problems are reviewed, showing the need for a new type of algorithm which would be able to cope efficiently with mixed flow regimes and very strong shocks in non-prismatic channels.;The proposed Godunov method is introduced through application to two scalar problems: the linear advection equation and Burgers' equation. The one-dimensional open-channel flow equations (the de St. Venant equations) are then solved with two variants of the Godunov method: one based on linear interpolation, the other on Colella and Woodward's piecewise parabolic interpolation (PPM). The latter approach is first applied to open-channel flow problems in this work. To evaluate the utility of the proposed Godunov methods (linear and PPM) comparisons with the analytical solution, the shock-fitting method of characteristics, the Preissmann, Lax-Wendroff and MacCormack methods are presented. Both Godunov methods agree well with the analytical solutions, and perform significantly better than the other compared methods, in solving discontinuous problems.;Guidance for generalization of the Godunov method to two-dimensional open-channel flow problems is also presented, as well as some suggestions for the possible future applications of the one-dimensional algorithm in an industrial code. |
