International Journal of Computational Engineering ScienceVol. 03, No. 01, pp. 13-55 (2002) No AccessHIGHER ORDER NUMERICAL METHODS EVALUATION FOR THE COMPUTATION OF ONE DIMENSIONAL FREE SURFACE SHALLOW WATER FLOWSA. I. DELISA. I. DELISDepartment of Applied Mathematics, University of Crete, 71409 Heraklion, Crete, Greece Search for more papers by this author https://doi.org/10.1142/S1465876302000538Cited by:3 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractSeveral 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.Keywords:Finite DifferencesShallow WaterTVDComputational Hydraulics Engineering FiguresReferencesRelatedDetailsCited By 3A finite volume method parallelization for the simulation of free surface shallow water flowsA.I. Delis and E.N. Mathioudakis1 Jul 2009 | Mathematics and Computers in Simulation, Vol. 79, No. 11Application of the HLL Approximate Riemann Solver to One-Dimensional Open Channel Flows with Irregular GeometryXinya Ying and Sam S. Y. Wang26 April 2012Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flowsXinya Ying and Sam S.Y. Wang26 April 2010 | Journal of Hydraulic Research, Vol. 46, No. 1 Recommended Vol. 03, No. 01 Metrics History KeywordsFinite DifferencesShallow WaterTVDComputational Hydraulics EngineeringPDF download