@article { author = {Jomehzadeh, M. and Jafarzadeh, M.R.}, title = {The Analytical and Numerical Solutions of the Shallow Water Equations with the Concentrated Discontinuities in the Bed}, journal = {Journal of Hydraulics}, volume = {4}, number = {1}, pages = {1-13}, year = {2009}, publisher = {Iranian Hydraulic Association}, issn = {2345-4237}, eissn = {2645-8063}, doi = {10.30482/jhyd.2009.85509}, abstract = {In this article the influence of the concentrated bed discontinuities (i.e. raising or falling steps) on thesolution of the Reimann problem in the shallow water equations is studied. First, the analyticalsolution of one-dimensional dambreak problem, using the mass-momentum equations over acontinuous flat and frictionless bed is reviewed. Next this solution is extended to a discontinuous bed(i. e. a step), using the mass momentum equations at the continuous places and the mass-energyequations at the discontinuities. Then, for the first time, the dambreak problem over a rectangularbump is solved, analytically. In the next section, the mass-momentum equations are numericallysolved over the bump. For the discretisation of these equations over the flat continuous bed, the finitevolume Roe-TVD scheme with a minmod slope limiter is applied. At the discontinuities, however, themass-energy equations are discretised. The numerical results are found close to the analytical solution.Finally, the dam break problem in a cavity is similarly investigated both analytically and numerically.}, keywords = {}, title_fa = {حل تحلیلی و عددی معادلات آبهای کم عمق با ناپیوستگی های متمرکز در بستر}, abstract_fa = {}, keywords_fa = {}, url = {https://jhyd.iha.ir/article_85509.html}, eprint = {https://jhyd.iha.ir/article_85509_2d1a912fb1e5154926777c48df49c4fb.pdf} }