انجمن هیدرولیک ایران
نشریه هیدرولیک
2345-4237
4
1
2009
05
22
The Analytical and Numerical Solutions of the Shallow Water Equations with the Concentrated Discontinuities in the Bed
حل تحلیلی و عددی معادلات آبهای کم عمق با ناپیوستگی های متمرکز در بستر
1
13
85509
10.30482/jhyd.2009.85509
FA
محبوبه
جمعه زاده
محمدرضا
جعفرزاده
Journal Article
2009
03
23
In this article the influence of the concentrated bed discontinuities (i.e. raising or falling steps) on the<br />solution of the Reimann problem in the shallow water equations is studied. First, the analytical<br />solution of one-dimensional dambreak problem, using the mass-momentum equations over a<br />continuous flat and frictionless bed is reviewed. Next this solution is extended to a discontinuous bed<br />(i. e. a step), using the mass momentum equations at the continuous places and the mass-energy<br />equations at the discontinuities. Then, for the first time, the dambreak problem over a rectangular<br />bump is solved, analytically. In the next section, the mass-momentum equations are numerically<br />solved over the bump. For the discretisation of these equations over the flat continuous bed, the finite<br />volume Roe-TVD scheme with a minmod slope limiter is applied. At the discontinuities, however, the<br />mass-energy equations are discretised. The numerical results are found close to the analytical solution.<br />Finally, the dam break problem in a cavity is similarly investigated both analytically and numerically.
http://jhyd.iha.ir/article_85509_2d1a912fb1e5154926777c48df49c4fb.pdf