Numerical solutions of the shallow water equations with discontinuous bed topography Export

@article{citeulike:1923540, abstract = {A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with zb- for the left and zb+ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam-break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright {\copyright} 2002 John Wiley \& Sons, Ltd.}, address = {Centre for Mathematical Modelling and Flow Analysis, The Manchester Metropolitan University, Manchester M1 5GD, U.K.}, author = {Zhou, J. G. and Causon, D. M. and Ingram, D. M. and Mingham, C. G.}, citeulike-article-id = {1923540}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/fld.243}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/90512154/ABSTRACT}, doi = {10.1002/fld.243}, journal = {International Journal for Numerical Methods in Fluids}, keywords = {numerical-methods, saint-venant}, number = {8}, pages = {769--788}, posted-at = {2007-11-15 18:27:02}, priority = {0}, title = {Numerical solutions of the shallow water equations with discontinuous bed topography}, url = {http://dx.doi.org/10.1002/fld.243}, volume = {38}, year = {2002} }

TY - JOUR ID - citeulike:1923540 L3 - citeulike-article-id:1923540 N2 - A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with zb- for the left and zb+ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam-break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd. IS - 8 JF - International Journal for Numerical Methods in Fluids AD - Centre for Mathematical Modelling and Flow Analysis, The Manchester Metropolitan University, Manchester M1 5GD, U.K. EP - 788 TI - Numerical solutions of the shallow water equations with discontinuous bed topography VL - 38 SP - 769 KW - numerical-methods KW - saint-venant AU - Zhou, JG AU - Causon, DM AU - Ingram, DM AU - Mingham, CG PY - 2002/// UR - http://dx.doi.org/10.1002/fld.243 ER -