Abstract
An explicit numerical algorithm for solving two-dimensional system of shallow-water equations is presented. The algorithm is based on the control volume method with recording mass and momentum fluxes through the faces of the volume with the use of an approximate solution of the Riemann problem. A numerical solution is compared with analytical solutions for a flow over a bottom step and with data of laboratory experiments in a flume with a sloped bed or a bed with an obstacle.
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REFERENCES
Veksler, A.B., Ivashintsov, D.A., and Stefanishin, D.V., Nadezhnost’, sotsial’naya i ekologicheskaya bezopasnost’ gidrotekhnicheskikh ob’‘ektov: otsenka riska i prinyatie reshenii (Reliability and Social and Environmental Safety of Hydraulic-Engineering Structures: Risk Assessment and Decision Making), St. Petersburg, 2002.
Girgidov, A.A., Modeling of Oil Spreading after a Failure of Oil Storage, Tr. V mezhdunar. konf. “Akvaterra” (Proc. V Intern. Conf. “Aquaterra”), St. Petersburg, 2002, pp. 45–46.
Klimovich, V.I. and Prokof’ev, V.A., Numerical Modeling of Interaction between Open Flows and Obstacles, Tr. Mezhdunar. konf. “Vodnye problemy-2001” (Proc. Intern. Conf. “Water Problems”), Yerevan, 2001, pp. 413–416.
Kulikovskii, A.G., Pogorelov, N.V., and Semenov, A.Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii (Mathematical Problems of Numerically Solving Hyperbolic Systems of Equations), Moscow: Fizmatlit, 2001.
Prokof’ev, V.A., Modern Numerical Schemes for Modeling Rapid Flows and Dam-Break Waves Based on the Control Volume Method, Gidrotekh. Stroit., 2002, no. 7, pp. 22–29.
Prokof’ev, V.A., Modeling the Consequences of Hydrodynamic Accidents: Numerical Algorithm and Software Implementation, Tr. V mezhdunar. konf. “Akvaterra” (Proc. V Intern. Conf. Aquaterra), St. Petersburg, 2002, pp. 118–119.
Alcrudo, F. and Benkhaldoun, F., Exact Solutions to the Riemann Problem of the Shallow Water Equations with Bottom Step, Computers Fluids, 2001, vol. 30, pp. 643–671.
Atzeni, A., Balzano, A., Falconer, R.A., et al., Comparison of Shallow Water Flow Models with Accurate Treatment of Flooding and Drying, Proc. XXIX IAHR Congr., Peking, 2000, pp. 211–222.
Aureli, F., Mignosa, P., and Tomirotti, M., Dam-Break Flows in Presence of Abrupt Bottom Variations, Proc. XXVIII IAHR Congr., Graz, 1999, pp. 163–171.
Aureli, F., Mignosa, P., and Tomirotti, M., Numerical Simulation and Experimental Verification of Dam-Break Flows with Shocks, J. Hydraulic Res., 2000, vol. 38, no.3, pp. 197–200.
Delis, A.I., Skeels, C.P., and Ryrie, S.C., Evaluation of Some Approximate Riemann Solvers for Transient Open Channel Flows, J. Hydraulic Res., 2000, vol. 38, no.3, pp. 217–231.
Nujic’, M., Efficient Implementation of Non-Oscillatory Schemes for the Computation of Free-Surface Flows, J. Hydraulic Res., 1995, vol. 33, no.1, pp. 101–111.
Sanders, B.F., High Resolution and Non-Oscillatory Solution of the St.Venant Equations in Non-Rectangular and Non-Prismatic Channels, J. Hydraulic Res., 2001, vol. 39, no.3, pp. 236–244.
Zuhua, C., Guangqian, W., and Zhishi, W., Numerical Solution of the Two-Dimensional Unsteady Depth-Averaged Flow and Solute Transport, Proc. XXIX IAHR Congr., Peking, 2000, pp. 192–205.
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Translated from Vodnye Resursy, Vol. 32, No. 3, 2005, pp. 282–294.
Original Russian Text Copyright © 2005 by Prokof’ev.
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Prokof’ev, V.A. Two-Dimensional Horizontal Numerical Model of Open Flow over a Bed with Obstacles. Water Resour 32, 252–264 (2005). https://doi.org/10.1007/s11268-005-0034-z
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DOI: https://doi.org/10.1007/s11268-005-0034-z