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Article information
2019 , Volume 24, ¹ 1, p.7-27
Demirel D.I., Iafrati A., Korobkin A., Yilmaz O.
Asymptotic behaviour of dam break flow for small times
Two dimensional impulsive flow of a fluid is studied within the potential flow theory. Initially the fluid is at rest and is held on one side of a vertical plate. The plate is withdrawn suddenly and gravity driven flow of the fluid starts. Attention is paid to the singular behaviour of the velocity field at the bottom point, where the vertical free surface meets the rigid bottom. The linear problem is solved by the Fourier series method. An inner region solution is found using Mellin transform at the bottom point. The jet formation is observed at the bottom point. Also the discontinuity at the upper corner point is dealt with Lagrangian variables. For the second order outer problem, domain decomposition method is used. Comparison of the shapes of the free surfaces near the upper corner point with leading and second order solutions shows that the second order outer solution outer makes a larger difference in the vertical free surface than in the horizontal portion, compared with leading order solution.The complete picture of the shapes of the free surfaces using Lagrangian description for the upper part and Eulerian description for the bottom part at the second order is obtained.
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Keywords: dam-break flow, free-surface flow, matched asymptotic expansions, domain decomposition method
doi: 10.25743/ICT.2019.24.1.002
Author(s):
Demirel Damla Isidici
PhD.
Position: Lecture
Office: Izmir Institute of Technology
Address: 35430, Turkey, Izmir
Phone Office: (900)232 244 05 00
E-mail: damlaisidici@gmail.com
Iafrati Alessandro
PhD.
Position: Research Scientist
Office: National Research Council of Italy Institute of Marine engineering
Address: 00128, Italy, Roma, Via di Vallerano 139
Phone Office: (39) 06 502991
E-mail: alessandroiafrati@cnr.it
Korobkin Alexander
Dr. , Professor
Position: Professor
Office: University of East Anglia, School of Mathematics, Norwich, UK,
Address: United kingdom, Norwich, Roma, Via di Vallerano 139
Phone Office: (440) 1603 593869
E-mail: A.Korobkin@uea.ac.uk
Yilmaz Oguz
PhD.
Position: Professor
Office: Izmir Institute of Technology
Address: 35430, Turkey, Izmir, Via di Vallerano 139
Phone Office: (900)232 7507751
E-mail: oguzyilmaz@iyte.edu.tr
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Bibliography link:
Demirel D.I., Iafrati A., Korobkin A., Yilmaz O. Asymptotic behaviour of dam break flow for small times // Computational technologies. 2019. V. 24. ¹ 1. P. 7-27
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