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Article information
2015 , Volume 20, ¹ 5, p.214-232
Shokin Y.I., Rychkov A.D., Khakimzyanov G.S., Chubarov L.B.
On numerical methods for solving run-up problems. I. Comparative analysis of numerical algorithms for one-dimensional problems
The article presents the results of comparative analysis for some algorithms aimed at numerical modeling of the run up of long waves in the framework of shallow water theory. Authors consider the problem of the waves run-up on a flat slope both including and excluding the forces of bottom friction. Considerable attention is paid to the verification and validation for algorithms of the mathematical model by comparing the calculated results with the known analytical solutions, calculations of other authors, as well as the results of laboratory experiments. Numerical methods considered in this paper include the method of large particles, a Godunov type method, the method of smoothed particles, a method of smoothed particle hydrodynamics and finite difference scheme with TVD properties (TVD + SPH) and the method with a moving mesh using an analytical solution for the calculation of the flow parameters on the shoreline. Some advantages of the TVD + SPH method for solving problems of the rolling waves on a beach are shown. Examples of a successful application of this method to simulate weakly nonlinear and essentially nonlinear (the breaking) waves are presented. In the latter case, the quality of the result is largely dependent on the successful selection of parameters defining the bottom friction. The authors propose a continuation of the research presented in this paper for the simulation of more complex wave propagation phenomena and in extending the effective TVD + SPH method for the case of two spatial (horizontal) dimensions.
[full text]
Keywords: surface waves, shallow water, run-up, numerical simulation
Author(s):
Shokin Yuriy Ivanovich
Dr. , Academician RAS, Professor
Position: Scientific Director of the Institute
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave., 6
Phone Office: (383) 334 91 10
E-mail: shokin@ict.nsc.ru
SPIN-code: 6442-4180Rychkov Aleksandr Dmitrievich
Dr. , Professor
Position: Leading research officer
Address: 63009, Russia, Novosibirsk, Ac. Lavrentiev ave., 6
Phone Office: (383) 330 86 56
E-mail: rych@ict.nsc.ru
Khakimzyanov Gayaz Salimovich
Dr. , Professor
Position: Leading research officer
Office: Federal Research Center for Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave. 6
Phone Office: (383) 330 86 56
E-mail: khak@ict.nsc.ru
SPIN-code: 3144-0877Chubarov Leonid Borisovich
Dr. , Professor
Position: General Scientist
Office: Institute of Computational Technologies SB RAS
Address: 630090, Russia, Novosibirsk, ac. Lavrentyev Ave., 6
Phone Office: (383) 333 18 82
E-mail: chubarov@ict.nsc.ru
SPIN-code: 3048-2318 References:
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Bibliography link:
Shokin Y.I., Rychkov A.D., Khakimzyanov G.S., Chubarov L.B. On numerical methods for solving run-up problems. I. Comparative analysis of numerical algorithms for one-dimensional problems // Computational technologies. 2015. V. 20. ¹ 5. P. 214-232
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