Abstract:
A mathematical model for the wave hydrodynamics problem, describing wash ashore and taking into account such physical parameters as turbulence exchange, complexity of domain and coastal line geometry, and bottom friction is developed. For the given mathematical model a discrete model is constructed, taking into account dynamical changing of the calculation domain. Proposed technique for mathematical models sampling takes into account fullness of the control cells. This technique allows improving the real accuracy of a solution in case of complex domain geometry, by improving approximation of the boundary. A software implementation and numerical experiments of the posed problem of the wave hydrodynamics are performed.
Citation:
A. I. Sukhinov, A. E. Chistyakov, E. F. Timofeeva, A. V. Shishenya, “Mathematical model for calculating coastal wave processes”, Mat. Model., 24:8 (2012), 32–44; Math. Models Comput. Simul., 5:2 (2013), 122–129
This publication is cited in the following 46 articles:
Alexander Sukhinov, Elena Protsenko, Sofya Protsenko, Lecture Notes in Computer Science, 15406, Supercomputing, 2025, 74
Martin Føre, Morten Omholt Alver, Jo Arve Alfredsen, Adil Rasheed, Thor Hukkelås, Hans V. Bjelland, Biao Su, Sveinung J. Ohrem, Eleni Kelasidi, Tomas Norton, Nikos Papandroulakis, “Digital Twins in intensive aquaculture — Challenges, opportunities and future prospects”, Computers and Electronics in Agriculture, 218 (2024), 108676
A. I. Sukhinov, E. A. Protsenko, S. V. Protsenko, N. D. Panasenko, “Parallel Numerical Implementation of Mathematical Wave Hydrodynamics Models Taking into Account the Features of the Vertical Turbulent Exchange Using Remote Sensing Data”, Math Models Comput Simul, 16:2 (2024), 267
O. S. Yazovtseva, “Numerical Study of Wave Processes during Oxidative Regeneration of a Stationary Catalyst Layer”, Math Models Comput Simul, 16:S2 (2024), S272
E. Protsenko, A. Sukhinov, S. Protsenko, S. Kovačević, K.V. Kamyshev, “Predictive modeling of wave hydrodynamics and relief formation in the presence of multi-scale turbulent exchange”, E3S Web of Conf., 376 (2023), 01082
E. A. Protsenko, N. D. Panasenko, A. V. Strazhko, “Original article Spatial-three-dimensional wave processes' modeling in shallow water bodies taking into account the vertical turbulent exchange features”, CMIT, 6:1 (2023), 34
A. I. Sukhinov, E. A. Protsenko, S. V. Protsenko, N. D. Panasenko, “Parallel numerical implementation of mathematical wave hydrodynamics models taking into account the features of vertical turbulent exchange using remote sensing data”, Matem. Mod., 35:12 (2023), 51–68
Sofya Protsenko, 2023 Applied Mathematics, Computational Science and Mechanics: Current Problems (AMCSM), 2023, 1
Alexander Sukhinov, Alexander Chistyakov, Inna Kuznetsova, Yulia Belova, Elena Rahimbaeva, “Solving Hydrodynamic Problems Based on a Modified Upwind Leapfrog Scheme in Areas with Complex Geometry”, Mathematics, 10:18 (2022), 3248
A I Sukhinov, A E Chistyakov, E A Protsenko, S V Protsenko, “Coastal protection structures influence on diffraction and reflection of waves simulation based on 3D wave hydrodynamics model”, J. Phys.: Conf. Ser., 1902:1 (2021), 012133
A I Sukhinov, A E Chistyakov, I Y Kuznetsova, E A Protsenko, A M Atayan, “Modeling of soil dumping based on a modified Upwind Leapfrog difference scheme”, J. Phys.: Conf. Ser., 1745:1 (2021), 012120
T V Lyashchenko, I A Lyapunova, A E Chistyakov, A V Nikitina, A A Filina, A L Leontiev, “Modelling the pollutants transport in the “air-water” system of a shallow water”, IOP Conf. Ser.: Mater. Sci. Eng., 1029:1 (2021), 012080
Protsenko V S., Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 1479, IOP Publishing Ltd, 2020
Sukhinov I A. Chistyakov A.E. Kuznetsova I.Y. Protsenko E.A., Applied Mathematics, Computational Science and Mechanics: Current Problems, Journal of Physics Conference Series, 1479, IOP Publishing Ltd, 2020
A. I. Sukhinov, A. E. Chistyakov, E. A. Protsenko, A. M. Atayan, “Lineinaya kombinatsiya skhem «kabare» i «krest» s vesovymi koeffitsientami, poluchennymi iz usloviya minimizatsii poryadka pogreshnosti approksimatsii”, Chebyshevskii sb., 21:4 (2020), 243–256
A. I. Sukhinov, A. E. Chistyakov, E. A. Protsenko, V. V. Sidoryakina, S. V. Protsenko, “Set of coupled suspended matter transport models including three-dimensional hydrodynamic processes in the coastal zone”, Math. Models Comput. Simul., 12:5 (2020), 757–769
S. V. Protsenko, A. M. Atayan, A. E. Chistyakov, A. V. Nikitina, V. N. Litvinov, A. A. Filina, “Eksperimentalnoe issledovanie silovykh nagruzok na opory nadvodnoi konstruktsii na osnove matematicheskoi modeli volnovykh protsessov”, Vestn. YuUrGU. Ser. Vych. matem. inform., 8:3 (2019), 27–42
Sukhinov A.I. Chistyakov A.E. Protsenko S.V. Sidoryakina V.V., “Coupled 3D Wave and 2D Bottom Deposit Transportation Models For the Prediction of Harmful Phenomena in Coastal Zone”, Trends in the Analysis and Design of Marine Structures, Proceedings in Marine Technology and Ocean Engineering, 2, ed. Parunov J. Soares C., Crc Press-Balkema, 2019, 597–603
A. I. Sukhinov, A. E. Chistyakov, E. A. Protsenko, V. V. Sidoryakina, S. V. Protsenko, “Accounting method of filling cells for the hydrodynamics problems solution with complex geometry of the computational domain”, Math. Models Comput. Simul., 12:2 (2020), 232–245
Yu. V. Belova, A. M. Atayan, A. E. Chistyakov, A. V. Strazhko, “Study on stationary solutions to the problem of phytoplankton dynamics considering transformation of phosphorus, nitrogen and silicon compounds”, Vestnik Donskogo gosudarstvennogo tehničeskogo universiteta, 19:1 (2019), 4