Информация о публикации

Просмотр записей
Инд. авторы: Khakimzyanov G., Dutykh D.
Заглавие: Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models
Библ. ссылка: Khakimzyanov G., Dutykh D. Long Wave Interaction with a Partially Immersed Body. Part I: Mathematical Models // Communications in Computational Physics. - 2020. - Vol.27. - Iss. 2. - P.321-378. - ISSN 1815-2406. - EISSN 1991-7120. - http://admin.global-sci.org/uploads/online_news/CiCP/201908101604-12317.pdf
Внешние системы: DOI: 10.4208/cicp.OA-2018-0294; РИНЦ: 41285946; WoS: 000501534800001;
Реферат: eng: In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the framework of a hierarchy of mathematical models. Namely, in this first part we formulate the problem at every hierarchical level. The special attention is paid to fully nonlinear and weakly dispersive models since they are most likely to be used in practice. For this model we have to consider separately the inner (under the body) and outer domains. Various approached to the gluing of solutions at the boundary is discussed as well. We propose several strategies which ensure the global conservation or continuity of some important physical quantities.
Ключевые слова: nonlinear dispersive waves; free surface flows; long waves; SHALLOW-WATER EQUATIONS; NUMERICAL-SIMULATION; SOLITARY WAVE; RIEMANN PROBLEM; REGULARIZATION; DERIVATION; PROPAGATION; SCHEMES; Floating body; wave/body interaction;
Издано: 2020
Физ. характеристика: с.321-378
Ссылка: http://admin.global-sci.org/uploads/online_news/CiCP/201908101604-12317.pdf
Цитирование:
1. F. Alcrudo and F. Benkhaldoun. Exact solutions to the Riemann problem of the shallow water equations with a bottom step. Comput. & Fluids, 30(6):643-671, jul 2001. 52, 57
2. R. Ariew. Ockham's Razor: A Historical and Philosophical Analysis of Ockham's Principle of Parsimony. PhD thesis, University of Illnois at Urbana-Champaign, 1976. 8
3. V. B. Barakhnin and G. S. Khakimzyanov. The splitting technique as applied to the solution of the nonlinear dispersive shallow-water equations. Doklady Mathematics, 59(1):70-72, 1999. 41, 42
4. G. K. Batchelor. An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge, 1967. 37
5. R. Bernetti, V. A. Titarev, and E. F. Toro. Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry. J. Comp. Phys., 227(6):3212- 3243, mar 2008. 26, 52, 57
6. H. S. Bhat and R. C. Fetecau. On a regularization of the compressible Euler equations for an isothermal gas. J. Math. Anal. Appl., 358(1):168-181, oct 2009. 38
7. H. S. Bhat, R. C. Fetecau, and J. Goodman. A Leray-type regularization for the isentropic Euler equations. Nonlinearity, 20(9):2035-2046, sep 2007. 38
8. J. L. Bona, T. Colin, and D. Lannes. Long wave approximations for water waves. Arch. Rational Mech. Anal., 178:373-410, 2005. 27, 30
9. J. V. Boussinesq. Essai sur la theorie des eaux courantes. Memoires presentes par divers savants a l'Acad. des Sci. Inst. Nat. France, XXIII:1-680, 1877. 8
10. M. Brocchini. A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics. Proc. R. Soc. A, 469(2160):20130496, oct 2013. 8
11. L. J. F. Broer. On the Hamiltonian theory of surface waves. Applied Sci. Res., 29(6):430-446, 1974. 21
12. R. A. Carmigniani. Redresseurs de vagues: vers une nouvelle strategie d'extraction de l'energie houlomotrice. Phd, Universite Paris-Est, 2017. 7, 12
13. R. A. Carmigniani, M. Benoit, D. Violeau, and M. Gharib. Resonance wave pumping with surface waves. J. Fluid Mech., 811:1-36, jan 2017. 8, 12
14. E. Chiodaroli, C. De Lellis, and O. Kreml. Global Ill-Posedness of the Isentropic System of Gas Dynamics. Comm. Pure Appl. Math., 68(7):1157-1190, 2015. 38
15. E. Chiodaroli and L. Gosse. A Numerical Glimpse at Some Non-standard Solutions to Compressible Euler Equations. In L. Gosse and R. Natalini, editors, Innovative Algorithms and Analysis, pages 111-140. Springer International Publishing, Cham, Switzerland, 2017. 38
16. E. Chiodaroli and O. Kreml. An overview of some recent results on the Euler system of isentropic gas dynamics. Bull. Braz. Math. Soc., New Series, 47(1):241-253, 2016. 38
17. D. Clamond and D. Dutykh. Practical use of variational principles for modeling water waves. Phys. D, 241(1):25-36, 2012. 39
18. D. Clamond and D. Dutykh. Non-dispersive conservative regularisation of nonlinear shallow water (and isentropic Euler equations). Comm. Nonlin. Sci. Num. Sim., 55:237-247, 2018. 38
19. D. Clamond, D. Dutykh, and D. Mitsotakis. Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics. Comm. Nonlin. Sci. Num. Sim., 45:245- 257, 2017. 30
20. F. Coquel, E. Godlewski, K. Haddaoui, C. Marmignon, and F. Renac. Choice of measure source terms in interface coupling for a model problem in gas dynamics. Math. Comp., 85(301):2305-2339, feb 2016. 44
21. M. H. Dao and P. Tkalich. Tsunami propagation modelling - a sensitivity study. Nat. Hazards Earth Syst. Sci., 7:741-754, 2007. 39
22. A. J. C. de Saint-Venant. Theorie du mouvement non-permanent des eaux, avec application aux crues des rivieres et a l'introduction des marees dans leur lit. C. R. Acad. Sc. Paris, 73:147-154, 1871. 8
23. F. V. Dolzhansky. Fundamentals of Geophysical Hydrodynamics, volume 103 of Encyclopaedia of Mathematical Sciences. Springer Berlin Heidelberg, Berlin, Heidelberg, 2013. 32
24. V. A. Dougalis and D. E. Mitsotakis. Theory and numerical analysis of Boussinesq systems: A review. In N. A. Kampanis, V. A. Dougalis, and J. A. Ekaterinaris, editors, Effective Computational Methods in Wave Propagation, pages 63-110. CRC Press, 2008. 8, 39
25. A. Duran, D. Dutykh, and D. Mitsotakis. On the Galilean Invariance of Some Nonlinear Dispersive Wave Equations. Stud. Appl. Math., 131(4):359-388, nov 2013. 40
26. A. Duran, D. Dutykh, and D. Mitsotakis. Peregrine's System Revisited. In N. Abcha, E. N. Pelinovsky, and I. Mutabazi, editors, Nonlinear Waves and Pattern Dynamics, pages 3-43. Springer International Publishing, Cham, 2018. 30, 39
27. D. Dutykh. Mathematical modelling of tsunami waves. Phd thesis, Ecole Normale Superieure de Cachan, 2007. 37
28. D. Dutykh, D. Clamond, P. Milewski, and D. Mitsotakis. Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations. Eur. J. Appl. Math., 24(05):761-787, 2013. 36
29. D. Dutykh and F. Dias. Energy of tsunami waves generated by bottom motion. Proc. R. Soc. A, 465:725-744, 2009. 37
30. D. Dutykh, T. Katsaounis, and D. Mitsotakis. Dispersive wave runup on non-uniform shores. In J. Fort, editor, Finite Volumes for Complex Applications VI - Problems & Perspectives, pages 389-397, Prague, 2011. Springer Berlin Heidelberg. 41
31. D. Dutykh, T. Katsaounis, and D. Mitsotakis. Finite volume schemes for dispersive wave propagation and runup. J. Comput. Phys., 230(8):3035-3061, apr 2011. 36, 39
32. D. Dutykh, R. Poncet, and F. Dias. The VOLNA code for the numerical modeling of tsunami waves: Generation, propagation and inundation. Eur. J. Mech. B/Fluids, 30(6):598-615, 2011. 37, 41
33. A. P. Engsig-Karup, C. Monteserin, and C. Eskilsson. A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves, Part 2: Wave-body interaction. Submitted, 2017. 7
34. R. P. Fedorenko. Introduction to Computational Physics. MIPT Press, Moscow, 1994. 44
35. Z. I. Fedotova and E. D. Karepova. Variational principle for approximate models of wave hydrodynamics. Russ. J. Numer. Anal. Math. Modelling, 11(3):183-204, 1996. 39
36. Z. I. Fedotova, G. S. Khakimzyanov, and D. Dutykh. Energy equation for certain approximate models of long-wave hydrodynamics. Russ. J. Numer. Anal. Math. Modelling, 29(3):167-178, jan 2014. 25, 30, 41
37. M. Folley, A. Babarit, B. Child, D. Forehand, L. O'Boyle, K. Silverthorne, J. Spinneken, V. Stratigaki, and P. Troch. A Review of Numerical Modelling of Wave Energy Converter Arrays. In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering, pages 535-545, Rio de Janeiro, Brazil, jul 2012. ASME. 8
38. U. Frisch. Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge, apr 1995. 57
39. Y. Goda. Random Seas and Design of Maritime Structures, volume 33 of Advanced Series on Ocean Engineering. World Scientific, 2010. 7
40. A. E. Green, N. Laws, and P. M. Naghdi. On the theory of water waves. Proc. R. Soc. Lond. A, 338:43-55, 1974. 8
41. A. E. Green and P. M. Naghdi. A derivation of equations for wave propagation in water of variable depth. J. Fluid Mech., 78:237-246, 1976. 8
42. R. Henn, S. D. Sharma, and T. Jiang. Influence of Canal Topography on Ship Waves in Shallow Water. In 16th International Workshop on Water Waves and Floating Bodies, pages 49-52, Hiroshima, 2001. 14
43. H. Holden, K. H. Karlsen, K.-A. Lie, and N. H. Risebro. Splitting Methods for Partial Differential Equations with Rough Solutions. European Mathematical Society, Zurich, 2010. 42
44. H. Hugoniot. Memoire sur la propagation des mouvements dans les corps et specialement dans les gaz parfaits (premiere partie). Journal de l'Ecole Polytechnique, 57:3-97, 1887. 44
45. M. D. S. Q. Isaacson. Nonlinear-wave effects on fixed and floating bodies. J. Fluid Mech., 120:267-281, jul 1982. 7
46. T. Jiang. Ship Waves in Shallow Water. VDI-Verlag, Dusseldorf, 2001. 14
47. E. Y. Kamynin, V. V. Maximov, I. S. Nudner, K. K. Semenov, and G. S. Khakimzyanov. Interaction of the solitary wave with a partially submerged stationary construction. Fundamental and Applied Hydrophysics, 4(10):39-54, 2010. 7
48. M. Kashiwagi. Non-linear simulations of wave-induced motions of a floating body by means of the mixed Eulerian-Lagrangian method. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 214(6):841-855, 2000. 7
49. G. S. Khakimzyanov and D. Dutykh. Numerical Modelling of Surface Water Wave Interaction with a Moving Wall. Commun. Comput. Phys., 23(5):1289-1354, 2018. 8
50. G. S. Khakimzyanov, D. Dutykh, and Z. I. Fedotova. Dispersive shallow water wave modelling. Part III:Model derivation on a globally spherical geometry. Commun. Comput. Phys., 23(2):315-360, 2018. 22, 42
51. G. S. Khakimzyanov, D. Dutykh, Z. I. Fedotova, and D. E. Mitsotakis. Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space. Commun. Comput. Phys., 23(1):1-29, 2018. 22, 23, 24, 25, 27, 39, 42, 47
52. G. S. Khakimzyanov, D. Dutykh, and O. Gusev. Dispersive shallow water wave modelling. Part IV: Numerical simulation on a globally spherical geometry. Commun. Comput. Phys., 23(2):361-407, 2018. 42
53. G. S. Khakimzyanov, D. Dutykh, and O. Gusev. Long wave interaction with a partially immersed body. Part II: Numerical results. Submitted, pages 1-40, 2019. 8, 13, 32, 43, 44, 48, 57
54. G. S. Khakimzyanov, D. Dutykh, O. Gusev, and N. Y. Shokina. Dispersive shallow water wave modelling. Part II: Numerical modelling on a globally flat space. Commun. Comput. Phys., 23(1):30-92, 2018. 36, 42, 47
55. G. S. Khakimzyanov, D. Dutykh, D. E. Mitsotakis, and N. Y. Shokina. Numerical solution of conservation laws on moving grids. Submitted, pages 1-28, 2019. 8
56. V. M. Kovenya and N. N. Yanenko. Splitting method in Gas Dynamics Problems. Nauka, Novosibirsk, 1981. 42
57. D. Kroner. Numerical Schemes for Conservation Laws. Wiley, Stuttgart, 1997. 52
58. H. Lamb. Hydrodynamics. Cambridge University Press, Cambridge, 1932. 8, 19
59. P. D. Lax. Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves. SIAM, Philadelphia, Penn., 1973. 36, 38
60. Y. A. Li. A shallow-water approximation to the full water wave problem. Communications on Pure and Applied Mathematics, 59(9):1225-1285, sep 2006. 38
61. P. Lin. A numerical study of solitary wave interaction with rectangular obstacles. Coastal Engineering, 51(1):35-51, mar 2004. 57
62. P. Lin. A multiple-layer _-coordinate model for simulation of wave-structure interaction. Computers & Fluids, 35(2):147-167, feb 2006. 8
63. C. M. Linton and P. McIver. Mathematical Techniques for Wave/Structure Interactions. Chapman & Hall/CRC, 2001. 7
64. M. S. Longuet-Higgins. Accelerations in Steep Gravity Waves. J. Phys. Ocean., 15(11):1570- 1579, nov 1985. 18
65. F. Lovholt, G. Pedersen, and G. Gisler. Oceanic propagation of a potential tsunami from the La Palma Island. J. Geophys. Res., 113(C9):C09026, sep 2008. 39
66. F. Lovholt, G. Pedersen, and S. Glimsdal. Coupling of Dispersive Tsunami Propagation and Shallow Water Coastal Response. The Open Oceanography Journal, 4(1):71-82, may 2010. 39
67. A. J. Majda and A. L. Bertozzi. Vorticity and Incompressible Flow. Cambridge University Press, Cambridge, 2001. 43
68. N. Makarenko. A second long-wave approximation in the Cauchy-Poisson problem. Dyn. Contin. Media, 77:56-72, 1986. 38
69. J. W. Miles and R. Salmon. Weakly dispersive nonlinear gravity waves. J. Fluid Mech., 157:519-531, 1985. 26
70. H. Miyata and S. Nishimura. Finite-difference simulation of nonlinear ship waves. J. Fluid.Mech., 157:327-357, aug 1985. 7
71. F. Nelli, L. G. Bennetts, D. M. Skene, J. P. Monty, J. H. Lee, M. H. Meylan, and A. Toffoli. Reflection and transmission of regular water waves by a thin, floating plate. Wave Motion, 70:209-221, apr 2017. 57
72. J. C. Newman. Marine Hydrodynamics. MIT Press, Cambridge, Massachusetts, USA, 1977. 7
73. I. S. Nudner, A. I. Urusov, G. S. Khakimzyanov, and V. N. Yanshin. On the interaction of long gravitational waves with bodies immersed in a fluid. Technical report, Computing Center, SB RAS, Krasnoyarsk, 1991. 14
74. I. S. Nudner, A. I. Urusov, G. S. Khakimzyanov, and V. N. Yanshin. On the effect of long waves on partially immersed objects. Modelling in Mechanics, 6(1):81-86, 1992. 14
75. O. Nwogu. Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterway, Port, Coastal and Ocean Engineering, 119:618-638, 1993. 39
76. N. Parolini and A. Quarteroni. Mathematical models and numerical simulations for the America's Cup. Comp. Meth. Appl. Mech. Eng., 194(9-11):1001-1026, mar 2005. 8
77. D. H. Peregrine. Long waves on a beach. J. Fluid Mech., 27:815-827, 1967. 30, 39, 40
78. A. A. Petrov. Variational statement of the problem of liquid motion in a container of finite dimensions. Prikl. Math. Mekh., 28(4):917-922, 1964. 21
79. O. M. Phillips. The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech., 4(4):426-434, aug 1958. 18
80. A. V. Pogorelov. Differential Geometry. Noordhoff, Groningen, 1959. 16
81. A. Rafiee, H. Wolgamot, S. Draper, J. Orszaghova, J. Fievez, and T. Sawyer. Identifying the design wave group for the extreme response of a point absorber wave energy converter. In Proceedings of the 3rd Asian Wave and Tidal Energy Conference, Singapore, 2016. Research Publishing. 8
82. W. J. M. Rankine. On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance. Phil. Trans. R. Soc. Lond, 160:277-288, jan 1870. 44
83. C. W. Richards and C. M. Crane. Pressure marching schemes that work. Int. J. Num. Meth. in Eng., 15(4):599-610, apr 1980. 43
84. V. Roeber. Boussinesq-type model for nearshore wave processes in fringing reef environment. Phd, University of Hawaii at Manoa, 2010. 39
85. C. G. Rossby. Planetary flow patterns in the atmosphere. Quart. J. R. Met. Soc., 66:68-87, 1940. 32
86. F. Serre. Contribution a l'etude des ecoulements permanents et variables dans les canaux. La Houille blanche, 8:374-388, 1953. 8
87. F. Serre. Contribution a l'etude des ecoulements permanents et variables dans les canaux. La Houille blanche, 8:830-872, 1953. 8
88. J. Serrin. Mathematical Principles of Classical Fluid Mechanics. In C. Truesdell, editor, Stromungsmechanik I, pages 125-263. Springer, Berlin, Heidelberg, 1959. 44
89. L. Shemer and S. H. Noskowitz. On Kinematics and Dynamics of Breaking Water Waves. Procedia IUTAM, 8:205-212, 2013. 18
90. Y. I. Shokin, Z. I. Fedotova, and G. S. Khakimzyanov. Hierarchy of nonlinear models of the hydrodynamics of long surface waves. Doklady Physics, 60(5):224-228, may 2015. 39
91. J.-M. Souriau. Structure of Dynamical Systems: a Symplectic View of Physics. Birkhauser, Boston, MA, 1997. 40
92. D. G. Stamos and M. R. Hajj. Reflection and Transmission of Waves over Submerged Breakwaters. J. Eng. Mech., 127(2):99-105, feb 2001. 57
93. J. J. Stoker. Water Waves: The mathematical theory with applications. Interscience, New York, 1957. 8, 26, 38
94. F. Ursell. The long-wave paradox in the theory of gravity waves. Proc. Camb. Phil. Soc., 49:685-694, 1953. 39
95. A. I. Urusov and Y. I. Shokin. On modelling the interaction of long surface waves with a body partially immersed in a fluid. In All-Union Workshop on Numerical Methods of Wave Hydrodynamics, pages 33-40, Krasnoyarsk, 1991. Krasnoyarsk University Press. 14
96. S. Wu. Global wellposedness of the 3-D full water wave problem. Inventiones mathematicae, 184(1):125-220, apr 2011. 21, 38
97. I. K. Yaushev. On the numerical simulation of non-stationary gas flow in 1D approximation in the channels with a jump in cross-section. Izv. Sib. Otd. Akad. Nauk SSSR. Tehn. Nauki, 8(2):39-48, 1967. 13, 14
98. I. K. Yaushev and G. S. Khakimzyanov. Computation of the initial work of an impulse pipe. In Numerical methods in fluid and gas mechanics, pages 122-129. Novosibirsk, 1980. 13
99. I. K. Yaushev and G. S. Khakimzyanov. Simulation of the initial stages of impulse pipe functionning. Technical report, Institute of Theoretical and Applied Mechanics, Siberian Branch of the USSR Academy of Sciences, Novosibirsk, 1980. 13, 14
100. V. E. Zakharov. Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys., 9:190-194, 1968. 21
101. M. Zhao, L. Cheng, and B. Teng. Numerical simulation of solitary wave scattering by a circular cylinder array. Ocean Engineering, 34(3-4):489-499, mar 2007. 7 62 / 63
102. B. Z. Zhou, G. X. Wu, and Q. C. Meng. Interactions of fully nonlinear solitary wave with a freely floating vertical cylinder. Engng. Anal. Bound. Elem., 69:119-131, aug 2016. 7
103. F. Zhuang and J.-J. Lee. A Viscous Rotational Model for Wave Overtopping over Marine Structure. In Coastal Engineering 1996, pages 2178-2191, New York, NY, aug 1997. American Society of Civil Engineers. 8