Numerical technology for landslide tsunami simulations based on Navier-Stokes equations
DOI:
https://doi.org/10.7242/1999-6691/2016.9.2.19Keywords:
Navier-Stokes equations, multi-phase flow, tsunami, landslides, free surface, multi-grid method, modelingAbstract
The paper presents an integral technology simulating all phases of a landslide-driven tsunami. The technology is based on the numerical solution of a set of Navier-Stokes equations for multi-phase flows. The numerical algorithm uses a fully implicit approximation method, in which the equations of continuity and momentum conservation are coupled through implicit summands of pressure gradient and mass flow. The method we propose removes strict constraints on the timestep and makes it possible to simulate tsunami propagation to arbitrarily large distances. The landslide origin is simulated as an individual phase being a Newtonian fluid with its own density and viscosity and separated from the water and air phases by an interface. The paper presents the basic equation discretization formulas and expressions for coefficients and describes the main steps of the computational procedure. To enable simulations of tsunami propagation across wide water areas, we propose a parallel technology implementation algorithm that employs an algebraic multi-grid method. The multi-grid method implementation is based on the global and cascade collection algorithms, which impose no limitations on the paralleling scale and make this technology applicable to petascale systems. We demonstrate the possibility of simulating all phases of a landslide-driven tsunami, including its generation, propagation and uprush. The technology has been verified against the problems supported by experimental data. The paper describes the mechanism of incorporating bathymetric data to simulate tsunamis in real water areas of the world ocean. Results of comparison with the non-linear dispersion theory, which demonstrated good agreement, are presented for the case of a historical tsunami of volcanic origin on the Montserrat island in the Caribbean Sea.
Downloads
References
http://tsun.sscc.ru/hiwg (data obrasenia: 18.04.2016).
2. Pelinovskij E.N. Gidrodinamika voln cunami. - N. Novgorod: Institut prikladnoj fiziki RAN, 1996. - 277 s.
3. Langford P.S. Modeling of tsunami generated by submarine landslides / PhD Dissertation. - New Zealand: University of Canterbury, 2007. - 410 p.
4. Rabinovich A.B., Thomson R.E., Bornhold B.D., Fine I.V., Kulikov E.A. Numerical modelling of tsunamis generated by hypothetical landslides in the strait of Georgia, British Columbia // Pure Appl. Geophys. - 2003. - Vol. 160, no. 7. - P. 1273-1313. DOI
5. Fine I.V., Rabinovich A.B., Bornhold B.D., Thomson R.E., Kulikov E.A. The Grand Banks landslide-generated tsunami of November 18, 1929: preliminary analysis and numerical modeling // Mar. Geol. - 2005. - Vol. 215, no. 1-2. - P. 45-57. DOI
6. Papadopoulos G.A., Kortekaas S. Characteristics of land-slide generated tsunamis from observational data // Submarine mass movements and their consequences. Advances in natural and technological hazards research. - 2003. - Vol. 19. - P. 267-374.
7. Fedotova Z.I., Cubarov L.B., Sokin U.I. Modelirovanie poverhnostnyh voln, porozdennyh opolznami // Vycislitel’nye tehnologii. - 2004. - T. 9, No 6. - S. 89-96.
8. Watts P., Grilli S.T. Underwater landslide shape, motion, deformation, and tsunami generation // Proc. of the 13th Intern. Offshore and Polar Eng. Conf., Honolulu, Hawaii, USA, 25-30 May 2003. - Vol. 3. - P. 364-371.
9. Heinrich P., Schindele F., Guibourg S., Ihmle P. Modeling of the February 1996 Peruvian tsunami // Geophys. Res. Lett. - 1998. - Vol. 25, no. 14. - P. 2687-2690. DOI
10. Imamura F., Imteaz M.M.A. Long waves in two-layers: Governing equations and numerical model // Science of Tsunami Hazards. - 1995. - Vol. 13, no. 1. - P. 3-24. (URL: http://library.lanl.gov/tsunami/00394724.pdf).
11. Dutykh D., Dias F. Energy of tsunami waves generated by bottom motion // Proc. Roy. Soc. A. - 2009. - Vol. 465. - P. 725-744. DOI
12. Gusev O.I., Sokina N.U., Kutergin V.A., Hakimzanov G.S. Modelirovanie poverhnostnyh voln, generiruemyh podvodnym opolznem v vodohranilise // Vycislitel’nye tehnologii. - 2013. - T. 18, No 5. - S. 74-90.
13. Saelevik G., Jensen A., Pedersen G. Experimental investigation of impact generated tsunami; related to a potential rock slide, Western Norway // Coast. Eng. - 2009. - Vol. 56, no. 9. - P. 897-906. DOI
14. Fritz H.M., Mohammed F., Yoo J. Lituya Bay landslide impact generated mega-tsunami 50th Anniversary // Pure Appl. Geophys. - 2009. - Vol. 166, no. 1. - P. 153-175. DOI
15. Horrillo J., Wood A., Kim G.-B., Parambath A. A simplified 3-D Navier-Stokes numerical model for landslide-tsunami: Application to the Gulf of Mexico // J. Geophys. Res.-Oceans. - 2013. - Vol. 118, no. 2. - P. 6934-6950. DOI
16. Mohammed F., Frits H.M. Experiments on tsunamis generated by 3D granular landslides // Submarine mass movements and their consequences. Advances in natural and technological hazards research. - 2010. - Vol. 28. - P. 705-718.
17. Mohammed F. Physical modeling of tsunamis generated by three-dimensional deformable granular landslides // PhD Dissertation. - Georgia Institute of Technology, 2010. - 212 p.
18. Beizel S.A., Chubarov L.B., Khakimzyanov G.S. Simulation of surface waves generated by an underwater landslide moving over an uneven slope // Russ. J. Numer. Anal. M. - 2011. - Vol. 26, no. 1. - P. 17-38. DOI
19. Harbitz C.B., Lovholt F., Pedersen G., Glimsdal S., Masson D.G. Mechanisms of tsunami generation by submarine landslides - a short review // Norwegian Journal of Geology. - 2006. - Vol. 86. - P. 255-264.
20. Pelinovsky E.N. Analytical models of tsunami generation by submarine landslides // Submarine Landslides and Tsunamis. NATO Science Series. - 2003. - Vol. 21. - P. 111-128. DOI
21. Didenkulova I., Nikolkina I., Pelinovsky E., Zahibo N. Tsunami waves generated by submarine landslides of variable volume: analytical solutions for a basin of variable depth // Nat. Hazards Earth Syst. Sci. - 2010. - Vol. 10. - P. 2407-2419. DOI
22. Macias J., Vazquez J.T., Fernandez-Salas L.M., Gonzalez-Vida J.M., Barcenas P., Castro M.J., Diaz-del-Rio V., Alonso B. The Al-Borani submarine landslide and associated tsunami. A modelling approach // Mar. Geol. - 2015. - Vol. 361. - P. 79-95. DOI
23. Okal E.A., Synolakis C.E. A theoretical comparison of tsunamis from dislocations and landslides // Pure Appl. Geophys. 2003. - Vol. 160, no. 10. - P. 2177-2188. DOI
24. Lynett P. Hydrodynamic modeling of tsunamis generated by submarine landslides: generation, propagation, and shoreline impact // Submarine mass movements and their consequences. Advances in natural and technological hazards research. - 2010. - Vol. 28. - P. 685-694.
25. Watts P., Grilli S.T., Kirby J.T., Fryer G.J., Tappin D.R. Landslide tsunami case studies using a Boussinesq model and a fully nonlinear tsunami generation model // Nat. Hazards Earth Syst. Sci. - 2003. - Vol. 3. - P. 391-402. DOI
26. Cecioni C., Bellotti G. Modeling tsunamis generated by submerged landslides using depth integrated equations // Appl. Ocean Res. - 2010. - Vol. 32, no. 3. - P. 343-350. DOI
27. Grilli S.T., Vogelmann S., Watts P. Development of 3D numerical wave tank for modeling tsunami generation by underwater landslides // Eng. Anal. Boun. Elem. - 2002. - Vol. 26, no. 4. - P. 301-313. DOI
28. Ma G., Kirby J.T., Shi F. Numerical simulation of tsunami waves generated by deformable submarine landslides // Ocean Modelling. - 2013. - Vol. 69. - P. 146-165. DOI
29. Liu P.L.-F., Wu T.-R., Raichlen F., Synolakis C.E., Borrero J.C. Runup and rundown generated by three-dimensional sliding masses // J. Fluid Mech. - 2005. - Vol. 536. - P. 107-144. DOI
30. Kozelkov A.S., Kurulin V.V., Tatuskina E.S., Puckova O.L. Modelirovanie turbulentnyh tecenij vazkoj neszimaemoj zidkosti na nestrukturirovannyh setkah s ispol’zovaniem modeli otsoedinennyh vihrej // Matematiceskoe modelirovanie. - 2014. - T. 26, No 8. - S. 81-96.
31. Kozelkov A.S., Kurulin V.V. Cislennaa shema dla modelirovania turbulentnyh tecenij neszimaemoj zidkosti s ispol’zovaniem vihrerazresausih podhodov // ZVMMF. - 2015. - T. 55, No 7. - S. 1255-1266. DOI
32. Lynett P., Liu P.L.-F. A numerical study of the run-up generated by three-dimensional landslides // J. Geophys. Res. - 2005. - Vol. 110, no. C3. DOI
33. Volkov K.N., Derugin U.N., Emel’anov V.N., Karpenko A.G., Kozelkov A.S., Teterina I.V. Metody uskorenia gazodinamiceskih rascetov na nestrukturirovannyh setkah. - M.: Fizmatlit, 2014. - 536 s.
34. Kozelkov A.S., Derugin U.N., Laskin S.V., Silaev D.P., Simonov P.G., Tatuskina E.S. Realizacia metoda rasceta vazkoj neszimaemoj zidkosti s ispol’zovaniem mnogosetocnogo metoda na osnove algoritma SIMPLE v pakete programm LOGOS // VANT. Ser.: Matematiceskoe modelirovanie fiziceskih processov. - 2013. - No 4. - S. 44-56.
35. Kozelkov A.S., Sagaliev R.M., Dmitriev S.M., Kurkin A.A., Volkov K.N., Derugin U.N., Emel’anov V.N., Pelinovskij E.N., Legcanov M.A. Matematiceskie modeli i algoritmy dla cislennogo modelirovania zadac gidrodinamiki i aerodinamiki: Uceb. posobie. - Niznij Novgorod: NGTU im. R.E. Alekseeva, 2014. - 163 s.
36. Hirt C.W., Nichols B.D. Volume of fluid (VOF) method for the dynamics of free boundaries // J. Comput. Phys. - 1981. - Vol. 39, no. 1. - P. 201-225. DOI
37. Ubbink O. Numerical prediction of two fluid systems with sharp interfaces // PhD Dissertation. - Department of Mechanical Engineering Imperial College of Science, Technology & Medicine, 1997. - 69 p.
38. Zajnakov A.Z., Kurbanaliev A.Y. Verifikacia otkrytogo paketa OpenFOAM na zadacah proryva damb // Teplofizika i aeromehanika. - 2013. - T. 20, No 4. - S. 461-472.
39. Volkov K.N., Emel’anov V.N. Tecenia gaza s casticami. - M.: Fizmatlit, 2008. - 600 s.
40. Ferziger J.H., Peric M. Computational methods for fluid dynamics. - Springer, 2001. 426 p.
41. Chen Z.J., Przekwas A.J. A coupled pressure-based computational method for incompressible/compressible flows // J. Comput. Phys. - 2010. - Vol. 229, no. 24. - P. 9150-9165. DOI
42. Rhie C.M., Chow W.L. A numerical study of the turbulent flow past an airfoil with trailing edge separation // AIAA Journal. - 1983. - Vol. 21, no. 11. - P. 1525-1532. DOI
43. Jasak H. Error analysis and estimation for the finite volume method with applications to fluid flows / PhD Dissertation in Mechanical Engineering. - London: Imperial College of Science, 1996. - 394 p.
44. Volkov K.N., Derugin U.N., Emel’anov V.N., Kozelkov A.S., Teterina I.V. Raznostnye shemy v zadacah gazovoj dinamiki na nestrukturirovannyh setkah. - M.: Fizmatlit, 2014. - 416 s.
45. Rouc P. Vycislitel’naa gidrodinamika. - M.: Mir, 1980. - 618 s.
46. Waclawczyk T. Remarks on prediction of wave drag using VOF method with interface capturing approach // Archives of Sivil and Mechanical Engineering. - 2008. - Vol. 8, no. 1. - P. 5-14. (URL: http://www.acme.pwr.wroc.pl/repository/177/online.pdf).
47. Samarskij A.A. Teoria raznostnyh shem. - M.: Nauka, 1989. - 616 s.
48. Kozelkov A.S, Derugin U.N., Cibereva U.A., Kornev A.V., Denisova O.V., Strelec D.U., Kurkin A.A., Kurulin V.V., Saripova I.L., Rubcova D.P., Legcanov M.A., Tatuskina E.C., Laskin S.V., Alozo A.V., Acevic S.V., Tarasova N.V., Ginniatullin R.R., Sizova M.A., Krutakova O.L. Minimal’nyj bazis zadac dla validacii metodov cislennogo modelirovania turbulentnyh tecenij vazkoj neszimaemoj zidkosti // Trudy Nizegorodskogo gosudarstvennogo tehniceskogo universiteta im. R.E. Alekseeva. - 2014. - No 4 (106). - C. 21-69.
49. Volkov K.N., Derugin U.N., Emel’anov V.N., Kozelkov A.S., Teterina I.V. Algebraiceskij mnogosetocnyj metod v zadacah vycislitel’noj fiziki // Vycislitel’nye metody i programmirovanie. - 2014. - T. 15, No 2. - S. 183-200.
50. Kozelkov A.S., Kurulin V.V., Puckova O.L., Laskin S.V., Modelirovanie turbulentnyh tecenij s ispol’zovaniem algebraiceskoj modeli rejnol’dsovyh naprazenij s universal’nymi pristenocnymi funkciami // Vycisl. meh. splos. sred. - 2014. - T. 7, No 1. - S. 40-51. DOI
51. Kozelkov A.S., Kurkin A.A., Pelinovskij E.N., Kurulin V.V. Modelirovanie cunami kosmogennogo proishozdenia v ramkah uravnenij Nav’e-Stoksa s istocnikami razlicnyh tipov // MZG. - 2015. - No 2. - S. 142-150. DOI
52. Kozelkov A.S. Effekty, soprovozdausie vhozdenie meteorita v vodnuu sredu // Trudy Nizegorodskogo gosudarstvennogo tehniceskogo universiteta im. R.E. Alekseeva. - 2014. - No 3 (105). - S. 48-77.
53. Kozelkov A.S., Kurkin A.A., Pelinovskij E.N. Cunami kosmogennogo proishozdenia // Trudy Nizegorodskogo gosudarstvennogo tehniceskogo universiteta im. R.E. Alekseeva. - 2014. - No 2 (104). - S. 26-35.
54. Eleckij S.V., Majorov U.B., Maksimov V.V., Nudner I.S., Fedotova Z.I., Hazoan M.G., Hakimzanov G.S., Cubarov L.B. Modelirovanie generacii poverhnostnyh voln peremeseniem fragmenta dna po beregovomu sklonu // Sovmestnyj vypusk zurnalov <> i <>. - 2004. - T. 9, c. 2. - S. 194-206.
55. Fedorenko R.P. Relaksacionnyj metod resenia raznostnyh ellipticeskih uravnenij // ZVMMF. - 1961. - T. 1, No 5. - S. 922-927.
56. Kozelkov A.S., Kurulin V.V., Laksin S.V., Sagaliev R.M., Alozo A.V. Issledovanie potenciala superkomp’uterov dla masstabiruemogo cislennogo modelirovania zadac gidrodinamiki v industrial’nyh prilozeniah // ZVMMF. - 2016. - T. 56, No 8. - S. 154-165. DOI
57. Pelinovskij E.N., Zaibo N., Dankli P., Talipova T.G., Kozelkov A.S., Kurkin A.A., Nikolkina I.F., Samarina N.M. Cunami, vyzvannye izverzeniami vulkana na ostrove Montserrat v Karibskom more // Izvestia AIN im. A.M. Prohorova. Prikladnaa matematika i mehanika. - 2004. - T. 6. - S. 31-59.
58. Pelinovsky E., Koselkov A., Zahibo N., Dunkly P., Edmonds M., Herd R., Talipova T., Nikolkina I. Tsunami generated by the volcano eruption on July 12-13, 2003 at Montserrat, Lesser Antilles // Science of Tsunami Hazards. - 2004. - Vol. 22, no. 1. - P. 44-57.
59. Kozelkov A.S. Ocenka cunamiopasnosti poberez’a Karibskogo mora // Diss... kand. fiz.-mat. nauk. - Niznij Novgorod, NGTU im. Alekseeva, 2006. - 171 c.
60. Goto C., Ogawa Y., Shuto N., Imamura N. Numerical method of tsunami simulation with the leap-frog scheme (IUGG/IOC Time Project), IOC Manual, UNESCO. - New York, 1997. - No. 35. - 96 r.
61. Watts P., Waythomas C.F. Theoretical analysis of tsunami generation by pyroclastic flows // J. Geophys. Res. - 2003. - Vol. 108, no. B12. - 21 p. DOI
62. Kirby J., Wei G., Chen Q., Kennedy A., Dalrymple R. Fully nonlinear Boussinesq wave model documentation and users manual // Center for Applied Coastal Research Department of Civil Engineering University of Delaware, Research Report No. CACR-98-06, 1998.
63. https://www.ngdc.noaa.gov (data obrasenia: 20.04.2016).
Downloads
Published
Issue
Section
License
Copyright (c) 2016 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.