The numerical modeling of lava dome evolution at volcán de Colima using VOF and SPH methods
DOI:
https://doi.org/10.7242/1999-6691/2022.15.3.20Keywords:
viscous flow, multiphase flow, Navier–Stokes equations, boundary value problem, numerical simulation, smooth particle hydrodynamics, volcanic eruption, volcan de ColimaAbstract
Lava flows from extrusive volcanic eruptions can have catastrophic consequences both for human life and the environment. Modeling such situations is an important scientific problem. The main driving forces in the evolution of the mentioned lava flows are gravitational forces, viscous friction forces on the surface of the spill, and the processes of crystallization of molten rocks into lava plateau, tubes, and domes. In this paper, the mathematical model of an extrusive volcanic eruption includes the Navier–Stokes equation, the incompressibility equation, the viscous phase transfer equation, as well as the corresponding initial and boundary conditions. Mathematical models of volcanic lava flows are considered and compared within the Euler (Volume Of Fluid – VOF) and Lagrange (Smooth Particle Hydrodynamic – SPH) formulations. ANSYS Fluent, OpenFOAM, and SPlisHSPlasH packages were used for computer simulation. Computer simulation algorithms for the problem are implemented in C++ language. Numerical modeling of the evolution of a real lava dome formed at the Colima volcano (Mexico) in February–March 2013 was carried out. For this experiment, information about the dynamics of lava dome growth, collected during the eruption, was used. It is shown how the computer simulation approach makes it possible to establish the dependence of the lava dome morphology on the rheology of a highly viscous fluid and the intensity of lava outflow.
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Costa A., Macedonio G. Computational modeling of lava flows: A review. Kinematics and dynamics of lava flows, ed. M. Manga, G. Ventura. Geological Society of America, 2005. P. 209-218. https://doi.org/10.1130/0-8137-2396-5.209
Cordonnier B., Lev E., Garel F. Benchmarking lava-flow models. Detecting, modelling and responding to effusive eruptions, ed. A.J.L. Harris, T. De Groeve, F. Garel, S.A. Carn. Geological Society of London, 2016. P. 425-445. https://doi.org/10.1144/SP426.7
Hirt C.W., Nichols B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys., 1981, vol. 39, pp. 201-225. https://doi.org/10.1016/0021-9991(81)90145-5
Monaghan J.J. Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys., 1992, vol. 30, pp. 543-574.
Patankar S.V. Computation of conduction and duct flow heat transfer. CRC Press, 2019. 370 p.
Tsepelev I., Ismail-Zadeh A., Melnik O. Lava dome morphology inferred from numerical modeling. Geophys. J. Int., 2020, vol. 223, pp. 1597-1609. https://doi.org/10.1093/gji/ggaa395
Zobin V.M., Arámbula R., Bretón M., Reyes G., Plascencia I., Navarro C., Téllez A., Campos A., González M., León Z., Martínez A., Ramírez C. Dynamics of the January 2013–June 2014 explosive-effusive episode in the eruption of Volcán de Colima, México: insights from seismic and video monitoring. Bull. Volcanol., 2015, vol. 77, p. 31. https://doi.org/10.1007/s00445-015-0917-z
Walter T.R., Harnett C.E., Varley N., Bracamontes D.V., Salzer J., Zorn E.U., Bretón M., Arámbula R., Thomas M.E. Imaging the 2013 explosive crater excavation and new dome formation at Volcan de Colima with TerraSAR-X, time-lapse cameras and modelling. J. Volcanol. Geoth. Res., 2019, vol. 369, pp. 224-237. https://doi.org/10.1016/j.jvolgeores.2018.11.016
Nigmatulin R.I. Dynamics of multiphase media. Vol. 1. Hemisphere Pub. Corp., 1991. 532 p.
Chandrasekhar S. Hydrodynamic and hydromagnetic stability. Clarendon Press, 1961. 652 p.
Tsepelev I.A., Ismail-Zadeh A.T., Melnik O.E. Lava dome evolution at Volcán de Colima, México during 2013: Insights from numerical modeling. J. Volcanolog. Seismol., 2021, vol. 15, pp. 491-501. https://doi.org/10.1134/S0742046321060117
Korotkii A.I., Starodubtseva Yu.V., Tsepelev I.A. Gravitational flow of a two-phase viscous incompressible liquid. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 4, pp. 61-73. https://doi.org/10.21538/0134-4889-2021-27-4-61-73
Chevrel M.O., Platz T., Hauberet E., Baratoux D., Lavallée Y., Dingwell D.B. Lava flow rheology: A comparison of morphological and petrological methods. Earth Planet. Sci. Lett., 2013, vol. 384, pp. 109-120. https://doi.org/10.1016/j.epsl.2013.09.022
Lejeune A.-M., Richet P. Rheology of crystal-bearing silicate melts: An experimental study at high viscosity. J. Geophys. Res., 1995, vol. 100, pp. 4215-4229. https://doi.org/10.1029/94JB02985
Costa A., Caricchi L., Bagdassarov N. A model for the rheology of particle-bearing suspensions and partially molten rocks. Geochem. Geophys. Geosys., 2009, vol. 10, Q03010. https://doi.org/10.1029/2008GC002138
Mardles E.W.J. Viscosity of suspensions and the Einstein equation. Nature, 1940, vol. 145, p. 970. https://doi.org/10.1038/145970a0
Jeffrey D.J., Acrivos A. The rheological properties of suspensions of rigid particles. AIChE J., 1976, vol. 22, pp. 417-432. https://doi.org/10.1002/aic.690220303
https://www.ansys.com/products/fluids/ansys-fluent (accessed 25 August 2022)
Lister J.R. Viscous flows down an inclined plane from point and line sources. J. Fluid Mech., 1992, vol. 242, pp. 631-653. https://doi.org/10.1017/S0022112092002520
https://openfoam.org/ (accessed 25 August 2022)
Liu G.R., Liu M.B. Smoothed particle hydrodynamics: A meshfree particle method. World Scientific. 2003. 472 p. https://doi.org/10.1142/5340
Violeau D. Dissipative forces for Lagrangian models in computational fluid dynamics and application to smoothed-particle hydrodynamics. Phys. Rev. E, 2009, vol. 80, 036705. https://doi.org/10.1103/PhysRevE.80.036705
Bender J., Koschier D. Divergence-free SPH for incompressible and viscous fluids. IEEE Trans. Visual. Comput. Graph., 2016, vol. 23, pp. 1193-1206. https://doi.org/10.1109/TVCG.2016.2578335
Bender J., Kugelstadt T., Weiler M., Koschier D. Proc. of the MIG '19: Motion, Interaction and Games. Newcastle upon Tyne, United Kingdom, October 28-30, 2019. Art. 26. 10 p. https://doi.org/10.1145/3359566.3360077
Sandim M., Cedrim D., Nonato L.G., Pagliosa P., Paiva A. Boundary detection in particle-based fluids. Comput. Graph. Forum, 2016, vol. 35, pp. 215-224. https://doi.org/10.1111/cgf.12824
https://splishsplash.readthedocs.io/en/2.9.0/about.html (accessed 25 August 2022)
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