Numerical coupled model of creeping flow of multi-phase fluid
DOI:
https://doi.org/10.7242/1999-6691/2020.13.2.12Keywords:
coupled model, viscous compaction, Reynolds equations, small parameter method, finite element method, ocean-continent active transient zoneAbstract
Two-dimensional couple numerical model of creeping flow of multi-phase fluid has been developed. The computational domain consists of relatively thick layer of two-phase medium overlaid by a thin multi-layered viscous sheet. There is mass transition at the conjunction boundary between light component of two-phase layer and the bottom layer of viscous sheet. The general system of governing equations consists of the equations of compaction describing the flow in the two-phase layer and the Reynolds equations describing the flow in the sheet. We take into account the layer structure of the sheet and surface processes of erosion and sedimentation as well. We use the additional asymptotic boundary condition to couple different-type hydrodynamic equations without any iterative improvements. That condition reduces significantly computational costs in comparison with the available coupled models. We fulfill numerical modeling of the evolution of the velocity field and layer boundaries. Numerical results reveal different regimes of evolution of velocity field and layer boundaries at short and long times. At least it consists of two stages with typical time scales, namely, a fast evolution at short times changed by slowly (quasistationary) stage at long times. That kind of evolution depends on geometrical and physical parameters of media rather than external causes. Some possible applications in tectonics and geophysics of these model results are outlined. They can be applied to investigate lithosphere thinning beneath large-scale tectonic depressions. Numerical calculations can be applied in geophysics to study the process of accumulation lightened mantle beneath the Earth crust of active transient zone of ocean-continent.
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Cai Z., Bercovici D. Two-phase damage models of magma-fracturing. Earth and Planet. Sci. Lett., 2011, vol. 368, pp. 1-8. https://doi.org/10.1016/j.epsl.2013.02.023">https://doi.org/10.1016/j.epsl.2013.02.023
Omlin S., Räss L., Podladchikov Y.Y. Simulation of three-dimensional viscoelastic deformation coupled to porous fluid flow. Tectonophysics, 2018, vol. 746, pp. 695-701. https://doi.org/10.1016/j.tecto.2017.08.012">https://doi.org/10.1016/j.tecto.2017.08.012
Nikolayevskiy V.N. Geomekhanika i flyuidodinamika [Geomechanics and fluid dynamics]. Moscow, Nedra, 1996. 447 p.
Nigmatulin R.I. Dynamics of multi-phase media. Vol. 1. CRC Press, 1990. 532p.
Pak V.V. Numerical model of solid-phase precipitation in a two-temperature fluid-saturated viscous medium. Vychisl. mekh. splosh. sred – Computational Continuum Mechanics, 2012, vol. 5, no. 2, pp. 151-157. https://doi.org/10.7242/1999-6691/2012.5.2.18">https://doi.org/10.7242/1999-6691/2012.5.2.18
Trubitsyn V.P., Kharybin E.V. Konvektivnaya neustoychivost’ rezhima sedimentatsii v mantii [Convective instability of the sedimentation regime in the mantle]. Izv. AN SSSR. Fizika Zemli – Izv., Phys. Solid Earth, 1987, no. 7, pp. 21-30.
Baes M., Sobolev S., Gerya T., Brune S. Plume-induced subduction initiation: Single-slab or multi-slab subduction? Geochemistry, Geophysics, Geosystems, 2020, vol. 21, no. 2. https://doi.org/10.1029/2019GC008663">https://doi.org/10.1029/2019GC008663
Schubert G., Turcotte D.L., Olsen P. Mantle convection in the Earth and planets. Cambridge University Press, 2001. 956 p. https://doi.org/10.1017/CBO9780511612879">https://doi.org/10.1017/CBO9780511612879
Pak V.V. Modeling the evolution of three-layered Stokes flow and some geophysical applications. Vychisl. mekh. splosh. Sred – Computational Continuum Mechanics, 2018, vol. 11, no. 3, pp. 275-287. https://doi.org/10.7242/1999-6691/2018.11.3.21">https://doi.org/10.7242/1999-6691/2018.11.3.21
Happel J., Brenner H. Low Reynolds number hydrodynamics with special applications to particulate media. Prentice-Hall, 1965. 553 p.
Tan E., Choi E., Thoutireddy P., Gurnis M., Aivazis M. GeoFramework: Coupling multiple models of mantle convection within a computational framework. Geochem. Geophys. Geosyst., 2006, vol. 7, no. 6, Q06001. https://doi.org/10.1029/2005GC001155">https://doi.org/10.1029/2005GC001155
Rodnikov A.G., Sergeyeva N.A., Zabarinskaya L.P., Filatova N.I., Piip V.B., Rashidov V.A. The deep structure of active continental margins of the Far East (Russia). Russ. J. Earth Sci., 2008, vol. 10, ES4002. https://doi.org/10.2205/2007ES000224">https://doi.org/10.2205/2007ES000224
Kiraly A., Portner D.E., Haynie K.L., Chilson-Parks B.H., Ghosh T., Jadamec M., Makushkina A., Manga M., Moresi L., O'Farrell K.A. The effect of slab gaps on subduction dynamics and mantle upwelling. Tectonophysics, 2020, vol. 785, 228458. https://doi.org/10.1016/j.tecto.2020.228458">https://doi.org/10.1016/j.tecto.2020.228458
Trubitsyn V.P. Viscosity distribution in the mantle convection models. Izv., Phys. Solid Earth, 2016, vol. 52, pp. 627-636. https://doi.org/10.1134/S1069351316050153">https://doi.org/10.1134/S1069351316050153
Chen A., Darbon J., Morel J.-M. Landscape evolution models: A review of their fundamental equations. Geomorphology, 2014, vol. 219, pp. 68-86. https://doi.org/10.1016/j.geomorph.2014.04.037">https://doi.org/10.1016/j.geomorph.2014.04.037
Fedotov S.A., Gusev A.A., Chernysheva G.V., Shumilina L.S. Seysmofokal’naya zona Kamchatki (geometriya, razmeshcheniye ochagov, svyaz’ s vulkanizmom) [Seismic focal zone of Kamchatka (geometry, location of foci, connection with volcanism)]. Vulkanologiya i seysmologiya – J. of Volcanology and Seismology, 1985, no. 4, pp. 91-107.
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