Articles | Volume 6, issue 4
https://doi.org/10.5194/gmd-6-1095-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/gmd-6-1095-2013
© Author(s) 2013. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
A hierarchical mesh refinement technique for global 3-D spherical mantle convection modelling
D. R. Davies
Department of Earth Science & Engineering, Imperial College London, London, UK
Research School of Earth Sciences, The Australian National University, Canberra, Australia
J. H. Davies
Department of Earth & Ocean Sciences, Cardiff University, Cardiff, Wales, UK
P. C. Bollada
Institute for Materials Research, Faculty of Engineering, Leeds University, Leeds, UK
O. Hassan
Civil and Computational Engineering Centre, School of Engineering, Swansea University, Swansea, Wales, UK
K. Morgan
Civil and Computational Engineering Centre, School of Engineering, Swansea University, Swansea, Wales, UK
P. Nithiarasu
Civil and Computational Engineering Centre, School of Engineering, Swansea University, Swansea, Wales, UK
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Gwynfor T. Morgan, J. Huw Davies, Robert Myhill, and James Panton
Solid Earth, 16, 297–314, https://doi.org/10.5194/se-16-297-2025, https://doi.org/10.5194/se-16-297-2025, 2025
Short summary
Short summary
Phase transitions can influence mantle convection, inhibiting or promoting vertical flow. We are motivated by two examples: the post-spinel reaction proceeding via akimotoite at cool temperatures and a curving post-garnet boundary. Some have suggested these could change mantle dynamics. We find this is unlikely for both reactions: the first due to the uniqueness of thermodynamic state and the second due to the low magnitude of the boundary’s slope in pressure–temperature space and density change.
Conor P. B. O'Malley, Gareth G. Roberts, James Panton, Fred D. Richards, J. Huw Davies, Victoria M. Fernandes, and Sia Ghelichkhan
Geosci. Model Dev., 17, 9023–9049, https://doi.org/10.5194/gmd-17-9023-2024, https://doi.org/10.5194/gmd-17-9023-2024, 2024
Short summary
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We wish to understand how the history of flowing rock within Earth's interior impacts deflection of its surface. Observations exist to address this problem, and mathematics and different computing tools can be used to predict histories of flow. We explore how modeling choices impact calculated vertical deflections. The sensitivity of vertical motions at Earth's surface to deep flow is assessed, demonstrating how surface observations can enlighten flow histories.
Duo Zhang and J. Huw Davies
Solid Earth, 15, 1113–1132, https://doi.org/10.5194/se-15-1113-2024, https://doi.org/10.5194/se-15-1113-2024, 2024
Short summary
Short summary
We numerically model the influence of an arc on back-arc extension. The arc is simulated by placing a hot region on the overriding plate. We investigate how plate ages and properties of the hot region affect back-arc extension and present regime diagrams illustrating the nature of back-arc extension for these models. We find that back-arc extension occurs not only in the hot region but also, surprisingly, away from it, and a hot region facilitates extension on the overriding plate.
Cited articles
Albers, M.: A local mesh refinement multigrid method for 3-D convection problems with strongly variable viscosity, J. Comput. Phys., 160, 126–150, https://doi.org/10.1006/jcph.2000.6438, 2000.
Atanga, J. and Silvester, D.: Iterative methods for stabilized mixed velocity pressure finite elements, Int. J. Numer. Meth. Fluids, 14, 71–81, https://doi.org/10.1002/fld.1650140106, 1992.
Bai, D. and Brandt, A.: Local mesh refinement and multilevel techniques, SIAM J. Sci. Stat. Comp., 8, 109–134, 1987.
Baumgardner, J. R.: Three-dimensional treatment of convective flow in the Earth's mantle, J. Stat. Phys., 39, 501–511, https://doi.org/10.1007/BF01008348, 1985.
Baumgardner, J. R. and Frederickson, P. O.: Icosahedral discretization of the two-sphere, SIAM J. Numer. Anal., 22, 1107–1115, 1985.
Bercovici, D., Schubert, G., and Glatzmaier, G. A.: 3-D spherical models of convection in the Earth's mantle, Science, 244, 950–955, 1989.
Bower, D. J., Gurnis, M., and Seton, M.: Lower mantle structure from paleogeographically constrained dynamic Earth models, Geochem. Geophy. Geosy., 14, 44–64, https://doi.org/10.1029/2012GC004267, 2013.
Brandt, A.: Multilevel adaptive solutions to boundary value problems, Math. Comput., 31, 333–390, https://doi.org/10.2307/2006422, 1977.
Brandt, A.: Multigrid techniques: 1984 guide with applications to fluid dynamics, GMD-Studien Nr. 85, Germany, 1984.
Briggs, W. L., Henson, V. E., and McCormick, S. F.: A multigrid tutorial, 2nd Edn., SIAM, USA, 2000.
Bunge, H.-P. and Baumgardner, J. R.: Mantle convection modeling on parallel virtual machines, Comput. Phys., 9, 207–215, 1996.
Bunge, H.-P., Richards, M. A., and Baumgardner, J. R.: The effect of depth-dependent viscosity on the planform of mantle convection, Nature, 279, 436–438, https://doi.org/10.1038/379436a0, 1996.
Bunge, H.-P., Richards, M. A., and Baumgardner, J. R.: A sensitivity study of 3-D-spherical mantle convection at 10$^8$ Rayleigh number: effects of depth-dependent viscosity, heating mode and an endothermic phase change, J. Geophys. Res., 102, 11991–12007, https://doi.org/10.1029/96JB03806, 1997.
Burstedde, C., Stadler, G., Alisic, L., Wilcox, L. C., Tan, E., Gurnis, M., and Ghattas, O.: Large-scale adaptive mantle convection simulation, Geophys. J. Int., 192, https://doi.org/10.1093/gji/ggs070, 2013.
Choblet, G., Cadek, O., Couturier, F., and Dumoulin, C.: OEDIPUS: a new tool to study the dynamics of planetary interiors, Geophys. J. Int., 170, 9–30, https://doi.org/10.1111/j.1365-246X.2007.03419.x, 2007.
Davies, D. R. and Davies, J. H.: Thermally-driven mantle plumes reconcile multiple hot–spot observations, Earth Planet. Sc. Lett., 278, 50–54, https://doi.org/10.1016/j.epsl.2008.11.027, 2009.
Davies, D. R., Davies, J. H., Hassan, O., Morgan, K., and Nithiarasu, P.: Investigations into the applicability of adaptive finite element methods to two-dimensional infinite Prandtl number thermal and thermochemical convection, Geochem. Geophy. Geosy., 8, Q05010, https://doi.org/10.1029/2006GC001470, 2007.
Davies, D. R., Davies, J. H., Hassan, O., Morgan, K., and Nithiarasu, P.: Adaptive finite element methods in geodynamics: convection dominated mid-ocean ridge and subduction zone simulations, Int. J. Numer. Method. H., 18, 1015–1035, https://doi.org/10.1108/09615530810899079, 2008.
Davies, D. R., Wilson, C. R., and Kramer, S. C.: Fluidity: a fully unstructured anisotropic adaptive mesh computational modeling framework for geodynamics, Geochem. Geophy. Geosy., 120, Q06001, https://doi.org/10.1029/2011GC003551, 2011.
Davies, D. R., Goes, S., Davies, J. H., Schuberth, B. S. A., Bunge, H., and Ritsema, J.: Reconciling dynamic and seismic models of Earth's lower mantle: the dominant role of thermal heterogeneity, Earth Planet. Sc. Lett., 353–354, 253–269, https://doi.org/10.1016/j.epsl.2012.08.016, 2012.
Davies, J. H.: Steady plumes produced by downwellings in Earth-like vigor spherical whole mantle convection models, Geochem. Geophy. Geosy., 6, https://doi.org/10.1029/2005GC001042, 2005.
Davies, J. H. and Stevenson, D. J.: Physical Model of Source Region of Subduction Zone Volcanics, J. Geophys. Res., 97, 2037–2070, https://doi.org/10.1029/91JB02571, 1992.
Gurnis, M. and Davies, G. F.: Mixing in numerical-models of mantle convection incorporating plate kinematics, J. Geophys. Res., 91, 6375–6395, https://doi.org/10.1029/JB091iB06p06375, 1986.
Hager, B. H. and O'Connell, R. J.: A simple global model of plate dynamics and mantle convection, J. Geophys. Res., 86, 4843–4867, https://doi.org/10.1029/JB086iB06p04843, 1981.
Hager, B. H., Clayton, R. W., Richards, M. A., Comer, R. P., and Dziewonski, A. M.: Lower mantle heterogeneity, dynamic topography and the geoid, Nature, 313, 541–545, https://doi.org/10.1038/313541a0, 1985.
Hassan, O., Probert, E. J., Morgan, K., and Peraire, J.: Mesh generation and adaptivity for the solution of compressible viscous high speed flows, Int. J. Numer. Meth. Eng., 38, 1123–1148, https://doi.org/10.1002/nme.1620380704, 1995.
Hunt, S. A., Davies, D. R., Walker, A. M., McCormack, R. J., Wills, A. S., Dobson, D. P., and Li, L.: On the increase in thermal diffusivity caused by the perovskite to post-perovskite phase transition and its implications for mantle dynamics, Earth Planet. Sc. Lett., 319, 96–103, https://doi.org/10.1016/j.epsl.2011.12.009, 2012.
Kameyama, M., Kageyama, A., and Sato, T.: Multigrid iterative algorithm using pseudo-compressibility for three-dimensional mantle convection with strongly variable viscosity, J. Comput. Phys., 206, 162–181, https://doi.org/10.1016/j.jcp.2004.11.030, 2005.
King, S. D.: On topography and geoid from 2D stagnant-lid convection calculations, Geochem. Geophy. Geosy., 10, Q3002, https://doi.org/10.1029/2008GC002250, 2009.
Koestler, C.: Iterative solvers for modeling mantle convection with strongly varying viscosity, Ph.D. thesis, Friedrich-Schiller-Universitat, Jena, Germany, 2011.
Kramer, S. C., Wilson, C. R., and Davies, D. R.: An implicit free-surface algorithm for geodynamical simulations, Phys. Earth Planet. In., 194, 25–37, https://doi.org/10.1016/j.pepi.2012.01.001, 2012.
Kronbichler, M., Heister, T., and Bangerth, W.: High accuracy mantle convection simulation through modern numerical methods, Geophys. J. Int., 191, 12–29, https://doi.org/10.1111/j.1365-246X.2012.05609.x, 2012.
Labrosse, S.: Hotspots, mantle plumes and core heat loss, Earth Planet. Sc. Lett., 199, 147–156, https://doi.org/10.1016/S0012-821X(02)00537-X, 2002.
Lee, C. and King, S. D.: Effect of mantle compressibility on the thermal and flow structures of subduction zones, Geochem. Geophy. Geosy., 10, Q1006, https://doi.org/10.1029/2008GC002151, 2009.
Leng, W. and Zhong, S.: Implementation and application of adaptive mesh refinement for thermo–chemical mantle convection studies, Geochem. Geophy. Geosy., 12, Q04006, https://doi.org/10.1029/2010GC003425, 2011.
Lopez, S. and Casciaro, R.: Algorithmic aspects of adaptive multigrid finite element analysis, Int. J. Numer. Meth. Eng., 140, 919–936, 1997.
Lowman, J. P., King, S. D., and Gable, C. W.: Steady plumes in viscously stratified, vigorously convecting, three-dimensional numerical mantle convection models with mobile plates, Geochem. Geophy. Geosy., 5, Q01L01, https://doi.org/10.1029/2003GC000583, 2004.
McKenzie, D. P., Roberts, J. M., and Weiss, N. O.: Convection in the Earth's mantle: towards a numerical simulation, J. Fluid Mech., 62, 465–538, https://doi.org/10.1017/S0022112074000784, 1974.
McNamara, A. K. and Zhong, S.: Thermo–chemical structures beneath Africa and the Pacific Ocean, Nature, 437, 1136–1139, https://doi.org/10.1038/nature04066, 2005.
Miller, M. S. and Becker, T. W.: Mantle flow deflected by interactions between subducted slabs and cratonic keels, Nat. Geosci., 5, 726–730, https://doi.org/10.1038/ngeo1553, 2012.
Mitrovica, J. X. and Forte, A. M.: A new inference of mantle viscosity based upon joint inversion of convection and glacial isostatic adjustment data, Earth Planet. Sc. Lett., 225, 177–189, https://doi.org/10.1016/j.epsl.2004.06.005, 2004.
Moresi, L. N. and Solomatov, V. S.: Numerical investigations of 2D convection with extremely large viscosity variations, Phys. Fluids, 7, 2154–2162, https://doi.org/10.1063/1.868465, 1995.
Nakagawa, T. and Tackley, P. J.: Lateral variations in CMB heat flux and deep mantle seismic velocity caused by a thermal-chemical-phase boundary layer in 3D spherical convection, Earth Planet. Sc. Lett., 271, 348–358, https://doi.org/10.1016/j.epsl.2008.04.013, 2008.
Nakagawa, T., Tackley, P. J., Deschamps, F., and Connolly, J. A. D.: Incorporating self-consistently calculated mineral physics into thermo-chemical mantle convection simulations in a 3-D spherical shell and its influence on seismic anomalies in Earth's mantle, Geochem. Geophy. Geosy., 10, Q3304, https://doi.org/10.1029/2008GC002280, 2009.
Nithiarasu, P. and Zienkiewicz, O. C.: Adaptive mesh generation for fluid mechanics problems, Int. J. Numer. Meth. Eng., 47, 629–662, 2000.
Oldham, D. N. and Davies, J. H.: Numerical investigation of layered convection in a three-dimensional shell with application to planetary mantles, Geochem. Geophy. Geosy., 5, Q12C04, https://doi.org/10.1029/2003GC000603, 2004.
Peraire, J., Vahdati, M., Morgan, K., and Zienkiewicz, O.: Adaptive remeshing for compressible flow computations, J. Comput. Phys., 72, 449–466, https://doi.org/10.1016/0021-9991(87)90093-3, 1987.
Ramage, A. and Wathen, A. J.: Iterative solution techniques for the Stokes and Navier-Stokes equations, Int. J. Numer. Meth. Fl., 19, 67–83, https://doi.org/10.1002/fld.1650190106, 1994.
Ratcliff, J. T., Schubert, G., and Zebib, A.: Steady tetrahedral and cubic patterns of spherical shell convection with temperature-dependent viscosity, J. Geophys. Res., 101, 25473–25484, https://doi.org/10.1029/96JB02097, 1996.
Richards, M. A. and Hager, B. H.: Geoid anomalies in a dynamic Earth, J. Geophys. Res., 89, 5987–6002, 1984.
Schuberth, B. S. A., Bunge, H.-P., Steinle-Neumann, G., Moder, C., and Oeser, J.: Thermal versus elastic heterogeneity in high-resolution mantle circulation models with pyrolite composition: high plume excess temperatures in the lowermost mantle, Geochem. Geophy. Geosyst., 10, Q01W01, https://doi.org/10.1029/2008GC002235, 2009.
Stadler, G., Gurnis, M., Burstedde, C., Wilcox, L. C., Alisic, L., and Ghattas, O.: The dynamics of plate tectonics and mantle flow: from local to global scales, Science, 329, 1033–1038, https://doi.org/10.1126/science.1191223, 2010.
Stemmer, K., Harder, H., and Hansen, U.: A new method to simulate convection with strongly temperature- and pressure-dependent viscosity in a spherical shell: Applications to the Earth's mantle, Phys. Earth Planet. In., 157, 223–249, https://doi.org/10.1016/j.pepi.2006.04.007, 2006.
Styles, E., Davies, D. R., and Goes, S.: Mapping spherical seismic into physical structure: biases from 3-D phase-transition and thermal boundary-layer heterogeneity, Geophys. J. Int., 184, 1371–1378, https://doi.org/10.1111/j.1365-246X.2010.04914.x, 2011.
Tackley, P. J.: Effects of strongly variable viscosity on three-dimensional compressible convection in planetary mantles, J. Geophys. Res., 101, 3311–3332, https://doi.org/10.1029/95JB03211, 1996.
Tackley, P. J.: Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the Yin-Yang grid, Phys. Earth Planet. In., 171, 7–18, https://doi.org/10.1016/j.pepi.2008.08.005, 2008.
Tackley, P. J., Stevenson, D. J., Glatzmaier, G. A., and Schubert, G.: Effects of an endothermic phase transition at 670 km depth in a spherical model of convection in the Earth's mantle, Nature, 361, 699–704, https://doi.org/10.1038/361699a0, 1993.
Tan, E., Leng, W., Zhong, S., and Gurins, M.: On the location of plumes and mobility of thermo-chemical structures with high bulk modulus in the 3-D compressible mantle, Geochem. Geophy. Geosy., 12, Q07005, https://doi.org/10.1029/2011GC003665, 2011.
Thompson, C. P., Leaf, G. K., and Van Rosendale, J.: A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equation - validation and model problems, Appl. Numer. Math., 9, 511–532, https://doi.org/10.1016/0168-9274(92)90005-X, 1992.
van Keken, P. E., Kiefer, B., and Peacock, S.: High resolution models of subduction zones: Implications for mineral dehydration reactions and the transport of water into the deep mantle, Geochem. Geophy. Geosy., 3, 1056, https://doi.org/10.1029/2001GC000256, 2002.
Verfuerth, R.: A combined Conjugate Gradient-multigrid algorithm for the numerical solution of the Stokes problem, IMA J. Numer. Anal., 4, 441–455, 1984.
Wolstencroft, M. and Davies, J. H.: Influence of the Ringwoodite-Perovskite transition on mantle convection in spherical geometry as a function of Clapeyron slope and Rayleigh number, Solid Earth, 2, 315–326, https://doi.org/10.5194/se-2-315-2011, 2011.
Wolstencroft, M., Davies, J. H., and Davies, D. R.: Nusselt-Rayleigh number scaling for spherical shell Earth mantle simulation up to a Rayleigh number of $10^9$, Phys. Earth Planet. In., 176, 132–141, https://doi.org/10.1016/j.pepi.2009.05.002, 2009.
Yang, W. S. and Baumgardner, J. R.: A matrix-dependent transfer multigrid method for strongly variable viscosity infinite Prandtl number thermal convection, Geophys. Astro. Fluid, 92, 151–195, https://doi.org/10.1080/03091920008203715, 2000.
Yoshida, M. and Kageyama, A.: Application of the Yin-Yang grid to a thermal convection of a Boussinesq fluid with infinite Prandtl number in a three-dimensional spherical shell, Geophys. Res. Lett., 31, https://doi.org/10.1029/2004GL019970, 2004.
Zhang, N., Zhong, S. J., Leng, W., and Li, Z. X.: A model for the evolution of Earth's mantle structure structure since the Early Paleozoic, J. Geophys. Res., 115, B06401, https://doi.org/10.1029/2009JB006896, 2010.
Zhong, S., Zuber, M. T., Moresi, L., and Gurnis, M.: Role of temperature-dependent viscosity and surface plates in spherical shell models of mantle convection, J. Geophys. Res., 105, 11063–11082, https://doi.org/10.1029/2000JB900003, 2000.
Zhong, S., McNamara, A., Tan, E., Moresi, L., and Gurnis, M.: A benchmark study on mantle convection in a 3-D spherical shell using CitcomS, Geochem. Geophy. Geosy., 9, Q10017, https://doi.org/10.1029/2008GC002048, 2008.