Articles | Volume 14, issue 4
https://doi.org/10.5194/gmd-14-1899-2021
https://doi.org/10.5194/gmd-14-1899-2021
Methods for assessment of models
 | 
09 Apr 2021
Methods for assessment of models |  | 09 Apr 2021

Analytical solutions for mantle flow in cylindrical and spherical shells

Stephan C. Kramer, D. Rhodri Davies, and Cian R. Wilson

Related authors

Anisotropic metric-based mesh adaptation for ice flow modelling in Firedrake
Davor Dundovic, Joseph G. Wallwork, Stephan C. Kramer, Fabien Gillet-Chaulet, Regine Hock, and Matthew D. Piggott
EGUsphere, https://doi.org/10.5194/egusphere-2024-2649,https://doi.org/10.5194/egusphere-2024-2649, 2024
Short summary
Automatic adjoint-based inversion schemes for geodynamics: reconstructing the evolution of Earth's mantle in space and time
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024,https://doi.org/10.5194/gmd-17-5057-2024, 2024
Short summary
Towards automatic finite-element methods for geodynamics via Firedrake
D. Rhodri Davies, Stephan C. Kramer, Sia Ghelichkhan, and Angus Gibson
Geosci. Model Dev., 15, 5127–5166, https://doi.org/10.5194/gmd-15-5127-2022,https://doi.org/10.5194/gmd-15-5127-2022, 2022
Short summary
Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations
Tuomas Kärnä, Stephan C. Kramer, Lawrence Mitchell, David A. Ham, Matthew D. Piggott, and António M. Baptista
Geosci. Model Dev., 11, 4359–4382, https://doi.org/10.5194/gmd-11-4359-2018,https://doi.org/10.5194/gmd-11-4359-2018, 2018
Short summary

Related subject area

Solid Earth
ShellSet v1.1.0 parallel dynamic neotectonic modelling: a case study using Earth5-049
Jon B. May, Peter Bird, and Michele M. C. Carafa
Geosci. Model Dev., 17, 6153–6171, https://doi.org/10.5194/gmd-17-6153-2024,https://doi.org/10.5194/gmd-17-6153-2024, 2024
Short summary
FastIsostasy v1.0 – a regional, accelerated 2D glacial isostatic adjustment (GIA) model accounting for the lateral variability of the solid Earth
Jan Swierczek-Jereczek, Marisa Montoya, Konstantin Latychev, Alexander Robinson, Jorge Alvarez-Solas, and Jerry Mitrovica
Geosci. Model Dev., 17, 5263–5290, https://doi.org/10.5194/gmd-17-5263-2024,https://doi.org/10.5194/gmd-17-5263-2024, 2024
Short summary
Automatic adjoint-based inversion schemes for geodynamics: reconstructing the evolution of Earth's mantle in space and time
Sia Ghelichkhan, Angus Gibson, D. Rhodri Davies, Stephan C. Kramer, and David A. Ham
Geosci. Model Dev., 17, 5057–5086, https://doi.org/10.5194/gmd-17-5057-2024,https://doi.org/10.5194/gmd-17-5057-2024, 2024
Short summary
Benchmarking the accuracy of higher-order particle methods in geodynamic models of transient flow
Rene Gassmöller, Juliane Dannberg, Wolfgang Bangerth, Elbridge Gerry Puckett, and Cedric Thieulot
Geosci. Model Dev., 17, 4115–4134, https://doi.org/10.5194/gmd-17-4115-2024,https://doi.org/10.5194/gmd-17-4115-2024, 2024
Short summary
REHEATFUNQ (REgional HEAT-Flow Uncertainty and aNomaly Quantification) 2.0.1: a model for regional aggregate heat flow distributions and anomaly quantification
Malte Jörn Ziebarth and Sebastian von Specht
Geosci. Model Dev., 17, 2783–2828, https://doi.org/10.5194/gmd-17-2783-2024,https://doi.org/10.5194/gmd-17-2783-2024, 2024
Short summary

Cited articles

Backus, G.: Poloidal and toroidal fields in geomagnetic field modeling, Rev. Geophys., 24, 75–109, 1986. a, b
Balay, S., Gropp, W. D., McInnes, L. C., and Smith, B. F.: Efficient management of parallelism in object-oriented numerical software libraries, in: Modern software tools for scientific computing, Birkhauser, Boston Inc., 163–202, 1997. a
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. a
Bernardi, C.: Optimal finite-element interpolation on curved domains, SIAM J. Numer. Anal., 26, 1212–1240, 1989. a
Blankenbach, B., Busse, F., Christensen, U., Cserepes, L., Gunkel, D., Hansen, U., Harder, H., Jarvis, G., Koch, M., Marquart, G., Moore, D., Olson, P., Schmeling, H., and Schnaubelt, T.: A benchmark comparison for mantle convection codes, Geophys. J. Int., 98, 23–38, https://doi.org/10.1111/j.1365-246X.1989.tb05511.x, 1989. a
Download
Short summary
Computational models of Earth's mantle require rigorous verification and validation. Analytical solutions of the underlying Stokes equations provide a method to verify that these equations are accurately solved for. However, their derivation in spherical and cylindrical shell domains with physically relevant boundary conditions is involved. This paper provides a number of solutions. They are provided in a Python package (Assess) and their use is demonstrated in a convergence study with Fluidity.