Common numerical problems in geodynamic modelling including drunken sailor instability, chequerboard patterns, and mesh dependency.

Common numerical problems in geodynamic modelling. (a) They include a Rayleigh-Taylor instability problem termed „drunken sailor“ instability, which arises from a numerical time step that is too large (e.g. Kaus et al., 2010; Rose et al., 2017) for the stress perturbations deriving from surface topography due to the typical crust-air density difference being much larger than density differences inside the Earth. The large time step size leads to a fast sloshing of the surface, as seen from the velocity vectors. Note that the vectors in the model without stabilisation are scaled down by one order of magnitude. The high velocities also lead to overshooting of the advected compositional field, i.e., values exceed 1. (b) The lid-driven cavity model (e.g. Erturk et al., 2005; Erturk, 2009; Thieulot, 2014) demonstrates the need for smoothing the pressure field when using Q1 x P0 elements in the finite element method. (c) Extension of a visco-plastic medium with shear bands forming at a viscous weak seed along the bottom (e.g. Lemiale et al., 2008; Kaus, 2010; Spiegelman et al., 2016; Glerum et al., 2018). The angle and thickness of the shear bands is dependent on the mesh resolution. Regularised plasticity implementations and sufficient resolution are required to achieve convergence with resolution (e.g. Duretz et al., 2020).

  • Creator: Fabio Crameri
  • This version: 12.11.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from van Zelst et al. (2021) is available via the open-access s-Ink repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2021, in review), 101 Geodynamic modelling: How to design, carry out, and interpret numerical studies, Solid Earth Discuss. [preprint], doi:10.5194/se-2021-14
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