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Tag: Numerical modelling

Numerical modelling is explained in this collection of accurate, accessible science graphics, designed to make understanding complex Earth science simulations clear and engaging. These visuals show how computational models are used to study processes such as plate tectonics, mantle convection, and subduction, turning abstract data into intuitive, easy-to-grasp representations. Ideal for educators, students, and geoscience enthusiasts, this numerical modelling graphic collection brings cutting-edge geoscience research to life with visually rich resources for teaching and learning.

Solid-state convection

Simulation of infinite Prandtl number, thermal convection (e.g., mantle convection).

Simulation of infinite Prandtl number, thermal convection (e.g., mantle convection). Simulations are run for variable Rayleigh numbers (Ra) and with or without internal heating (H) on a grid with 64×64 discrete nodes using an isoviscous formulation (unless marked otherwise). Equations solved are non-dimensionalised (nd) and the domain boundaries free-slip (impermeable) and insulating on both domain sides, and isothermally hot at the bottom and cold at the top. The Scientific colour map ‘vik‘ is used to represent data accurately and to all readers.

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Solid-state convection (animation)

Simulation of infinite Prandtl number, thermal convection (e.g., mantle convection).

Animated simulation of infinite Prandtl number, thermal convection (e.g., mantle convection). Simulations are run for variable Rayleigh numbers (Ra) and with or without internal heating (H) on a grid with 64×64 discrete nodes using an isoviscous formulation (unless marked otherwise). Equations solved are non-dimensionalised (nd) and the domain boundaries are free-slip (impermeable) and insulating on both domain sides, and isothermally hot at the bottom and cold at the top. The stream-function indicates the instantaneous direction of the flow at any given point in time. The Scientific colour maps ‘vik’ and ‘cork‘ are used to represent data accurately and to all readers.

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Geodynamic modelling philosophies

The two overarching geodynamic modelling philosophies: Specific modelling and generic modelling.

The two overarching geodynamic modelling philosophies. (a) Specific modelling and (b) generic modelling have different scientific goals and need to be used, communicated, and reviewed differently.

  • 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.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
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Manuscript structure (geodynamic modelling)

Manuscript structure for a geodynamic numerical modelling study following the IMRAD structure.

Manuscript structure for a geodynamic numerical modelling study following the IMRAD structure. In particular, the methods section should include a description of the physical and numerical model, the design of the study, and of any techniques used to visualise and analyse the numerical data.

  • 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.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
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Geodynamic model complexity

Different model complexities for the heart (top) and the Earth (bottom).

Different model complexities for the heart (top) and the Earth (bottom). A simpler model can be more useful: the basic shape of the heart has likely become the most successful model, indeed a true icon, only because it was neither too complex (it can be reproduced easily), nor too simple (its characteristic shape is still recognisable). Finding the right level of complexity is challenging and must repeatedly be considered carefully by the modeller for each new modelling task at hand.

  • 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.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
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Geodynamic model simplification

Potential options for geodynamic model simplification.

Potential options for geodynamic model simplification. Note that ‘multiphysics’ is meant beyond the already coupled system.

  • 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.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
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Effective visualisation (geodynamic modelling)

Effective visualisation through a scientific use of colours.

Effective visualisation through a scientific use of colours. Non-scientific colour maps (a,b) like rainbow always misrepresent data, are often not intuitive, and are inaccessible to a large portion of the readers, while scientific colour maps (c,d) like lajolla or vik (Crameri et al., 2020) ensure unbiased and intuitive data representation and are inclusive to readers with colour-vision deficiencies and even colour blindness.

  • 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.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
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Geodynamic modelling kinematic descriptions

Kinematical descriptions for a compressed upper-mantle geodynamic numerical model setup.

Examples of two-dimensional domain and material discretisation. The domain discretisation in the left-hand side column Kinematical descriptions for a compressed upper-mantle model setup. The left column shows the undeformed, initial model setups and the right column shows the deformed model after a certain amount of model time has passed. In the Eulerian kinematical description the computational mesh is fixed and the generated positive topography is accommodated by implementing a layer of sticky air above the crust. When an Arbitrary Lagrangian-Eulerian approach is used, the domain width is often kept constant in geodynamic applications, such that the mesh only deforms vertically to accommodate the topography. In the Lagrangian formulation, the mesh deforms with the velocity computed on its nodes.

  • 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.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
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Geodynamic modelling problems

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.org repository.
  • Related reference: van Zelst, I., F. Crameri, A.E. Pusok, A.C. Glerum, J. Dannberg, C. Thieulot (2022), 101 geodynamic modelling: how to design, interpret, and communicate numerical studies of the solid Earth, Solid Earth, 13, 583–637, doi:10.5194/se-13-583-2022
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