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Governing equations

The governing equations of numerical modelling include conservation of mass, momentum, and energy with different types of rheology.

The governing equations of geodynamic numerical modelling include conservation of mass, momentum, and energy with different types of rheology. ρ is the density, t is time, v the velocity vector, σ the stress tensor, g the gravitational acceleration vector, Cp the heat capacity, T the temperature, k the thermal conductivity, H a volumetric heat production term (e.g., due to radioactive decay) and the term S = S + S2 + S3 accounts for friction heating, adiabatic heating, and the release or consumption of latent heat (e.g., associated with phase changes), respectively. Note that the plastic rheology depicted here is the geodynamic approximation of brittle failure.

  • Creator: Fabio Crameri
  • This version: 19.01.2022
  • 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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Computing

Different computation paradigms including sequential and parallel programming each with the corresponding discretised domain.

Different computation paradigms including sequential and parallel programming each with the corresponding discretised domain shown on the left. For sequential programming, the code performs two tasks A and B in a sequential manner, on a single thread which has access to all of the computer’s memory. When the same code is executed in parallel relying on OpenMP, each processor of the computer concurrently carries out a part of tasks A and B so that the compute wall clock time is shorter. If relying on MPI-based parallelisation, the domain is usually broken up so that each thread ‘knows’ only a part of the domain. Tasks A and B are also executed in parallel by all the CPUs, but now, there is a distributed architecture of processors and memory interlinked by a dedicated network. The Scientific colour map ‘batlow‘ is used to represent individual domain parts to all readers.

  • Creator: Fabio Crameri
  • This version: 11.11.2021
  • 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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Numerical discretisation (space & time)

One-dimensional discretisation in space and time based on discrete temporal and spatial steps.

One-dimensional discretisation used in geodynamic numerical models in space (horizontal axis) and time (vertical axis) based on discrete steps in space (h) and time (Δt).

  • Creator: Fabio Crameri
  • This version: 11.11.2021
  • 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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Deformation mechanisms

The three deformation mechanisms viscous, elastic, and brittle (a.k.a. plastic).

Icons representing the three deformation mechanisms viscous, elastic, and brittle (a.k.a. plastic).

  • Creator: Fabio Crameri
  • This version: 22.09.2021
  • 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 scales

Spatial and temporal scales of common geodynamic processes, which occur over a wide range of time and length scales.

Spatial and temporal scales of common geodynamic processes, which occur over a wide range of time and length scales. The Scientific colour map batlow is used to represent the space-time areas of individual processes to all readers.

  • Creator: Fabio Crameri
  • This version: 07.09.2021
  • 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
  • Dark version
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  • Colour-vision deficiency friendly
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Faulty or missing link? – Please report them via a reply below!

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