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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.

Geodynamic modelling procedure

The procedure of a geodynamic modelling study.

The procedure of a geodynamic modelling study encompasses everything from the assemblage of both a physical and a numerical models based on a verified numerical code, to the design of a simplified model setup based on a certain modelling philosophy, the validation of the model through careful testing, the unbiased analysis of the produced model output, the oral, written, and graphical communication of the modelling approach and results, and the management of both software and data. Constant (re-)evaluation and potential subsequent adjustments of previous steps are key, and indeed necessary, throughout this process.

  • 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 (domain & material)

Examples of numerical, two-dimensional domain and material discretisation.

Examples of two-dimensional domain and material discretisation. The domain discretisation in the left-hand side column illustrates different types of meshes. The top left mesh is built on a quadtree and also shown with several levels of mesh refinement (middle left) so as to better capture the circular interface. The bottom left panel shows an unstructured triangular mesh built so that element edges are aligned with the (quarter) circle perimeter. Note that non-rectangle quadrilateral elements can also be used to conform to an interface. The material discretisation is illustrated by different methods of material tracking in the right-hand side column based on either the particle-in-cell method (top right) or grid-based advection (bottom right) for the material contrasts indicated by the blueish colours.

  • 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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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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3-D subduction mantle flow

3-D subduction dynamics and mantle flow model animation showing the time evolution of oceanic plate subduction and resulting mantle flow.

Animation of 3-D subduction dynamics and mantle flow showing the time evolution of oceanic plate subduction with a continental part in the middle and resulting mantle flow computed in a 3-D numerical model. Although only one specific geometry, this model is useful to visualise how slabs deform at depth, how mantle flows around their edges, and how back-arc basins form.

Description of the model evolution (see below for detailed legend) – In this model, the subducting plate is mostly oceanic, but has continental lithosphere in the middle and the overriding plate is continental (see top panels at Time 0 Myr). The oceanic slab (in blue) sinks into the mantle and, at Time 8.1 Myr, continental collision happens in the middle of the subduction zone. At this point, the trench stays quasi-stationary in the middle, but starts to retreat quickly at the sides and the slab significantly deforms at depth (from Time 9.8 Myr onward). This causes the mantle to quickly flow around the slab (see how the spheres move). The large trench retreat generates a significant amount of extension in the overriding plate that eventually causes the overriding plate to break (Time 28.4 Myr). At this point, the mantle material rises towards the surface and starts melting because of decompression in the back-arc region. Melt close to trench is due to the presence of fluids released from the slab and shows the location of the volcanic arc. As the slab keeps retreating, the opening of the back-arc basin, associated with mantle melting, continues creating a wider and wider basin that will be composed of new oceanic crust generated by mantle melting.

Legend – The 3 panels are showing different views of the same model: side/top view (top left panel), top view (top right panel), and front view (bottom panel). The slab is shown in blue, continental crust in grey. In the top view (top right panel), the subducting plate is on the left side and the overriding plate is the grey area to the left. The slab will subduct towards the right. The contour in the red-to-white colour map indicates the regions where the mantle melts and the amount of melt fraction. The spheres are tracers passively transported in the mantle and colour-coded by depth; they are useful to show how the mantle flows around the slab (toroidal flow).

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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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Plume-induced subduction

Temporal evolution of subduction initiation in a global, 3-D spherical numerical experiment showing the cold plates and hot mantle plumes.

Temporal evolution of subduction initiation in a global, 3-D spherical numerical experiment showing the cold plates as viscosity isosurfaces (grey) and mantle plumes as a temperature isosurface (red). Individual snapshots highlight the different phases of plume-induced subduction initiation characterised by (a) onset of hot mantle plumes, (b) local lithospheric thinning, (c-d) development of strong lithosphere-asthenosphere boundary topography through shallow horizontal mantle flow and an additional plume pulse, (e-f) plate failure and, finally, (g-h) buoyancy-driven subduction.

  • Creator: Fabio Crameri
  • This version: 01.09.2021
  • License: Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
  • Specific citation: This graphic by Fabio Crameri from Crameri and Tackley (2016) is available via the open-access s-Ink repository.
  • Related reference: Crameri, F., and P. J. Tackley (2016), Subduction initiation from a stagnant lid and global overturn: new insights from numerical models with a free surface, Progress in Earth and Planetary Science, 3(1), 1–19, doi:10.1186/s40645-016-0103-8
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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
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