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Tag: Numerical modeling

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 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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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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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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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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