Governing equations

The governing equations of 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 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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