Geodynamic modelling provides a powerful tool to investigate processes in the Earth’s crust, mantle and core, which are not directly observable and span massive scales in time and space.
To ensure high-quality modelling studies, fair external interpretation, and sensible use of published work, a basic understanding of numerical modelling is necessary.
A short overview is given below. For more details, see here.
A modelling study encompasses everything from the assemblage of both a physical and a numerical model 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 via 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.
The governing equations are the conservation of mass, the conservation of momentum, and conservation of energy with different types of rheology.
Here, 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., for radioactive decay), and the term S can account 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 represents the geodynamic approximation of brittle failure.
The panel on the right outlines the 1D discretisation in space (horizontal axis) and time (vertical axis).
The 2-D domain discretisation on the bottom left illustrates different mesh types. The top half mesh is build on a quadtree with several levels of mesh refinement (top right) to better capture the interface of the circular feature. The bottom left quarter is based on an unstructured triangular mesh adjusted to align its element edges with the interface of the circular feature. Different methods of material tracking are available based on either the particle-in-cell method (top) or grid-based advection (bottom) .
A simpler model can be more useful: the basic shape of the heart is likely the most successful model to-date, indeed a true icon: it is 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 evaluated by the modeller for each new modelling task using the potential options for geodynamic model simplification.
Specific modelling and generic modelling are the two overarching modelling philosophies. Each one has a different scientific goal and needs to be used, communicated, and reviewed differently from the other.