“Introduction to numerical geodynamic modelling”
– Sète, 1-5 February 2016 –
In this first course, taught by Prof. Paul Tackley and Prof. Taras Gerya from the ETH in Zurich, we learned the basics of Matlab programming for the modelling of geodynamic problems. The main goal of the course was to develop a code, based on a finite difference scheme, for solving partial differential equations which represent the basic tools in various geodynamical problems for continuous media. The course was mainly organized in theoretical and practical sessions. In the theoretical sessions we obtained a general overview on the state-of-the-art, applications, potentiality and limits of the numerical techniques currently used in geodynamic modelling, especially focused on mantle convection and plate tectonics. Some examples of their applications (figure 1), for the studying of different phenomena, have been shown and discussed in class.
Figure 1. Pictures showing different applications of numerical simulation in geodynamic problems. (a) 3D mantle convection model showing subductions and their downward sinking in the lowermost mantle; viscosity variation is also showed. (b) dynamics of subduction zones and P-T path reconstructions suitable for comparison with actual rock samples from tectono-metamorphic events in continental collision zones. (c) global seismic waves propagation inside the Earth taken from http://www.geophysik.uni-muenchen.de/research/seismology. (d) interaction of a compositionally-stratified subducted slab with the core-mantle boundary region (CMB) and consequent plumes formation and rising. (a), (b) and (d) courtesy of Paul Tackley.
Along with this theoretical overview, we also adopted the aforementioned Finite Difference Method in order to build a numerical geodynamic model. We started from solving the Poisson equation in 1D and 2D on a collocated grid and, day by day, we updated our code increasing the level of complexity in order to build a full Thermo-Mechanical solver in 2D. In these practicals, we learned how to solve the Stokes equations of motion on a staggered grid and then how to implement them coupled with the advection equation and the temperature equation in order to track the time evolution of our temperature-dependent system making use of markers. Using this approach, we were able to model the thermal and density perturbations related to the upwelling of a hot and less dense material, bounded by a colder and denser one, which can be directly connected to the buoyancy forces of a plume inside the Earth’s mantle. An example of the output results obtained is showed in figures 2-3-4 for different time steps.
Figure 2-Rise of a plume in the Earth’s mantle. Initial configuration of velocity and density field distributions.
Figure 3-Rise of a plume in the Earth’s mantle. Time: 0.9 Myr. The stress field starts to deform the uprising plume.
Figure 4-Rise of a plume in the Earth’s mantle. Time:3.5 Myr. The plume reached the free surface where it gets flattened and broader.
