Understanding the dynamics and evolution of terrestrial planetary interiors requires the use of sophisticated numerical simulations of mantle convection. The latter can be described by solving the conservation equations of mass, momentum, energy and chemical transport appropriate for highly viscous media. To this end, two different approaches are generally employed. On the one hand, spherically-symmetric, one-dimensional (1D) models can be used in which convective heat transport is simply parameterized in terms of suitable scaling laws. These models provide useful insight into the long-term and global-scale behavior of planetary interiors and have the important advantage of being computationally inexpensive. They permit therefore to widely test parameters which are poorly constrained but can strongly affect the model outcomes. On the other hand, a fully numerical approach can be adopted, according to which the full set of conservation equations is solved numerically on two-dimensional (2D) or three-dimensional (3D) discrete grids in rectangular, cylindrical or spherical geometries. 2D and 3D models generally allow for a more realistic description of the physical processes governing the mantle but require the intensive use of large computational resources.

An important part of our research activity is dedicated to the development of computer codes both based on the 1D-parameterized approach and on the fully numerical 2D-3D approach described above. During the past few years, we have been developing three main computational tools:

Evolution is a 1D code written in Matlab that solves the energy balance equations for the core, mantle and lithosphere (i.e. the uppermost mantle layer) assuming scaling laws that parametrize the transport of heat due to convection (Fig. 1a). Among several capabilities, it allows for a sophisticated modelling of partial melt production and its accompanying processes such as crust formation. Fig. 1b shows the evolution of partial melt and crust formation from a model of Mercury’s thermal history (Grott et al., 2011).

Figure 1: (a) schematic diagram of the interior of a terrestrial planet as can be treated by Evolution. The code allows one to model the evolution of a radial temperature profile (solid black line) from the surface to bottom of the core. (b) Time-evolution of the partial melt zone (gray area), lithosphere thickness (solid line) and crustal thickness (dashed line) from a model of Mercury’s thermal history.

YACC (Yet Another Convection Code) is a 2D finite-volume code written in Fortran that solves the full set of conservation equations in two-dimensional rectangular boxes (YACC code). The program allows for the study of both regional- and global-scale processes for which quantitative information about the actual structure of mantle convection is important. Figure 2 shows a calculation from YACC of Earth’s mantle convection featuring multiple phase transitions (Tosi et al., 2013).

Figure 2: Temperature anomalies calculated with YACC from a simulation of mantle convection considering the principal phase transitions occurring in the Earth’s mantle (phase boundaries are indicated by black lines).

GAIA is a finite-volume code written in C++ that solves the full set of conservation equations in a variety of 2D and 3D domains, including 2D rectangular box, 2D and 3D sphere. Because of the large computational resources needed to perform 3D simulations, the code is highly parallelized and typically runs on large clusters available at national and international supercomputing centers. Figure 3 shows a temperature snapshot from a simulation of thermal convection in a spherical shell at high convective vigor (Huettig et al., 2013).

Figure 3: Temperature isosurfaces from a 3D spherical shell simulation performed with GAIA of thermal convection at high convective vigor.

Ausgewählte Publikationen

Grott, M., Breuer, D., & Laneuville, M. (2011): Thermo-chemical evolution and global contraction of Mercury. Earth and Planetary Science Letters, 307(1), 135-146.

Tosi, N., Yuen, D. A., de Koker, N., & Wentzcovitch, R. M. (2013): Mantle dynamics with pressure-and temperature-dependent thermal expansivity and conductivity. Physics of the Earth and Planetary Interiors, 217, 48-58.

Hüttig, C., Tosi, N., & Moore, W. B. (2013): An improved formulation of the incompressible Navier-Stokes equations with variable viscosity. Physics of the Earth and Planetary Interiors, 220, 11-18.

Dynamik des Inneren und thermische Entwicklung von Planeten und Monden