Applicant
PD Dr. Bernhard Schuberth
Department of Earth and Environmental Sciences – Geophysics
Ludwig-Maximilians-Universität München (LMU)
Project Overview
Computer simulations are a key tool to further our understanding of the convective processes inside the Earth’s mantle that drive plate tectonics and vertical motions of the Earth’s lithosphere. On a time scale of millions of years, the mantle can be modelled as a viscous fluid and one can use theNavier-Stokes equations in the stationary Stokes limit coupled to a suitable advection-diffusion energy conservation equation to simulate its behaviour. In order to facilitate realistic mantleconvection simulations, a high numerical resolution beyond 10^9 degrees of freedom (preferably even 10^12, resulting in ~1 km global grid spacing) and nonlinear, compressible flow models are required.
The goal of this project is to build upon the existing matrix-free, large-scale compressible mantle convection code TerraNeo (https://terraneo.fau.de) to allow for realistic, massively parallel, high performance mantle convection simulations that also include the take-up and release of the latent heat that occurs due to solid–solid phase transitions of mantle minerals.
Even though the effects of such phase transitions play an important role for the qualitative behaviour and layering of convective mantle flow, they are omitted in most of the currently available mantle convection codes. Assuming a bulk chemical composition of the Earth’s mantle, mineral phase transitions can be incorporated by means of replacing the thermal expansivity and specific heat capacity with effective parameters. The effective parameters can nowadays be calculated using thermodynamic lookup tables determined based on mineral physics databases and a thermodynamic framework. This way, (effective) material properties of mantle rocks can be calculated for the entire pressure and temperature range of the mantle.
However, the take-up and release of the latent heat leads to jumps in the temperature and its dependent physical parameters across phase transitions, leading to numerically challenging nonlinear, high-contrast problems. Additionally specific mineral phase transitions inside the Earth’s mantle can happen on a scale of only hundreds of meters, a resolution which even on supercomputers currently cannot be realistically achieved in case of a global 3D convection model. Hence the mesh’s cell limits the phase transition thickness that can be accurately modelled.A central goal of the project is to extend TerraNeo to leverage the recently developed entropy formulation (https://doi.org/10.1093/gji/ggac293) and projected density approximation (https://doi.org/10.1093/gji/ggaa078), which reformulates the energy conservation equation partially in terms of specific entropy and allows for realistic simulations including thin phase transitions without the need for sub-kilometer resolutions. This implementation will then be tested against existing benchmarks and in large-scale global mantle convection simulations.
In a second step we focus on analyzing and improving solver performance for different assumed chemical compositions and algorithmic approaches, with a special emphasis on the time-discretization of the energy conservation equation and the Stokes system solver when introducing high-contrast densities in the projected density approximation.
During its course the project also aims to switch from the currently CPU based MPI code to a GPU based implementation in the C++, Kokkos and MPI based framework developed in the “Jump-robust and GPU-supported Solvers for Geophysical Flow Problems” KONWIHR project.
The project code is open-source and will be published at https://i10git.cs.fau.de/hyteg/hyteg (CPU) or https://github.com/mantleconvection/terraneo (GPU).