Christian Hüttig

A community benchmark for viscoplastic thermal convection in a 2‐D square box

Numerical simulations of thermal convection in the Earth’s mantle often employ a pseudoplastic rheology in order to mimic the plate-like behavior of the lithosphere. Yet the benchmark tests available in the literature are largely based on simple linear rheologies in which the viscosity is either assumed to be constant or weakly dependent on temperature. Here we present a suite of simple tests based on nonlinear rheologies featuring temperature, pressure, and strain rate-dependent viscosity. Eleven different codes based on the finite volume, finite element, or spectral methods have been used to run five benchmark cases leading to stagnant lid, mobile lid, and periodic convection in a 2-D square box. For two of these cases, we also show resolution tests from all contributing codes. In addition, we present a bifurcation analysis, describing the transition from a mobile lid regime to a periodic regime, and from a periodic regime to a stagnant lid regime, as a function of the yield stress. At a resolution of around 100 cells or elements in both vertical and horizontal directions, all codes reproduce the required diagnostic quantities with a discrepancy of at most

Large Scale Numerical Simulations of Planetary Interiors

3% in the presence of both linear and nonlinear rheologies. Furthermore, they consistently predict the critical value of the yield stress at which the transition between different regimes occurs. As the most recent mantle convection codes can handle a number of different geometries within a single solution framework, this benchmark will also prove useful when validating viscoplastic thermal convection simula- tions in such geometries.

Modeling the Interior Dynamics of Terrestrial Planets

The massive increase of computational power over the past decades has established numerical models of planetary interiors to one of the principal tools to investigate the thermo-chemical evolution of terrestrial bodies. Large scale computational models have become state of the art to investigate the interior heat transport, surface tectonics and chemical differentiation of planetary bodies across the Solar System and beyond. In the present work we present large scale numerical simulations performed using the mantle convection code Gaia in spherical and Cartesian geometry. The results have been obtained on the HLRS system Hornet running on 54 × 103 computational cores. The strong scaling results show an optimal speedup for a grid with 55 million computational points corresponding to 275 million unknowns.

Thermo-Chemical Mantle Convection Simulations Using Gaia

Over the past years, large scale numerical simulations of planetary interiors have become an important tool to understand physical processes responsible for the surface features observed by various space missions visiting the terrestrial planets of our Solar System. Such large scale applications need to show good scalability on thousands of computational cores while handling a considerable amount of data that needs to be read from and stored to a file system. To this end, we analyzed numerous approaches to write files on the Cray XC40 Hazel Hen supercomputer. Our study shows that HPC applications parallelized using MPI highly benefit from utilizing the MPI I/O facilities. By implementing MPI I/O in Gaia, we improved the I/O performance up to a factor of 100. Additionally, in this study we present applications of the fluid flow solver Gaia using high resolution regional spherical shell grids to study the interior dynamics and thermal evolution of terrestrial bodies of our Solar System.

Finite volume discretization for dynamic viscosities on Voronoi grids

Thermally and chemically driven buoyancy in planetary mantles cause the slow creep of material, which is ultimately responsible for the heat transport from the deep interior and the large-scale dynamics inside the Earth and other terrestrial planets. With the increasing computational power and the improvement of numerical methods, numerical simulations of planetary interiors have become one the principal tools for understanding the processes active during the thermo-chemical evolution of a terrestrial planet considering constraints posed by geological and geochemical surface observations delivered by various planetary missions. In the present work we present technical aspects and applications to solid-state mantle convection using our code Gaia in Cartesian/cylindrical/spherical geometry. We test the convergence of several numerical solvers that have been implemented in our code, and show the code performance on the HLRS System with up to 10,000 cores. Further we compare our results with published benchmark values.