Entwicklung und Anwendung von Hochleistungs-Software für Mantelkonvektionssimulationen

The Earth mantle convects on a global scale, coupling the stress
field at every point to every other location at an instant. This
way, any change in the buoyancy field has an immediate impact on
the convection patterns worldwide. At the same time, mantle
convection couples to processes at scales of a few kilometers or
even a few hundred meters. Dynamic topography and the geoid are
examples of such small-scale expressions of mantle convection.
Also, the depth of phase transitions varies locally, with strong
influences on the buoyancy, and thus the global stress field. In
order to understand these processes dynamically it is essential to
resolve the whole mantle at very high numerical resolutions. At the
same time, geodynamicists are trying to answer new questions with
their models, for example about the rheology of the mantle, which
is most likely highly nonlinear. Also, due to the extremely long
timescales we cannot observe past mantle states, which calls for
simulations backwards in time. All these issues lead to an extreme
demand in computing power. To cater to those needs, the physical
models of the mantle have to be matched with efficient solvers and
fast algorithms, such that we can efficiently exploit the enormous
computing power of current and future high performance systems.
Here, we first give an extensive overview over the physical models
and introduce some numerical concepts to solve the equations. We
present a new two-dimensional software as a testbed and elaborate
on the implications of realistic mineralogic models for efficient
mantle convection simulations. We find that phase transitions
present a major challenge and suggest some procedures to
incorporate them into mantle convection modeling. Then we give an
introduction to the high-performance mantle convection prototype
HHG, a multigrid-based software framework that scales to some of
the fastest computers currently available. We adapt this framework
to a spherical geometry and present first application examples to
answer geodynamic questions. In particular, we show that a very
thin and very weak asthenosphere is dynamically plausible and
consistent with direct and indirect geological observations.