Mantle Convection in a Spherical Shell: Comparison of Numerical Simulations with the GeoFlow Experiment on the ISS

Abstract

Convection in not directly observable fluids or objects with a central
symmetry buoyancy field in spherical shells plays an important role in
geophysical and astrophysical research. The main focus of this study is
to compare two different numerical approaches based on two Navier-Stokes
solvers (RESPECT code and GAIA code) with the 'on orbit' experiments
called GeoFlowI and GeoFlowII. The numerical simulation of flows in the
spherical gap geometry is challenging and requests high accuracy to
resolve all relevant scales. Beside isoviscous Rayleigh-B'enard
convection the influence of temperature dependent viscosity on the
temperature field is investigated. The Simulation of Geophysical Fluid
Flow under Microgravity (Geoflow) is an ESA investigation running inside
the Fluid Science Laboratory (FSL) on the International Space Station
ISS and has the goal to better understand the interior dynamics of our
planet [1]. The GeoFlowI mission focused on the simulation of
iso-viscous flows, whereas in the GeoFlowII mission the effects of
temperature-dependent viscosity are investigated - the latter is more
relevant for mantle material. The GAIA software package, developed at
DLR, solves the conservation equations of thermal convection for an
incompressible Boussinesq fluid with infinite Prandtl number. The
discretization of the governing equations is based on the finite-volume
method with the advantage of using fully irregular grids [2, 3]. The
code can handle viscosity variations of up to 8 orders of magnitude from
cell-to-cell and up to 45 orders of magnitude system wide. We further
use the pseudo spectral method based code RESPECT modified after [4] to
be able to handle viscosity contrast up to 10. The main property of the
underlying algorithm is the implicitly treatment of the linear parts and
the pseudo spectral calculation of the non-linearities. While the
spectral method based code is fast and accurate for small viscosity
ratios, the GAIA suite provides stable simulations for ratios with
magnitudes of 10 and higher. The results of the numerical tests show a
good agreement in global structures and Nusselt numbers for both
isoviscous and temperature-dependent viscosity cases. However,
substantial differences between isoviscous and temperature-dependent
viscosity cases with a viscosity contrast of only 2.0 which have been
observed in the GeoFlowII experiment could not be reproduced with the
numerical codes. One possible explanation for this discrepancy is that
the thermal expansivity of the material used in the GeoFlowII experiment
is temperature dependent. This has been neglected so far and therefore
further tests need to be done.

Full text

Geophysical Research Abstracts
Vol. 14, EGU2012-9939, 2012
EGU General Assembly 2012
© Author(s) 2012
Mantle Convection in a Spherical Shell: Comparison of Numerical
Simulations with the GeoFlow Experiment on the ISS
F. Zaussinger (1), A. Plesa (2), C. Egbers (1), and D. Breuer (2)
(1) BTU-Cottbus, Aerodynamics and Fluid Mechanics, Cottbus, Germany (florian.zaussinger@tu-cottbus.de), (2) Institute of
Planetary Research, DLR, Berlin, Germany
Convection in not directly observable fluids or objects with a central symmetry buoyancy field in spherical
shells plays an important role in geophysical and astrophysical research. The main focus of this study is to
compare two different numerical approaches based on two Navier-Stokes solvers (RESPECT code and GAIA
code) with the ’on orbit’ experiments called GeoFlowI and GeoFlowII. The numerical simulation of flows in
the spherical gap geometry is challenging and requests high accuracy to resolve all relevant scales. Beside
isoviscous Rayleigh-B’enard convection the influence of temperature dependent viscosity on the temperature field
is investigated.
The Simulation of Geophysical Fluid Flow under Microgravity (Geoflow) is an ESA investigation running
inside the Fluid Science Laboratory (FSL) on the International Space Station ISS and has the goal to better
understand the interior dynamics of our planet [1]. The GeoFlowI mission focused on the simulation of iso-viscous
flows, whereas in the GeoFlowII mission the effects of temperature-dependent viscosity are investigated – the
latter is more relevant for mantle material.
The GAIA software package, developed at DLR, solves the conservation equations of thermal convection
for an incompressible Boussinesq fluid with infinite Prandtl number. The discretization of the governing equations
is based on the finite-volume method with the advantage of using fully irregular grids [2, 3]. The code can handle
viscosity variations of up to 8 orders of magnitude from cell-to-cell and up to 45 orders of magnitude system wide.
We further use the pseudo spectral method based code RESPECT modified after [4] to be able to handle
viscosity contrast up to 10. The main property of the underlying algorithm is the implicitly treatment of the linear
parts and the pseudo spectral calculation of the non-linearities. While the spectral method based code is fast and
accurate for small viscosity ratios, the GAIA suite provides stable simulations for ratios with magnitudes of 10
and higher.
The results of the numerical tests show a good agreement in global structures and Nusselt numbers for
both isoviscous and temperature-dependent viscosity cases. However, substantial differences between isoviscous
and temperature-dependent viscosity cases with a viscosity contrast of only 2.0 which have been observed in
the GeoFlowII experiment could not be reproduced with the numerical codes. One possible explanation for this
discrepancy is that the thermal expansivity of the material used in the GeoFlowII experiment is temperature
dependent. This has been neglected so far and therefore further tests need to be done.
References
[1] T. von Larcher, B. Futterer, C. Egbers, R. Hollerbach, P. Chossat, P. Beltrame, L. Tuckerman, F. Feudel,
Journal of The Japan Society of Microgravity Application, 25 (3), 121-126, (2008);
[2] C. Huettig and K. Stemmer, Geochemistry Geophysics Geosystems, 9, 13, (2008);
[3] C. Huettig and K. Stemmer, Physics of the Earth and Planetary Interiors, 171, 137-146, (2008);
[4] R. Hollerbach, Int. J. of Numerical Methods in Fluids, Vol 32, 773-797, (2000).