ŒDIPUS: a new tool to study the dynamics of planetary interiors

Abstract

S U M M A R YWe present a new numerical method to describe the internal dynamics of planetary mantles through the coupling of a dynamic model with the prediction of geoid and surface topography. Our tool is based on the simulation of thermal convection with variable viscosity in a spherical shell with a finite-volume formulation. The grid mesh is based on the 'cubed sphere' technique that divides the shell into six identical blocks. An investigation of various numerical advection schemes is proposed: we opted for a high-resolution, flux-limiter method. Benchmarks of thermal convection are then presented on steady-state tetrahedral and cubic solutions and time-dependent cases with a good agreement with the few recent programs developed to solve this problem.A dimensionless framework is proposed for the calculation of geoid and topography introducing two dimensionless numbers: such a formulation provides a good basis for the systematic study of the geoid and surface dynamic topography associated to the convection calculations. The evaluation of geoid and surface dynamic topography from the gridded data is performed in the spectral domain. The flow solver is then tested extensively against a precise spectral program, producing response functions for geoid as well as bottom and surface topographies. For a grid mesh of a reasonable size (6 × 64 × 64 × 64) a very good agreement (to within ∼1 per cent) is found up to spherical harmonic degree 15.Several of today's questions in the study of planetary interiors imply the use of models simulating thermal convection in a spherical geometry. This is either implicitly required by the internal dynamics (effect of curvature on thermal instabilities and heat flux budget, correct scaling of mass flux when addressing compositional gradients, modelling plate motion on a sphere) or due to a better comparison of these with geophysical data often expressed as a decomposition into spherical harmonics (e.g. in the case of data from space exploration). In addition, in order to address many problems a numerical model of thermal convection should handle large viscosity gradients: (i) the effective viscosity of silicates or ices is very sensitive to thermodynamical parameters, inducing very specific dynamical regimes such as the asymptotic conductive lid regime (e.g. Davaille & Jaupart 1993); (ii) in order to mimic the plate behaviour, more complex rheologies have been proposed that imply even larger viscosity gradients (e.g. Tackley 2000a,b; see also Bercovici 2003 for a review).The first programs simulating thermal convection in a spherical shell were based on a spectral approach (Glatzmaier 1988; Zhang 1995) since this allows an elegant treatment in the case of a viscosity field that is constant or radius-dependent. However, these methods lose part of their interest in the case of large lateral viscosity variations. A first attempt to solve variable viscosity convection with a grid-based method is proposed by Hsui et al. (1995) after a finite element discretization developed in the isovi...

Impact of tidal heating on the onset of convection in Enceladus’s ice shell

“…Both processes are coupled via the viscosity field. For the viscous flow, the equations describing the mass, momentum and energy conservations are solved using the finite volume method OEDIPUS (Choblet, 2005;Choblet et al, 2007). In the case of the viscoelastic response, the deformations (mass and momentum conservations) are solved in the time domain (Tobie et al, 2008).…”

Coupling of thermal evolution and despinning of early Iapetus

“…The classical conservation equations for thermal convection (mass, momentum and energy) are considered in the Boussinesq approximation with a viscosity that strongly depends on temperature and is solved using the numerical tool OEDIPUS (Choblet, 2005;Choblet et al, 2007) (see Appendix A.2). The whole spherical shell is divided into six identical blocks.…”

“…We perform simulations of thermal convection for fluids with large viscosity contrasts in 3-D spherical geometry, using the numerical tool OEDIPUS (Choblet, 2005;Choblet et al, 2007). A large range of plausible initial conditions are considered to investigate: (1) the onset time of convection, (2) the evolution of the viscous structure, (3) the resulting despinning rate, and (4) the evolution of Iapetus' flattening.…”

Despinning and shape evolution of Saturn’s moon Iapetus triggered by a giant impact

“…Tackley, 2010;Choblet et al, 2007;Šrámek and Zhong, 2010;Běhounková et al, 2010) usually neglect the centrifugal force due to the body spin and assume that the body is spherical. For the majority of the solid bodies in the Solar System, dynamical flattening and topography induced by thermal convection are small in comparison with the body radius.…”