A community benchmark for 2-D Cartesian compressible convection in the Earth's mantle

King, Scott D.; Lee, Changyeol; Keken, Peter E. van; Leng, Wei; Zhong, Shijie; Tan, Eh; Tosi, Nicola; Kameyama, Masanori

doi:10.1111/j.1365-246x.2009.04413.x

Cited by 98 publications

(117 citation statements)

References 33 publications

Supporting

Mentioning

114

Contrasting

Order By: Relevance

“…The complexity may be increased by introducing the advection of chemical components with low or zero diffusivity, which is often achieved by using particle-based methods (van Keken et al, 1997). Compressible flow, which normally uses an anelastic approximation to filter out seismic waves and timescales, may also introduce reference equations of state derived from models of seismic wave propagation (King et al, 2010). These simulations are 22 Figure 10: The "drunken sailor" instability.…”

Section: Geodynamicsmentioning

confidence: 99%

Multiphysics simulations: challenges and opportunities.

Keyes¹,

McInnes²,

Woodward³

et al. 2012

149

View full text Add to dashboard Cite

We consider multiphysics applications from algorithmic and architectural perspectives, where "algorithmic" includes both mathematical analysis and computational complexity and "architectural" includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

show abstract

Section: Geodynamicsmentioning

confidence: 99%

Multiphysics simulations: challenges and opportunities.

Keyes¹,

McInnes²,

Woodward³

et al. 2012

149

View full text Add to dashboard Cite

show abstract

“…5. In the first series of runs, we solved the conservation equations under the extended Boussinesq approximation (EBA) (King et al 2010). The EBA distinguishes itself from the well-known Boussinesq approximation simply in that adiabatic heating and viscous dissipation are taken into account in the energy conservation equation.…”

Section: Non-dimensional Numbersmentioning

confidence: 99%

“…In the second series of model runs, we adopted a compressible formulation, the so-called truncated anelastic liquid approximation (TALA) (King et al 2010). When using TALA, we accounted for, in addition to viscosity, the depth-dependence of α, k c , and ρ ( Fig.…”

Section: Non-dimensional Numbersmentioning

confidence: 99%

Rocky super-Earth interiors

Wagner

Tosi

Sohl

et al. 2012

A&A

View full text Add to dashboard Cite

Aims. We present interior structure models of the recently discovered exoplanets CoRoT-7b and Kepler-10b addressing their bulk compositions, present thermal states, and internal dynamics. We investigate how mantle convection patterns are influenced by the depth-dependence of thermodynamic parameters (e.g., thermal expansivity and conductivity) caused by the extended pressure and temperature ranges within rocky super-Earths. Methods. To model the interior of rocky exoplanets, we construct a four-layer structural model solving the mass and energy balance equations in conjunction with a generalized Rydberg equation of state providing the radial density distribution within each layer. The present thermal state is calculated according to a modified mixing-length approach for highly viscous fluids. Furthermore, the obtained internal structure is used to carry out two-dimensional convection simulations to visualize the mantle convection pattern within massive exoplanets such as CoRoT-7b and Kepler-10b. Results. Both CoRoT-7b and Kepler-10b most likely have large iron cores and a bulk composition similar to that of Mercury. For a planetary radius of R p = (1.58 ± 0.10) R ⊕ , a revised total mass of M p = (7.42 ± 1.21) M ⊕ , and the existence of a third planet in the CoRoT-7 planetary system, calculations suggest that an iron core of 64 wt-% and a silicate mantle of 36 wt-% is produced owing to the relatively high average compressed density of ρ avg = (10.4±1.8) g cm −3 . Kepler-10b's planetary radius and total mass yield an iron core of 59.5 wt-%, which complements the silicate mantle of 40.5 wt-%. An enhanced radiogenic heating rate owing to CoRoT-7b's young age (1.2−2.3 Gyr) raises the radial distribution of temperature by only a few hundred Kelvin, but reduces the viscosity by an order of magnitude. The planform of mantle convection is found to be strongly modified for depth-dependent material properties, with hot plumes rising across the whole mantle and cold slabs, which stagnate in the mid-mantle because of the loss of buoyancy. Conclusions. We use a new model approach to determine the detailed interior structures and present thermal states of CoRoT-7b and Kepler-10b. Both planets are found to be enriched in iron. The results imply that modest radiogenic heating does not play a significant role in determining the internal structure of rocky exoplanets. The depth-dependence of thermodynamic properties, however, strongly influences the mantle convection patterns within exoplanets such as . This may have a significant effect on the thermal evolution and magnetic field generation of close-in super-Earths.

show abstract

“…1 This is particularly the case whenever numerical computation is involved, as this example serves as a convenient benchmark. [2][3][4][5][6][7][8][9] A related problem which has often been discussed in tandem concerns the case when the horizontal boundaries are made no-slip instead. [10][11][12] Whilst Roberts, 10 Jimenez and Zufiria, 11 and Fowler 12 have tackled many analytical aspects of the problem, a number of unresolved issues remain.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh-Bénard convection at high Rayleigh number and infinite Prandtl number: Asymptotics and numerics

Vynnycky

Masuda

2013

Physics of Fluids

View full text Add to dashboard Cite

The problem of fast viscous steady Rayleigh-Bénard convection in a rectangular enclosure is revisited using asymptotic and numerical methods. There are two generic cases: in the first, there is zero shear stress at all boundaries; in the second, there is zero shear stress at the vertical boundaries, but no slip at the horizontal ones. For the first case, we reconcile our new numerical solutions to the full equations with earlier asymptotic results for large Rayleigh number and effectively infinite Prandtl number. For the second case, we first derive the corresponding asymptotic theory and then reconcile it also with the relevant full numerical solutions. However, the latter also indicate behavior which the asymptotic theory does not predict, for Rayleigh numbers in excess of just over 10 6 and aspect ratios in excess of around 1.

show abstract

A community benchmark for 2-D Cartesian compressible convection in the Earth's mantle

Cited by 98 publications

References 33 publications

Multiphysics simulations: challenges and opportunities.

Multiphysics simulations: challenges and opportunities.

Rocky super-Earth interiors

Rayleigh-Bénard convection at high Rayleigh number and infinite Prandtl number: Asymptotics and numerics

Contact Info

Product

Resources

About