Modelling of planetary accretion and core-mantle structure formation

Tomas Roubicek, Ulisse Stefanelli (Korresp. Autor*in)

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

We advance a thermodynamically consistent model of self-gravitational accretion and differentiation in planets. The system is modeled in actual variables as a compressible thermoviscoelastic fluid in a fixed, sufficiently large domain. The supply of material to the accreting and differentiating system is described as a bulk source of mass, volume, impulse, and energy localized in some border region of the domain. Mass, momentum, and energy conservation, along with constitutive relations, result in an extended compressible Navier-Stokes-Fourier-Poisson system. The centrifugal and Coriolis forces are also considered. After studying some single-component setting, we consider a two-component situation, where metals and silicates mix and differentiate under gravity, eventually forming a core-mantle structure. The energetics of the models are elucidated. Moreover, we prove that the models are stable, in that self-gravitational collapse is excluded. Eventually, we comment on the prospects of devising a rigorous mathematical approximation and existence theory.

OriginalspracheEnglisch
Aufsatznummer455701
FachzeitschriftJournal of Physics A: Mathematical and Theoretical
Jahrgang57
Ausgabenummer45
DOIs
PublikationsstatusVeröffentlicht - 29 Nov. 2024

ÖFOS 2012

  • 101028 Mathematische Modellierung

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