TY - JOUR
T1 - Modelling of planetary accretion and core-mantle structure formation
AU - Roubicek, Tomas
AU - Stefanelli, Ulisse
N1 - Publisher Copyright:
© 2024 The Author(s). Published by IOP Publishing Ltd.
PY - 2024/11/29
Y1 - 2024/11/29
N2 - 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.
AB - 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.
KW - Navier-Stokes-Fourier-Poisson system
KW - open thermodynamical systems
KW - self-gravitation
KW - transport equations
KW - two-component flow
KW - viscoelastic fluids
UR - http://www.scopus.com/inward/record.url?scp=85208380624&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/ad75d9
DO - 10.1088/1751-8121/ad75d9
M3 - Article
AN - SCOPUS:85208380624
SN - 1751-8113
VL - 57
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 45
M1 - 455701
ER -