Dr. Oguzcan Karagoz

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Mantle Interaction and Lithospheric Evolution in Viscous Annuli

MILEVA

A finite-volume mantle-convection code in Julia.

MILEVA simulates thermal and compositional convection in Earth-like and planetary mantles. It solves the coupled Stokes, energy and composition equations on a staggered finite-volume grid, with velocities on cell faces and pressure at cell centres, while temperature and composition ride on Lagrangian markers.

Language
Julia
Method
Finite volume, staggered grid
Transport
Lagrangian markers
Geometry
2-D spherical and cylindrical annulus · 3-D spherical chunk and Yin-Yang sphere
Three-dimensional plumes in the Yin-Yang spherical shell at Ra = 10^6.
Three-dimensional plumes in the Yin-Yang spherical shell at Ra = 106.

How it is built and run

A flat-include research code. include/mileva.jl pulls in config/, utils/, markers/, physics/, solvers/ and parallel/; main_SphCon.jl holds the time loop.

julia --project=. -t 4 examples/annulus_convection_2d.jl 1e4 64

A run is a Julia script: edit the three configuration structs cfg, mat and temp, then call main_SphCon. VTK frames, checkpoints and diagnostics.csv land in cfg.outputDir.

Physics

  • Thermochemical Stokes flow with the full deviatoric stress at variable viscosity, in Boussinesq or anelastic form.
  • Composite rheology: diffusion and dislocation creep, Arrhenius and Frank-Kamenetskii laws, yielding, viscoelastoplasticity, damage and grain-size evolution.
  • Thermal and compositional buoyancy: basalt, depletion, thermochemical piles and phase transitions.
  • Partial melting with depletion feedback, eruption, intrusion and heat-pipe cooling.
  • Radiogenic heating, fixed or cooling core boundaries, a free surface and isostasy.

Numerics and solvers

  • Direct solvers including MUMPS in 2-D, geometric multigrid, and MPI domain decomposition.
  • Stokes solvers that hold up at viscosity contrasts to 1018.
  • Conservative markers, with the energy budget logged on every run.

Verification

  • The 2-D annulus is checked against Hernlund & Tackley (2008) and the annulus column of Fleury et al. (2024).
  • Conservation identities are checked every run.
  • The primordial-material case reproduces reference case M100dD of Gülcher, Ballmer & Tackley (2021).

From the example gallery

The four geometries MILEVA solves in: the 2-D spherical and cylindrical annulus, the 3-D spherical chunk, and the 3-D Yin-Yang sphere built from two overlapping latitude–longitude patches coupled by Schwarz iteration.
The four geometries MILEVA solves in: the 2-D spherical and cylindrical annulus, the 3-D spherical chunk, and the 3-D Yin-Yang sphere built from two overlapping latitude–longitude patches coupled by Schwarz iteration.
MILEVA's own mark: a cutaway of the spherical annulus the code solves in.
MILEVA's own mark: a cutaway of the spherical annulus the code solves in.
A stagnant lid failing and regrowing, as a time strip.
A stagnant lid failing and regrowing, as a time strip.
Temperature above a dense primordial layer. Reference case M100dD of Gülcher, Ballmer & Tackley (2021).
Temperature above a dense primordial layer. Reference case M100dD of Gülcher, Ballmer & Tackley (2021).
Convection under Mars-like conditions, from the Mars and Mercury example.
Convection under Mars-like conditions, from the Mars and Mercury example.

Worked examples

Each ships as a runnable case in the documentation.

  • Onset of convection
  • Isoviscous convection
  • Plume from the core-mantle boundary
  • Stagnant lid, failing and regrowing
  • Primordial material and thermochemical piles
  • Continents
  • Mars and Mercury
  • 3-D Yin-Yang plumes
Documentation All code

Updated: