Dr. Oguzcan Karagoz

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Modeling in Lithospheric Evolution Tectonics

MILET

A thermomechanical finite-element framework for lithosphere and mantle dynamics.

MILET couples Stokes flow to heat transport on an inf-sup stable Taylor–Hood discretisation, with material carried by markers. It is built for problems where composition, rheology and metamorphic phase change evolve together: lithospheric foundering, delamination, drips and subduction.

Language
Julia, built on Gridap.jl
Method
Finite element, Taylor–Hood Q2/Q1
Transport
Marker-in-cell, RK4 advection
Geometry
2-D and 3-D Cartesian · Projected spherical chunk
Three-dimensional thermal convection in a box at Ra = 10^5.
Three-dimensional thermal convection in a box at Ra = 105.

How it is built and run

Built on Gridap.jl. Runs are driven from main.jl; shipped cases include SolCx, Blankenbach 1a, subduction and a 3-D plume run on the multigrid solver.

julia --project=. main.jl cases/solcx_fixed.toml

Each simulation is a TOML parameter file merged onto cases/_defaults.toml. Results are written to output/<case>/ and viewed in ParaView.

Physics

  • Incompressible Boussinesq and truncated anelastic liquid approximation (TALA) Stokes flow; markers carry composition, temperature, stress, plastic strain, grain size and porosity.
  • Visco-elasto-plastic composite creep with Drucker–Prager yield, strain softening and Arrhenius healing.
  • Rate-limited divariant metamorphic reactions with reaction-progress softening, and melting with melt weakening.
  • McKenzie-type two-phase flow: porous melt migration through a compacting matrix, reducing to single-phase Stokes at zero porosity.
  • Grain growth balanced against paleowattmeter reduction, coupled back into the creep mechanisms.
  • Shear, adiabatic and radiogenic heating; sticky-air and ALE free surfaces.

Numerics and solvers

  • Direct (MUMPS) and iterative solvers, including a geometric-multigrid FGMRES solver for 3-D Stokes.
  • Picard and Newton nonlinear loops with CFL-limited time stepping.
  • Adaptive mesh refinement, checkpoint/restart and VTK output for ParaView.

Verification

  • SolCx Stokes benchmark (Duretz et al. 2011).
  • Blankenbach et al. (1989) case 1a.
  • Smoke and benchmark tests shipped under test/.

From the example gallery

Mantle plumes in a 2-D spherical chunk.
Mantle plumes in a 2-D spherical chunk.
Three-dimensional thermal convection in a box at Ra = 10^5.
Three-dimensional thermal convection in a box at Ra = 105.
A mid-ocean ridge with a transform in 3-D, showing seafloor dynamic topography.
A mid-ocean ridge with a transform in 3-D, showing seafloor dynamic topography.

Worked examples

Each ships as a runnable case in the documentation.

  • Subduction
  • Continental collision
  • Continental rifting
  • Mid-ocean ridge spreading
  • Ridge with a transform (3-D)
  • Transform and strike-slip
  • Lithospheric drip and delamination
  • Eclogite foundering on a Venus plateau
  • Stagnant lid and plutonic squishy lid
  • Mantle plumes in a spherical chunk
  • 3-D thermal convection in a box
  • Sagduction

Citation

Karagoz, O. (2026). A Mantle Viscosity Threshold for Eclogite Foundering on Venus. Journal of Geophysical Research: Planets, in revision.

Documentation Simulations and figure scripts (Zenodo) All code

Updated: