Geophysics – Geodynamics

We are developing a 2D/3D geodynamics simulation package using Firedrake, a Python-based framework built on the Unified Form Language (UFL) abstraction layer. UFL is a high-level language that enables the expression of partial differential equations (PDEs) in weak form which is close to the mathematical representation of the equations, facilitating automated matrix assembly. Firedrake integrates numerous packages, including PETSc, to create a comprehensive tool for PDE solutions.

For solving the Stokes equations, Eulerian and Lagrangian approaches can be used. In this package, we use the Arbitrary Lagrangian-Eulerian (ALE) method, which effectively tracks interfaces and facilitates the movement of different materials. Both Augmented Lagrangian and Pseudo-Jacobian methods are implemented, and we apply techniques like geometric multigrid and Schur complement to enhance computational efficiency. The methods we employ allow us to avoid using sticky air layer on top of the free surface.

Figure 1 shows the result of a benchmark problem investigating the stability of Stokes solvers involving elasto-plastic rheology (as in Spiegelman et al., 2016), which we have used to demonstrate the stability of our code. The accompanying animation demonstrates Rayleigh-Taylor instability. Both simulations were developed within our evolving framework.

Dr. Karim Norouzi Moghanjoghi, 2023-2026

Funding from the University of Bremen.

Conference presentation at 2024 Firedrake Workshop: "On the Nullspaces and Boundary Conditions of the Viscous Flow in Geodynamics and Glacier Simulations."

Spiegelman, M., D. A. May, and C. R. Wilson (2016), On the solvabilityof incompressible Stokes withviscoplastic rheologies ingeodynamics, Geochem. Geophys.Geosyst., 17, 2213–2238, doi:10.1002/2015GC006228.