Free surface methods applied to global scale numerical geodynamic models

The study of coupled Earth systems, and in particular the coupled interactions between the lithosphere, atmosphere, and biosphere, have received greater attention in recent years (Gerya et al. 2020). Interactions between these systems occur primarily at the surface, and are driven on the large scale by topographic and bathymetric evolution controlled by deep mantle processes. However, due to the large difference in length scales between the mantle and the surface, it is difficult to capture topographic evolution to a high degree of accuracy in existing global mantle convection models including a free surface boundary condition.

Global mantle convection models incorporating a free surface often employ a marker-in-cell technique with a layer of “sticky air” (i.e. material with the density of the air and sufficiently low viscosity, which is still much higher than that of real air) to characterise the surface. However, accurate topographic evolution using this method requires a high density of markers near the surface. This need for additional computational resources motivates alternative methods of tracking the interface between the air and rock layers, as is done frequently in existing multiphase fluid flow codes. We demonstrate the implementation of two such methods of modelling the surface. The first is a Lagrangian marker chain (or mesh in 3D models) which, when combined with an appropriate remeshing procedure, directly tracks the rock-air interface. The second is a volume of fluid approach adapted from the open source code gVOF using the unsplit volume of fluid library gVOF (López & Hernández, 2022).

We demonstrate toy models and benchmarks (based on those in Crameri, 2012) comparing the Lagrangian marker method and the volume of fluid methods as implemented in the global scale mantle convection code StagYY (Tackley, 2008). Models of global scale topography and evolution produced using StagYY may then be used as a tool for further studies on the coupling of mantle dynamics with modelling of the landscape, and the evolution of the atmosphere and biosphere. Initial applications include modelling hypsometric curves from global scale numerical models, and the tracking of sea level changes over time.