Multi-material forward and inverse modelling in G-ADOPT via the conservative level-set approach

The geodynamic evolution of Earth's mantle is often studied via the thermochemical convection of a heterogeneous, highly viscous fluid using high-performance numerical methods. Implicit in this approach is the presence of immiscible fluid parcels with contrasting physical properties, such as density and viscosity, which persist throughout the system’s entire convective evolution. Classic examples of such parcels are those derived from subducting lithospheric plates, as subduction dynamics effectively introduce a considerable volume of crustal rocks into Earth's mantle circulation over billions of years. To effectively model the joint evolution of contrasting rock parcels, geodynamicists have often employed interface-capturing, multi-phase flow approaches, also referred to as multi-material methods, such as the volume-of-fluid, level-set, phase-field, and particle-in-cell techniques. In G-ADOPT, a next-generation computational platform for simulating geoscientific flows using adjoint-based methods, we have implemented a conservative level-set approach. In addition to the Stokes and energy systems, we solve the advection and reinitialisation steps for as many level-set fields as material interfaces tracked in the numerical evolution. We employ a discontinuous Galerkin spatial discretisation on finite elements and rely on a strong stability-preserving Runge-Kutta scheme for temporal integration. We verify the accuracy and performance of our framework by reproducing several benchmarks from the geodynamics community. Moreover, we showcase the robustness of the framework in a visco-plastic subduction incorporating a range of viscous creep mechanisms, a yield criterion, and a free surface. Finally, we demonstrate the compatibility of our approach with the inversion framework built into G-ADOPT, leveraging an adjoint-based method, which opens an avenue to reconstruct thermochemical convective history.