Gang Lu

Two-phase flow modelling for geological problems: Background, method, and applications

Gang Lu^1,* Dave A. May², and Ritske S. Huismans¹

¹Department of Earth Science, Bergen University, Bergen, N-5007, Norway

²Scripps Institution of Oceanography, UC San Diego

*Corresponding author: gang.lu@geo.uib.no

Two-phase flow, a system where Stokes flow and Darcy flow are coupled, is of great importance in Earth sciences. Examples of two-phase system include water migration in sedimentary basins/subduction zones/glaciers, and magma migration in subduction zones/mid-ocean ridges/hotspots. While the governing equations of the coupled two-phase system have been proposed long time ago, it remains challenging to solve the coupled system accurately in the zero-porosity limit, for example when melt is fully frozen below solidus temperature. In the limit when fluid phase is absent, the Darcy equation is redundant such that the coupled system becomes underdetermined. Here we propose a new three-field formulation of the two-phase system and present a robust finite-element implementation, which can successfully solve for the system where zero and non-zero porosity domains are both present. The new formulation is implemented using a 2-D finite-element discretization in FANTOM. We demonstrate the correctness of our implementation based on benchmarks against analytical solutions, which gives expected convergence rates in both space and time. We further present a number of example experiments, such as self-compaction, falling block, and mid-ocean ridge spreading, showing that this approach can robustly resolve zero- and non-zero-porosity domains simultaneously, and be used for a large range of applications in various geodynamic settings.