Finite element methods for the simulation of two-phase Darcy-Stokes flows

The goal of this project is to develop and analysis stabilized finite element methods for the simulation of a two-phase model arising from mantle dynamics. In this multi-phase model, the fluid melt velocity obeys Darcy?s law while the deformable solid matrix is governed by a highly viscous Stokes equation. The system is then coupled through mass conservation and compaction relations. Together these equations form a coupled Darcy-Stokes system on a continuous single-domain mixture of fluid and matrix. When coupled with solute transport and thermal evolution in a time-dependent problem, the model transitions dynamically from a non-porous single phase solid to a two-phase porous medium. Such mixture models have an advantage for numerical approximation since the free boundary between the one and two-phase regions need not be determined explicitly.

The goal of this project is to develop and analysis stabilized finite element methods for the simulation of a two-phase model arising from mantle dynamics. In this multi-phase model, the fluid melt velocity obeys Darcy?s law while the deformable solid matrix is governed by a highly viscous Stokes equation. The system is then coupled through mass conservation and compaction relations. Together these equations form a coupled Darcy-Stokes system on a continuous single-domain mixture of fluid and matrix. When coupled with solute transport and thermal evolution in a time-dependent problem, the model transitions dynamically from a non-porous single phase solid to a two-phase porous medium. Such mixture models have an advantage for numerical approximation since the free boundary between the one and two-phase regions need not be determined explicitly.