Fluid flow in deformable porous media is of high relevance in both France and Norway. Applications with a strong multi-physics coupling range from subsurface activities as CO2 storage, geothermal energy, and nuclear waste management, to biomedical engineering as studying Alzheimer’s and osteoporosis. Many of these applications involve several interacting fluids, necessitating the study of multi-phase poromechanics.
State-of-the-art, fully coupled poromechanics models used in practice simply merge existing, partially linearized single-physics models for flow and deformation. This results in thermodynamical inconsistencies (e.g. possibly negative porosity and fluid mass), which does not allow for unconditional well-posedness as well as the development of unconditionally robust numerical methods.
The main goal of the GradFlowPoro project is to develop a methodology for realiable simulation of multi-phase poromechanics. This encompasses modeling, and development and analysis of numerical methods. First, a novel, thermodynamically consistent model for multi-phase poromechanics with a variational gradient flow structure will be established. Based on that, structure-preserving discretization methods, as well as robust nonlinear solvers will be developed and analyzed. The numerical methods will be implemented and practically tested using the open-source numerical library PorePy, tailored to multiphysics subsurface simulations in complex media.
To reach the goals of the GradFlowPoro project, the complementary expertise of the chosen partners of this project are paramount. Synergy is expected from active exchange of knowledge and research practice, which will also support the two secondary goals of this project: (i) to establish a new collaborative research environment between the Norwegian and French institutions; and (ii) to increase research networks in particular among the young researchers involved.