Robust iterative schemes for coupled partial differential equations (PDEs)
16th March 2018 to 15th October 2018
The proposed project focuses on the development and optimization of robust iterative schemes for nonlinear partial differential equations. The underlying applications are the fluid flow and reactive transport in deformable porous media. In particular we refer to situations where the geometry of the medium at the pore scale is changing in time, depending on the flow and the transported species, which may react and form an immobile layer attached to the pore walls. Next to the flow and transport through the porous medium, such processes are affecting the geomechanical properties of the medium. The corresponding mathematical models are fully coupled, nonlinear partial and ordinary differential equations of different types, and possibly degenerated. This makes finding robust numerical schemes for solving such kind of equations avery challenging task.
In this project we propose a four step approach:
- Optimize the iterative schemes for saturated/unsaturated flow in porous media.
- Design and optimize a robust scheme for two coupled linear, parabolic equations.
- Optimize the fixed stress scheme for the linear Biot model.
- Extend the results above to nonlinear Biot and reactive transport in porous media.