Internal Research Project I-01

Efficient iterative solution methods for coupled free-flow and porous-media flow problems


January 2019 - August 2019


About this project

In models concerning coupled free-flow and porous-medium flow, the different behavior of the two flow regimes typically results in an unbalanced system of equations. As a result, a fully coupled system often becomes computationally expensive, sometimes even infeasible, to solve in a monolithic manner.

The main objective of this project is to develop and analyse efficient solution methods for coupled free-flow porous-media flow problems based on iterative decoupling strategies, implement the proposed methods numerically in a unified software framework, and extend the approaches to related, more complex flow problems. Two extensions have a central focus within this project, namely the adaptation to multi-rate time stepping and generalizations to non-linear
problems. These non-linear extensions include using the Navier-Stokes equations in the free flow domain and introducing multi-phase flow to the system.


We formulated and analysed the flux-mortar method in an abstract setting. Through rigorous analysis, we obtained estimates for the numerical error due to non-matching grids. Moreover, we discovered that the same domain decomposition framework can be used for a wide range of problems, including linearized elasticity.

The flux-mortar method has been successfully applied to the coupled Stokes-Darcy problem, leading to an iterative solution scheme that is robust with respect to physical parameters and ensures mass conservation at each iteration. Third, we have commenced with a general implementation of the mortar method within the framework of DuMux. The current implementation is capable of handling non-matching grids and a wide range of discretization methods for coupled Darcy-Darcy systems.

Publications in Internal Project I-01

  1. Boon, W. M., & Nordbotten, J. M. (2020). Stable mixed finite elements for linear elasticity with thin inclusions. Computational Geosciences.
  2. Budisa, A., Boon, W. M., & Hu, X. (2020). Mixed-Dimensional Auxiliary Space Preconditioners. SIAM Journal on Scientific Computing, 42(5), Article 5.
  3. Boon, W. M., Gläser, D., Helmig, R., Weishaupt, K., & Yotov, I. (2024). A mortar method for the coupled Stokes-Darcy problem using the MAC scheme for Stokes and mixed finite elements for Darcy. Computational Geosciences.
  4. Boon, W. M. (2020). A parameter-robust iterative method for Stokes–Darcy problems retaining local mass conservation. ESAIM: Mathematical Modelling and Numerical Analysis, 54(6), Article 6.
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