Internal Research Project I-01

January 2019 - August 2019

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.