Partitioned black-box coupling for porous-media applications

Many real-world applications problems involve flow in porous media and some other medium that can be separated into subdomains by a sharp interface. An example is the flow of water (free flow) over a river bed (porous-medium flow). Modeling such an application involves different mathematical models in each of the subdomains and, thus, leads to ill-conditioned systems of equations when solved monolithically. Due to the ill-conditioning of the matrix, in the monolithic approach one has to use direct linear solvers or has to develop specialized preconditioners [1]. Additionally, the monolithic approach can be restrictive with respect to time and memory requirements and it prevents the reuse of already implemented solvers that are highly specialized for one of the problems. Partitioned methods that solve the coupled problem based on the ideas of domain decomposition techniques are a good alternative. These methods have been especially popular for finite-element discretizations of porous media problems [3]. We use partitioned coupling methods to couple free and porous-media flow via a “black-box” approach that has been especially popular in the field of fluid-structure interaction. The coupling does not make any assumptions on the discretization in any of the domains. The partitioned coupling is realized via the open-source coupling library preCICE [2]. We identify suitable coupling variants and numerically investigate the behavior of the coupling schemes. In addition, the influence of the partitioned coupling on the numerical solution is examined.

References

[1] M. Benzi, G. H. Golub, and J. Liesen. “Numerical solution of saddle point problems”. In: Acta numerica 14 (2005), pp. 1–137.

[2] H.-J. Bungartz, F. Lindner, B. Gatzhammer, M. Mehl, K. Scheufele, A. Shukaev, and B. Uekermann. “preCICE – A fully parallel library for multi-physics surface coupling”. In: Computers and Fluids 141 (2016). Advances in Fluid-Structure Interaction, pp. 250–258.

[3] M. Discacciati and A. Quarteroni. “Navier-Stokes/Darcy coupling: Modeling, analysis, and numerical approximation”. In: Revista Matemática Complutense 22.2 (2009).