Partitioned treatment of surface-coupled problems with application to the fluid-porous-media interaction

Employing a decoupled solution strategy for the numerical treatment of the set of governing equations describing a surface-coupled phenomenon is a common practice. In this regard, many partitioned solution algorithms have been developed, which usually either belong to the family of Schur-complement methods or to the group of staggered integration schemes. To select a decoupled solution strategy over another is, however, a case-dependent process that should be done with special care. In particular, the performances of the algorithms from the viewpoints of stability and accuracy of the results on the one hand, and the solution speed on the other hand should be investigated. In this contribution, two strategies for a partitioned treatment of the surface-coupled problem of fluid-porous-media interaction (FPMI) are considered. These are one parallel solution algorithm, which is based on the method of localised Lagrange multipliers (LLM), and one sequential solution method, which follows the block-Gauss-Seidel (BGS) integration strategy. In order to investigate the performances of the proposed schemes, an exemplary initial-boundary-value problem is considered and the numerical results obtained by employing the solution algorithms are compared. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)