# zbMATH — the first resource for mathematics

Partitioned coupling schemes for free-flow and porous-media applications with sharp interfaces. (English) Zbl 1454.65146
Klöfkorn, Robert (ed.) et al., Finite volumes for complex applications IX – methods, theoretical aspects, examples. FVCA 9, Bergen, Norway, June 15–19, 2020. In 2 volumes. Volume I and II. Cham: Springer. Springer Proc. Math. Stat. 323, 605-613 (2020).
Summary: We investigate a partitioned coupling scheme applied to a system of free flow over a porous medium. The coupling scheme follows a partitioned approach which means that the flow fields in the two domains are solved separately and information is exchanged over the sharp interface that separates the free-flow and the porous-medium domain. Technically, the coupling is realized via the open-source library preCICE, employing a pure black-box approach such that different solver frameworks can be used with highly specialized solvers in each of the flow domains. We investigate the partitioned coupling approach numerically by comparing it to a monolithic coupling scheme with respect to convergence and accuracy. This is the first time a partitioned black-box coupling is used for coupling free flow and porous-media flow. The coupling approach is numerically validated and different partitioned coupling approaches are compared with each other.
For the entire collection see [Zbl 1445.65003].
##### MSC:
 65N08 Finite volume methods for boundary value problems involving PDEs 76M12 Finite volume methods applied to problems in fluid mechanics 76S05 Flows in porous media; filtration; seepage 76D07 Stokes and related (Oseen, etc.) flows 76T06 Liquid-liquid two component flows 35R35 Free boundary problems for PDEs
##### Software:
UMFPACK; preCICE; DuMuX
Full Text:
##### References:
 [1] Benzi, M., Golub, G.H., Liesen, J.: Numerical solution of saddle point problems. Acta Numer. 14, 1-137 (2005). https://doi.org/10.1017/s0962492904000212 · Zbl 1115.65034 [2] Bungartz, H.J., Lindner, F., Gatzhammer, B., Mehl, M., et al.: preCICE - a fully parallel library for multi-physics surface coupling. Advances in Fluid-Structure Interaction. Comput. Fluids 141, 250-258 (2016). https://doi.org/10.1016/j.compfluid.2016.04.003 · Zbl 1390.76004 [3] Caiazzo, A., John, V., Wilbrandt, U.: On classical iterative subdomain methods for the Stokes-Darcy problem. Comput. Geosci. 18(5), 711-728 (2014). https://doi.org/10.1007/s10596-014-9418-y · Zbl 1392.76074 [4] Davis, T.A.: Algorithm 832: UMFPACK V4.3—an Unsymmetric-Pattern Multifrontal Method. ACM Trans. Math. Softw. 30(2), 196-199 (2004). https://doi.org/10.1145/992200.992206 · Zbl 1072.65037 [5] Degroote, J.: Partitioned simulation of fluid-structure interaction. Arch. Comput. Methods Eng. 20(3), 185-238 (2013). https://doi.org/10.1007/s11831-013-9085-5 · Zbl 1354.74066 [6] Discacciati, M., Gerardo-Giorda, L.: Optimized Schwarz methods for the Stokes-Darcy coupling. IMA J. Numer. Anal. 38(4), 1959-1983 (2017). https://doi.org/10.1093/imanum/drx054 · Zbl 06983868 [7] Discacciati, M., Quarteroni, A.: Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation. Rev. Mat. Complut. 22(2), 315-426 (2009). https://doi.org/10.5209/rev_REMA.2009.v22.n2.16263 · Zbl 1172.76050 [8] Flemisch, B., Darcis, M., Erbertseder, K., Faigle, B., et al.: $$DuMu^{\rm x}$$: DUNE for multi-(phase, component, scale, physics,$$\ldots )$$ flow and transport in porous media. Adv. Water Resour. 34(9), 1102-1112 (2011). https://doi.org/10.1016/j.advwatres.2011.03.007 [9] Harlow, F.H., Welch, J.E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8(12), 2182-2189 (1965). https://doi.org/10.1063/1.1761178 · Zbl 1180.76043 [10] Koch, T., Gläser, D., Weishaupt, K., Ackermann, S., et al.: DuMux 3—an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling. Comput Math Appl. (2020). https://doi.org/10.1016/j.camwa.2020.02.012 [11] Saffman, P.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.