Fluid‐Porous‐Media Interaction: A Decoupled Solution Algorithm via Localised Lagrange Multipliers. Issue 1 (21st October 2015)

• Record Type: Journal Article
• Authors: Zinatbakhsh, Seyedmohammad; Koch, David; Ehlers, Wolfgang
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 15:Issue 1(2015)
• Page Start: 445
• Page End: 446
• Publication Date: 2015-10-21
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201510213
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Fluid‐porous‐media interaction (FPMI) refers to a surface interaction among several non‐overlapping subsystems, composed of either a bulk fluid or a porous medium. This could be the interaction of blood with a blood vessel wall, a body of water with an earth‐dam structure, or acoustic waves with acoustic panels used in soundproofing, etc. These are highly coupled phenomena inheriting different coupling mechanisms which take place within the interacting subdomains as well as across common boundaries. Consequently, the mathematical models of such phenomena also consist of sets of coupled differential equations, which are commonly solved numerically, following a monolithic or a decoupled approach. Here, the focus is on the latter. The design of an algorithm for the decoupled solution of the fluid‐porous‐media‐interaction problem can be advantageous in several ways. First and foremost, the process of decoupling breaks down the problem into several subproblems, which can be solved efficiently employing specialised fluid and porous‐media solvers. Furthermore, solution of several decoupled subproblems instead of one highly coupled problem may be more economical in terms of computational costs. This is especially the case if the scheme permits parallel treatment of the produced subproblems. Here, the applicability of using the method of localised Lagrange multipliers for a partitioned solution of the problem of FPMI in the 2‐dimensional space is demonstrated. In this regard, the concept of modified Eulerian description for studying the motion of fluid bodies within moving boundaries is introduced. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)