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... forward by Terzaghi [4].sA great number of researches about fluid-solid coupling have been done based on these theories inspetroleum engineering, from conventional reservoirs to fractured reservoirs =-=[5]-=-.sThere exist several methods to simulate fluid flow in fractured porous media [6]. Warren and Rootsintroduced the dual continuum concept to characterize naturally fractured reservoirs [7]. The dualsc...

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...olid and the motion of the contained fluid is coupled, such that the flow changes the geometry of the solid which, in turn, changes the geometry of the fluid domain, a relevant subject is that of FSI =-=[12]-=-. There are primarily two approaches to FSI; the monolithic and the staggered approach. In the monolithic approach, the equations of the solid and fluid phases are solved simultaneously. In the stagge...

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...ons. A broad classification of FSI methods is basedson the type of mesh employed in the discretisation, where we can differentiate betweensboundary-conforming and non-boundary-conforming mesh methods =-=[1]-=-. A well-knownsconforming mesh method is the Arbitrarily Lagrangian-Eulerian method (ALE). For nonconforming mesh methods, usually an immersed boundary method is used and most recentsdevelopments in F...

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...ure 2.1. Schematic of coupling approaches for a one time step, a) monolithicscoupling, and b) partitioned coupling. Sf is fluid solution, Ss is solid solution, and Sfssis unified fluid-solid solution =-=[69]-=-. ....................................................................................26sFigure 2.2. Partitioned coupling with separate variables and separate meshes. ................26sFigure 2.3. Co...

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...however, more difficult. Over the last fifteen years, the development of efficient numerical methods for the solution of the coupled problem has been an extremely active field of research (see, e.g., =-=[42, 75]-=- for recent reviews). In general, the time discretization exploits the heterogeneous structure of the coupled problem. For instance, the fluid and the solid are discretized by different implicit time-...

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...nd the biomechanics of blood flow. Over the last decade, the development of efficient numerical methods for IFSI has been a very active field of research and the subject of numerous works (see, e.g., =-=[13, 26]-=- for recent reviews). This is due, in particular, to the fact that the coupling is known to be very stiff. So called explicit (or loosely coupled, see [31, 32, 12]) schemes, where time advancement is ...

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...tion in compliant vessels and the heart. Two major approaches to the solution of FSI problem can be distinguished: the monolithic approach and partitioned one. In the scope of the monolithic approach =-=[4, 5, 6, 7, 8]-=-, ∗This work has been supported by the Russian Science Foundation (RSF) grant 14-31-00024. †Department of Mathematics, Texas A&M University; lozovskiy@math.tamu.edu ‡Department of Mathematics, Univers...

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...system. This problem is particularlysemphasized under dynamic (seismic) conditions and it is commonly referred to assa Fluid-structure interaction (or a coupled, or a multi-field) problem, Hou et al.s=-=[1]-=-. Some of those structures can be seen in fig. 1.sOff-shore structure Underwater tank Underwater tunnel DamsFigure 1: Examples of structures in direct contact with fluid.sFluid-structure interaction (...