# One-Dimensional Fluid-Structure Interaction Models in Presurized Fluid-Filled Pipes: A Review
## 2 Definitions and Basic Concepts
### Coupling Mechanisms and Modelling Approaches  
Pipe systems subjected to water-hammer transients can be regarded as free-damped-deterministic vibrating systems with multiple modes of vibration, coupled or uncoupled, according to the degrees-of-freedom of the conduit and exposed to skin friction, dry friction and structural/hysteretic damping. Although not included in Equations (1)-(16), these damping mechanisms convert hydraulic transients into non-periodic and nonlinear phenomena that are difficult to analyse.  
The different degrees-of-freedom of a pipe system may interact one upon another. There are three basic kinds of coupling mechanisms [23]: (i) _Poisson coupling_ describes the interaction between the axial motion of the pipe-wall and the pressure in the fluid occurring by means of the Poisson effect; (Poisson effect refers to the phenomenon in which a material compresses in the directions perpendicular to those in which the expansion occurs, and vice versa); (ii) _friction coupling_ arises from the shear stress between the pipe-wall and the fluid; (iii) and _junction coupling_ results from unbalanced local forces and by changes in the fluid momentum that occur in pipe bends, T-junctions or cross-section changes.  
In time-domain analyses, the Method of Characteristics (MOC), the Finite Element Method (FEM), the Finite Difference Method (FDM) or the Finite Volume Method (FVM) are discretization methods used to solve the governing differential equations. Either a single or combined (hybrid) numerical method can be used for the description of the different degrees-of-freedom of the pipe. The method of characteristics (MOC) and the finite-element method (FEM), or a combination of both, are the most common numerical methods used for solving the one-dimensional basic equations [23]. One single integrating approach, such as MOC-MOC or FEM-FEM, is convenient as all the information flows into the same numerical scheme [11]. Other combinations are not that common in one-dimensional analyses; FVM is rather used for 3D simulations.  
A different coupling approach consists of setting up an interaction between two different computer codes, one specific for the fluid and another for the structure. In each time-step, output information is transferred in both directions. There are contributions proposing methodologies to carry out this data transfer, such as [28]. However, the main challenge of this approach is the requirement of a considerable computational effort and data transfer [29].  
An FDM code for the fluid and an FEM for the structure were coupled by [30] with the goal to simulate an interesting experimental research carried out at the Stanford Research Institute (SRI). Other authors who tried to simulate the same validating experiments are [31; 32; 33] who coupled FEM-FEM software. In addition, [PERSON]. [34; 35] used a FDM code for the fluid with an FEM for the structure with the goal to simulate field measurements from a pump shut-down and a closing valve in the nuclear power plant KRB II (Gundremmingen, Germany). MOC-FEM coupling was applied in [36; 37] aiming at describing the response of an experimental facility located at the Karlsruhe Nuclear Research Centre (KfK-Kernforschungszentrum Karlsruhe).  
FEM and FVM are compared for the fluid domain simulation and coupling techniques are proposed in [38]. The traditional MOC approach for the fluid is compared with a CFD \(k-\epsilon\) model in [39; 40], who coupled with an FEM model for the structure.