Keywords: hybrid numerical model, method of fundamental solutions, analytical solutions, multiple fluid-filled elastic shells.

The simulation of underwater acoustic waves has been addressed by many researchers in recent decades, making use of analytical methods and different numerical methods, such as finite differences, finite elements and boundary elements formulations. When the interaction between fluid and solid media is to be modelled, those approaches frequently lead to complex and computationally very demanding problems. One possible strategy to reduce computational effort has been the development of specific Green's functions. Some meshless methods have also been proposed more recently, for the analysis of underwater sound scattering in different conditions, namely radial basis function collocation methods or the method of fundamental solutions (MFS).

In this paper, the simulation of sound waves scattered by hollow elastic pipelines is considered by a hybrid numerical-analytical model. The hollow elastic structures are assumed to be fluid-filled and embedded in a water waveguide with a sedimentary (fluid-like) bottom. The proposed approach consists of performing the coupling of the analytical solutions, derived both for wave propagation in the host waveguide and near the circular hollow pipelines. The meshless MFS is adopted for coupling the analytical solutions, leading to precise results and a compact description of the propagation medium, very proficient from the computational point of view. This compatibilisation process is performed in the host fluid medium by using the MFS and considering a virtual coupling boundary around each elastic shell inclusion, along which the continuity of pressures and normal displacements must be assigned. This virtual interface between subregions can assume a smooth geometry, such as a circle, which leads to very accurate results. Despite the elastic inclusion's circular geometry, this approach can easily be extended to multiple circular scattering objects, with different properties, spatial distributions and dimensions. This method reproduces accurately the fluid-solid interaction that occurs at the physical interfaces of the system, as it is based on analytical solutions of each individual problem.

The proposed strategy was formulated and implemented, and was found to provide good results when compared with alternative numerical modelling techniques. Since it performs the coupling between closed-form solutions, the method provides accurate results, while allowing a compact and simple model description. One major advantage of the proposed model is that it allows the simulation of very thin solid structures, without the problems usually associated with thin bodies when using alternative methods. A numerical example is presented to illustrate the applicability of the proposed methodology, revealing interesting signal features of the modified wave field observed in the waveguide as a consequence of the presence of the hollow pipelines embedded in the bottom stratus.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £65 +P&P)