Interaction between a submarine and a far-field underwater explosion with a transient iterative FEM-BEM coupling
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This work aims at simulating the fluid-structure interaction (FSI) occurring when a submarine is subjected to a far-field underwater explosion. In this case, two physical phenomena occur: after a few milliseconds, an acoustic shock wave reaches the ship. It is then followed by a second fluid movement occuring over a longer time interval, at lower frequencies. These two phenomena can be studied in a decorrelated way. [2] proposes a model for this FSI phenomenon and a numerical method to quickly and accurately simulate the ship’s behaviour, for complex and realistic geometries. The structure response is computed using finite element (FEM) and the fluid response is formulated in the discrete-time domain, using a boundary integral equation and a ”Z-BEM” approach that combines a fast boundary element method (BEM) implemented in the Laplace domain with the convolution quadrature method (CQM). The computation is accelerated with a Fast Multipole Method and with the use of a high frequency approximation. Efficiency requires the Z-BEM to be applied on the entire time interval at once. We thus defined a ”global-in-time” iterative FEM/Z-BEM coupling alternating Z-BEM (fluid) and FEM (structure) resolutions on the whole time interval, which was initially found to be non-convergent and FEM were used instead. We only focus on the FSI generated by the shock wave. We aim at replacing the FEM-FEM method currently used for the fast shock wave response, which requires a very fine volumic mesh of the fluid domain, by a more efficient FEM/Z-BEM coupling, which allows to mesh only the surface of the submarine, and whose convergence is guaranteed. We justify the choice of transmission conditions between the domains by showing that Robin conditions are necessary to prove the convergence of the algorithm. Finally, the efficiency of this method is illustrated with examples from the naval engineering industry.