A Pure Lagrangian Formulation of a Hydroacoustic Fluid-Structure Problem for the Simulation of Underwater Transducers

The numerical simulation of the small acoustic perturbations produced by an underwater transducer must involve convected models to capture the interaction of the wave propagation phenomena and the underlying fluid motion.Obviously, the spatial location of the transducer is also affected by the fluid motion, and simultaneously, the physical region of interest will vary over time due to tidal and gravity waves.Both fluid-structure phenomena, the acoustic interaction of the transducer with the surrounding fluid motion, and the underlying coupled hydrodynamic phenomena have very different time and spatial scales, and they must be solved simultaneously.This work presents a novel approach where both time scales are considered separately, and both fluid-structure problems are solved numerically in a pure Lagrangian formulation based on velocity and displacement fields by finite element procedures using two different meshes.Galbrun's model is used to compute the time-harmonic acoustic response of the underwater transducer.In contrast, the underlying fluid motion and the position of the transducer, which is considered a rigid solid, are computed implicitly using an implicit Newmark's time marching scheme.Some numerical benchmarks in different scenarios are provided to illustrate the features of the proposed numerical method.