Fast Boundary Element solvers in the frequency domain to simulate coupled acoustic-elastic problems in the time domain. Application to the simulation of underwater explosions

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• Stephanie Chaillat-Loseille (CNRS (Centre national de la recherche scientifique))
• Friday 21 April 2023, 11:00-11:45
• Seminar Room 1, Newton Institute.

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MWSW03 - Computational methods for multiple scattering

Assessing the impact of a remote underwater explosion on a submerged structure (submarine) is an important naval engineering problem. An underwater explosion mainly induces two distinct phenomena: a ”shock wave” followed by an oscillating bubble of gas. I will concentrate on the modeling of the shock wave in this talk. 3D rapid transient acoustic problems are known to be difficult to solve numerically when dealing with large geometries, because numerical methods based on geometry discretisation, such as the BEM or the FEM , often require to solve a linear system (from the spacial discretisation) for each time step. In a first part, I will present  a numerical method to efficiently deal with 3D rapid transient acoustic problems set in large exterior domains. Using the Z-transform and the convolution quadrature method (CQM), a straightforward way to reframe the problem to the solving of a large amount of frequency-domain BEMs is derived. Then, taking advantage of a well-designed high-frequency approximation (HFA), the number of frequency-domain BEMs to be solved is drastically reduced, with little loss of accuracy. In a second part, I will discuss how to consider the FSI problem. A first approach  consists in iteratively solving the BEM -FEM coupling by alternating Neumann solutions in each domain. Unfortunately this simple approach fails. We can show that the transient BEM -FEM coupling based on Neumann-Neumann iterations is problematic since energy estimates indicate that each iteration degrades the regularity of boundary traces (unlike in the elliptic case). To avoid this issue, an iterative algorithm based on Robin boundary conditions for the coupled elastodynamic/acoustic problem will be presented and proved to converge. This is a join work with M. Bonnet, A. Nassor and D. Mavaleix-Marchessoux

This talk is part of the Isaac Newton Institute Seminar Series series.

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