École Nationale Supérieure de
Techniques Avancées

Abstract

In the first part we present two numerical methods for solving time-dependent fluid-structure interaction problem. These methods, robust and accurate, are based on mixed formulations known as dual-dual and primal-primal. They are explicit, but on the interface, and conservative, which ensures their stability. They are validated thanks to analytical solutions calculated by the Cagniard de Hoop method. In the second part, we obtain, via the Cagniard de Hoop method, error estimates for the use of absorbing boundary conditions (ABC) and perfectly matched layers (PML) for time-domain acoustics. The third part is devoted to the PML for advective acoustics: analysis via the Cagniard-de Hoop method and construction of stabilized PMLs. The last part is a detailed mathematical presentation of the Cagniard-de Hoop method.