A mechanic-acoustic coupling condition, including viscous and thermal boundary layer effects

Abstract

Acoustic-structural interaction can be modeled by coupling the linearized compressible flow equations and the balance of momentum, governing fluid and solid mechanics respectively. The flow equations can accurately model the boundary layer effects but require the boundary layer to be resolved sufficiently fine, which increases the computational cost. In this work, we extend the so called boundary condition approach which accounts for the boundary losses to include boundary motion, thereby arriving at a coupling condition between fluid and solid. So we describe the acoustics by the Helmholtz partial differential equation, the mechanics by the balance of momentum, and the coupling condition establishes the coupling and also accounts for the boundary losses. This strategy reduces the number of unknowns and the coupling condition does not require the boundary layer to be resolved explicitly, reducing the computational cost significantly. The formulation is validated using several test cases, and the results agree well with the analytical and fully resolved compressible flow equations.