Acoustic propagation/refraction through diffuse interface models

• Development of a model for acoustic propagation suitable for incompressible multiphase fluids. • Model discretization with an entropy-stable DGSEM formulation. • Quantification of modeling errors due to interface thickness in acoustic transmission. • Validation of acoustic transmission and refraction according to Snell’s law. • Three-dimensional spherical wave propagation across a flat air-water interface. We present a novel approach for simulating acoustic (pressure) wave propagation across different media separated by a diffuse interface through the use of a weak compressibility formulation. Our method builds on our previous work on an entropy-stable discontinuous Galerkin spectral element method for the incompressible Navier-Stokes/Cahn-Hilliard system (Manzanero et al. (2020)), and incorporates a modified weak compressibility formulation that allows different sound speeds in each phase. We validate our method through numerical experiments, demonstrating spectral convergence for acoustic transmission and reflection coefficients in one dimension and for the angle defined by Snell’s law in two dimensions. Special attention is given to quantifying the modeling errors introduced by the width of the diffuse interface. Our results show that the method successfully captures the behavior of acoustic waves across interfaces, allowing exponential convergence in transmitted waves. The transmitted angles in two dimensions are accurately captured for air-water conditions, up to the critical angle of 13 ∘ . In a final example, we show a three-dimensional wave transmission from air into water to demonstrate the potential of this methodology for addressing general multiphase acoustic problems. This work represents a step forward in modeling acoustic propagation in incompressible multiphase systems, with potential applications to marine aeroacoustics.