A boundary integral method for wave scattering in a heterogeneous medium with a moving obstacle

TL;DR

The paper introduces a boundary integral method for simulating wave scattering in heterogeneous media with moving obstacles, capturing Doppler and refractive effects without volumetric discretization.

Contribution

It extends boundary integral techniques to handle moving obstacles and heterogeneities using a geometric-optics parametrix and ray-based geometry, avoiding volumetric meshes.

Findings

Successfully models Doppler effects from moving obstacles, including rotating turbines.

Captures refractive effects around spherical inclusions like gas bubbles and fireballs.

Demonstrates stable performance up to Mach 0.9 in numerical experiments.

Abstract

We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method avoids volumetric discretization and yields a formulation posed only on the boundary of the obstacle. We combine two classical ingredients: a geometric--optics parametrix to capture leading-order behavior at propagating wavefronts, and a ray-based characterization of the distorted causal geometry. The former provides a framework for defining layer potentials and deriving the associated boundary integral equations, while the latter enables a pure boundary-only formulation. Taken together, these ingredients extend existing numerical techniques for the homogeneous, fixed-boundary case to the heterogeneous, moving-boundary setting, with appropriate modifications to capture the discrete causal structure arising from the intersection of distorted light cones with the worldsheet of the moving boundary. Numerical experiments demonstrate the ability of the method to resolve Doppler effects from moving obstacles, including a rotating turbine configuration, with stable performance up to Mach 0.9. In heterogeneous media, the method captures strong refractive effects from spherical inclusions: wave propagation wrapping around a gas bubble in water, and defocusing from a hot fireball rising through a stratified atmosphere.