Fictitious domain method to model a movable rigid body in a sound wave

Abstract

Motivated by experiments on the acoustics of submerged granular media, we have developed a new fictitious domain method that combines the acoustic wave equation with the equations of motion of a rigid body. The coupling is realized through the natural boundary conditions of the wave equation on the surface of the body and enforced with boundary Lagrange multipliers. The method is validated using analytic solutions for a movable rigid sphere in a sound wave. Results show that the method is promising because numerical results and analytic solutions are close for long wavelengths, although some deviations occur when the wavelength is smaller to the sphere radius. This method permits us to use a discrete element method for particle motion and interaction, and finite elements for wave propagation in the fluid.

Fictitious domain method for acoustic waves through a granular suspension of movable rigid spheres

“…On one hand, Perfectly Matched Layers (PML) [19] are set on the bottom side Γ 1 and the top side Γ 3 of the domain Ω but we will not focus on that point to keep equations simple. See [20] for details on the construction of the PML based on a coordinate stretching approach for Maxwell's equations and [17] for the acoustic wave equation.…”