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

Abstract

International audienceWe develop a model to couple acoustic waves and the motion of rigid movable grains in a submerged suspension. To do so, we use the fictitious domain method based on distributed Lagrange multipliers to enforce the natural jump condition of the wave equation and a rigidity constraint. One can then model the granular medium with “Molecular Dynamics” or related methods. Both dynamic and acoustic numerical results are compared with analytic solutions of acoustics and an estimation of the error is given. We show energy transfers between two submerged grains separated by water and linked to their own spring while oscillating. The model is applied at large scale with a suspension of many grains to foresee its future possibilities

Wave-induced motion of rigid bodies: beads, boats and buildings

“…In the former case, suppose first that the fluid is inviscid and compressible: this is the realm of acoustics, where the fluid motion is governed by the Helmholtz equation. Application areas include suspensions or aerosols, with solid particles in a liquid or gas [5,6], sonar [7] and fish bioacoustics: it is thought that the otolith organs in the ears of fish are sensitive to motion [8,9]. General formalisms for such acoustic problems were given by Haskind (Khaskind) [10] and Olsson [11].…”