A frequency domain method for scattering problems with moving boundaries

David Gasperini (1, 2, 3, 4) , Hans-Peter P Beise (3) , Udo Schroeder (3) , Xavier Antoine (1, 4) , Christophe Geuzaine (2)

1 IECL - Institut Élie Cartan de Lorraine
2 Institut Montefiore - Department of Electrical Engineering and Computer Science
3 IEE S.A.
4 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization

We propose a multi-harmonic numerical method for solving wave scattering problems with moving boundaries, where the scatterer is assumed to move smoothly around an equilibrium position. We first develop an analysis to justify the method and its validity in the one-dimensional case with small-amplitude sinusoidal motions of the scatterer, before extending it to large-amplitude, arbitrary motions in one-and two-dimensional settings. We compare the numerical results of the proposed approach to standard space-time resolution schemes, which illustrates the efficiency of the new method.

Mots clés: Doppler effect; high frequency acoustic scattering; moving boundary; high frequency scattering; scalar waves; multifrequency resolution

Domaines: Equations aux dérivées partielles [math.AP]; Modélisation et simulation; Electromagnétisme; Acoustique [physics.class-ph]

David Gasperini, Hans-Peter P Beise, Udo Schroeder, Xavier Antoine, Christophe Geuzaine. A frequency domain method for scattering problems with moving boundaries. Wave Motion, 2021, 102, pp.102717. ⟨10.1016/j.wavemoti.2021.102717⟩. ⟨hal-02540554v2⟩