Numerical modeling of mechanical wave propagation and diffraction

This document deals with direct problems of wave propagation in heterogeneous media and in the time domain. The main part of the work concerns the conception, the analysis, and the implementation of numerical methods: high-order schemes to integrate conservation laws, immersed interface method to discretize interfaces on a Cartesian grid. Various linear constitutive laws (inviscid fluid, elasticity, viscoelasticity, poroelasticity) and interface conditions (free surface, perfect or imperfect contact) are modeled. The numerical results are compared with analytical solutions. Putting together the various methods into a single optimized code yields an accurate numerical tool to study wave phenomena in complex media. As an illustration, we study the propagation of waves across a random network of scatterers, in 2D. The effective medium is characterized numerically. The accuracy of classical methods of multiple scattering is examined. More theoretical works are also proposed, concerning the interaction between elastic waves and a contact nonlinearity, in 1D. We study the generation of harmonics and the mean dilatation of the crack in terms of the forcing amplitude.