Conservative numerical schemes for high-frequency wave propagation in heterogeneous media

摘要: The present work focuses on the numerical resolution of acoustic or elastic wave equation in a piece-wise homogeneous medium, splitted by interfaces. We are interested high-frequency setting, introduced strongly oscillating initial conditions, for which one computes distribution energy density so-called kinetic approach (based use Wigner transform). This problem then reduces to Liouville-type transport supplemented reflection and transmission laws at Several techniques ranges application also reviewed. describes evolution phase space positions _ vectors is numerically solved finite differences. technique raises several difficulties related conservation total medium They may be alleviated dedicated schemes allowing reduce dissipation either global local approach. improvements presented this thesis concern interpolation densities obtained grid discrete vectors, correction difference variation scales celerity each side interest foregoing developments obtain conservative that satisfy usual convergence properties methods. construction such their effective implementation constitute main achievement thesis. relevance proposed methods illustrated simulations, emphasize efficiency rather coarse meshes.