Elastic surface waves in crystals – Part 2: Cross-check of two full-wave numerical modeling methods

• Published in: Ultrasonics Vol. 51; no. 8; pp. 878 - 889
• Main Authors: Komatitsch, Dimitri, Carcione, José M., Cavallini, Fabio, Favretto-Cristini, Nathalie
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2011; Elsevier
• Subjects: Acoustics; Algorithms; Anisotropy; apatite; Computer simulation; copper; Crystals; Engineering Sciences; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Mechanics; Media; Modeling; Physics; Solid mechanics; Spectra; Structural acoustics and vibration; Structural and continuum mechanics; Surface waves; Symmetry; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); zinc; Anisotropy; Modeling; Surface waves; Cubic lattices; Spectral method; Variability; Grid; Surface wave; Calcium phosphate; Free surface; Elastic wave; Experimental study; Anisotropic medium; Green function; Crystal symmetry; Surface stresses; Elastic crystals; Homogeneous medium; Hexagonal lattices; Symmetry group; Hexagonal crystals; Copper; Elastodynamics
• ISSN: 0041-624X; 1874-9968; 1874-9968
• DOI: 10.1016/j.ultras.2011.05.001

► Full-wave numerical solution at the surface of arbitrary anisotropic media. ► Focus on media of cubic and hexagonal symmetries. ► Simulations in heterogeneous media with large impedance variations at the interface. We obtain the full-wave solution for the wave propagation at the surface of anisotropic media using two spectral numerical modeling algorithms. The simulations focus on media of cubic and hexagonal symmetries, for which the physics has been reviewed and clarified in a companion paper. Even in the case of homogeneous media, the solution requires the use of numerical methods because the analytical Green’s function cannot be obtained in the whole space. The algorithms proposed here allow for a general material variability and the description of arbitrary crystal symmetry at each grid point of the numerical mesh. They are based on high-order spectral approximations of the wave field for computing the spatial derivatives. We test the algorithms by comparison to the analytical solution and obtain the wave field at different faces (stress-free surfaces) of apatite, zinc and copper. Finally, we perform simulations in heterogeneous media, where no analytical solution exists in general, showing that the modeling algorithms can handle large impedance variations at the interface.