A mimetic finite-difference method for acoustic-wave modeling on arbitrary meshes

Accurate modeling of wave propagation and scattering in media containing fine structures and sharp interfaces with complex shapes is a challenging task. We introduce a mimetic finite-difference method for modeling acoustic-wave propagation in complex media. This method incorporates fundamental physical principles in the discretization of the acoustic-wave equation. The free surface boundary conditions are naturally embedded into the scheme. Unstructured polygonal meshes are used to represent complex shapes of interfaces, irregular and fine inclusions, and complex surface topography. Locally refined meshes can be employed in regions with different wave speeds. We numerically demonstrate that the new method can accurately simulate complex wave phenomena.