A comparison between finite differences and the spectral-element method for the simulation of the propagation of mechanical waves through fluid/solid interfaces

Numerical simulators of the propagation of mechanical perturbations in heterogeneous media are an essential tool for numerous applications in underwater acoustics. Computing the evolution in time of acoustic and elastic waves traveling across fluid/solid boundaries is yet a challenging task. The study reported in this paper investigates the accuracy of various algorithms for the simulation of the two-dimensional propagation of a cylindrical pulse through a fluid/solid interface. Three solvers are employed for this numerical experiment: SPECFEM (Spectral Finite Element Method), a code based on a spectral-element method employing fourth-order polynomial basis functions; EFIT (Elastodynamic Finite Integration Technique), an algorithm based on a staggered second-order finite-difference time-domain method; ESIM-n (Explicit Simplified Interface Method), a solver which uses n
^th
-order finite-differences and Runge-Kutta time integrators. Despite its simplicity, this benchmark allows ascertaining the ability of such algorithms to correctly handle the interfaces between different media, and evaluating the scheme resolutions in terms of points-per-wavelength.