A coupled acoustic/elastic discontinuous Galerkin finite element method: Application to ultrasonic imaging of 3D-printed synthetic materials

Abstract

We present the derivation of upwind numerical fluxes for the space discontinuous Galerkin (dG) finite element method applied to the numerical modeling of wave propagation in multidimensional coupled acoustic/elastic media. The space dG method is formulated using the first-order velocity-pressure and velocity-stress systems for acoustic and elastic media, respectively. After eigenanalysis of the first-order hyperbolic systems highlighting the eigenmodes of wave propagation, the upwind numerical fluxes on the acoustic/acoustic and acoustic/elastic interface are obtained in terms of exact solutions of relevant Riemann problems. Thanks to the proposed approach, explicit closed-form expressions of the upwind numerical fluxes are obtained on the acoustic/elastic interface for the general case of multidimensional anisotropic heterogeneous solid media coupled with acoustic fluids. The developed numerical fluxes are validated by analytical/numerical comparison considering the example of an acoustic domain with a circular elastic inclusion. Finally, the coupled solver is used to perform a multiparametric study on the microstructure's echogenicity in a 3D-printed synthetic material under ultrasonic imaging.