An arbitrary-order immersed interface method for the two-dimensional propagation of acoustic and elastic waves

Abstract

This paper proposes an arbitrary-order immersed interface method for simulating the two-dimensional propagation of acoustic and elastic waves through fluid/solid interfaces. The present technique involves two main ingredients: (1) the linearized equations of continuum mechanics are simulated through an ADER (Arbitrary high-order schemes using DERivatives) scheme of arbitrary-order in both space and time [Schwartzkopff et al., J. Comput. Phys. 197(2), 532–539 (2004)]; (2) the jump conditions along the material interfaces are taken into account through the “explicit simplified interface method” (ESIM) derived by Lombard and Piraux [J. Comput. Phys. 195(1), 90–116, 2004]. To implement the ESIM, arbitrary-order spatial derivatives of the interface conditions must be calculated. To this end, an algorithm not requiring their explicit analytical expressions is developed for their numerical computation. Two numerical experiments involving flat and curved interfaces are finally discussed. When increasing the order of both the ADER scheme and of the interface treatment, the improvement of the convergence and of the accuracy of the numerical method is more specifically demonstrated by comparing the numerical results with analytical solutions.