A New Interface Method for Hyperbolic Problems with Discontinuous Coefficients: One-Dimensional Acoustic Example

A new numerical method, called the explicit simplified interface method (ESIM), is developed in the context of acoustic wave propagation in heterogeneous media. Equations of acoustics are written as a first-order linear hyperbolic system. Apart from interfaces, a standard scheme (Lax–Wendroff, TVD, and WENO) is used in a classical way. Near interfaces, the same scheme is used, but it is applied on a set of modified values deduced from numerical values and jump conditions at interfaces. It amounts to modifying the scheme so that its order of accuracy is maintained at irregular points, despite the nonsmoothness of the solution. This easy-to-implement interface method requires only a few additional computational resources, and it can be applied to other partial differential equations.