Stable and accurate wave-propagation in discontinuous media

A time stable discretization is derived for the second-order wave equation with discontinuous coefficients. The discontinuity corresponds to inhomogeneity in the underlying medium and is treated by splitting the domain. Each (homogeneous) sub domain is discretized using narrow-diagonal summation by parts operators and, then, patched to its neighbors by using a penalty method, leading to fully explicit time integration. This discretization yields a time stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension using high-order finite difference discretizations, and in three-dimensions using an unstructured finite volume discretization.