A 2-D enlarged cell technique (ECT) for elastic wave modelling on a curved free surface

The conventional finite-difference time-domain (FDTD) method for elastic waves suffers from the staircasing error when applied to model a curved free surface because of the structured grid. This is similar to the situation for the FDTD method in electromagnetics when it is applied to model a curved perfect conductor surface, where the conformal FDTD methods have been recently developed to avoid this error. In this work a stable and second-order accurate 2-D FDTD method for elastic wave modelling on a curved free surface is presented based on the finite volume method and enlarged cell technique (ECT). To achieve a sufficiently accurate implementation, a finite volume scheme is applied to the curved free surface to remove the staircasing error; in the meantime, to achieve the same stability as the FDTD method without reducing the time step increment, the ECT is introduced to preserve the solution stability even for small irregular cells. This method is verified by several 2-D numerical examples. Results show that the method is second-order accurate and stable at the Courant stability limit for a regular FDTD grid.