A simple and accurate discontinuous Galerkin scheme for modeling scalar-wave propagation in media with curved interfaces

Conventional high-order discontinuous Galerkin schemes suffer from interface errors caused by the misalignment between straight-sided elements and curved material interfaces. We develop a novel discontinuous Galerkin scheme to reduce the errors. Our new scheme use the correct normal vectors to the curved interfaces, while the conventional scheme uses the normal vectors to the element edge. We modify the numerical fluxes to account for the curved interface. Our numerical modeling examples demonstrate that our new discontinuous Galerkin scheme gives errors with much smaller magnitudes compared with the conventional scheme, although both schemes have second-order convergence. Moreover, our method significantly suppresses the spurious diffractions seen in the results obtained using the conventional scheme. The computational cost of our scheme is similar to that of the conventional scheme. Our new discontinuous Galerkin scheme is thus particularly useful for large-scale scalar-wave modeling involving complex subsurface structures.