Simulation of Wave Propagation in Discontinuous Media and Complex Geometries

Abstract: A strictly stable high order finite difference (HOFD) scheme for the scalar wave equation with discontinuous coefficients corresponding to inhomogeneity in the underlying media is constructed using summation - by - parts (SBP) operators. The domain of the equation is allowed to be complex in the sense that it can not be smoothly mapped from the unit square. The inhomogeneous media and complex geometries are handled by treating the problem in a domain decomposition setting. For each sub-domain there is a smooth one to one mapping from the unit square and its underlying media is smooth. The sub-domains are then coupled together with a penalty method, the simultaneous approximation term (SAT) method. Finally the scheme is extended to be able to handle local grid refinement, a feature quite new in the context of the SBP - SAT methodology. Accuracy and convergence properties are verified in numerical computations in 2 dimensions.