High Order Immersed Interface Method for Acoustic Wave Equation With Discontinuous Coefficients

This paper concerns the numerical solution of the acoustic wave equation that contains interfaces in the solution domain. To solve the interface problems with high accuracy, more attention should be paid to the interfaces. In fact, any direct application of a high order finite diffierence method to these problems leads to inaccurate proximate solutions with high oscillations at the interfaces. There is however, the possibility of deriving some high order methods to resolve this phenomenon at the interfaces. In this paper, a sixth order immersed interface method for acoustic wave equation is presented. The order of accuracy is also maintained at the discontinuity using the jump conditions. Some numerical experiments are included which confirm the order of accuracy and numerical stability of the presented method.