The immersed interface method for acoustic wave equations with discontinuous coefficients

A numerical method of second order accuracy is developed to solve acoustic wave equations in heterogeneous media, whose solutions are discontinuous across the interfaces between different wave speeds. High resolution multi-dimensional flux-limiter methods are used on a Cartesian grid. Near the interface, special formulas are developed using the immersed interface method that incorporate the jump conditions and give pointwise second order accuracy even when the interface is not aligned with the grid.