THE IMMERSED INTERFACE METHOD FOR ACOUSTIC-WAVE EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

A numerical method of second order accuracy is developed to solve acou stic wave equations in heterogeneous media, whose solutions are discon tinuous across the interfaces between different wave speeds. High reso lution multi-dimensional flux-limiter methods are used on a Cartesian grid. Near the interface, special formulas are developed using the imm ersed interface method that incorporate the jump conditions and give p ointwise second order accuracy even when the interface is not aligned with the grid.