Immersed Interface CIP for One Dimensional Hyperbolic Equations (Communications in Computational Physics, 2014)
The immersed interface technique is incorporated into CIP method to solveone-dimensional hyperbolic equations with piecewise constant coefficients. The proposed method achieves the third order of accuracy in time and space in the vicinity ofthe interface where the coefficients have jump discontinuities, which is the same orderof accuracy of the standard CIP scheme. Some numerical tests are given to verify theaccuracy of the proposed method.