Commun. Comput. Phys., 16 (2014), pp. 96-114.

Immersed Interface CIP for One Dimensional Hyperbolic Equations

Kazufumi Ito 1, Tomoya Takeuchi 2*

1 Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA.
2 Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, University of Tokyo, Tokyo, Japan; FIRST, Aihara Innovative Mathematical Modelling Project, JST, Kawaguchi, Japan.

Received 7 March 2013; Accepted (in revised version) 22 November 2013
Available online 10 April 2014


The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant coefficients. The proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities, which is the same order of accuracy of the standard CIP scheme. Some numerical tests are given to verify the accuracy of the proposed method.

AMS subject classifications: 65M12, 65M25

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Key words: CIP method, immersed interface method, hyperbolic equations in discontinuous media.

*Corresponding author.
Email: (K. Ito), (T. Takeuchi)

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