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Modifications to the Lax–Wendroff scheme for hyperbolic systems with source terms
Author(s) -
Zhang Yuangao,
Tabarrok Behrouz
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990110)44:1<27::aid-nme485>3.0.co;2-0
Subject(s) - mathematics , hyperbolic partial differential equation , wavefront , scheme (mathematics) , partial differential equation , computation , mathematical analysis , dimension (graph theory) , set (abstract data type) , pure mathematics , computer science , algorithm , physics , optics , programming language
For wave phenomena in one spatial dimension, governed by hyperbolic partial differential equations with source terms, the standard Lax–Wendroff scheme leads to oscillations at discontinuous wavefronts even if the Courant–Friedrich–Lewy (CFL) number is set equal to unity. We modify the Lax–Wendroff scheme for hyperbolic systems with source terms based on characteristic analysis to preserve the wave profile correctly when the CFL number is set equal to 1. The new scheme can be used as easily as the original Lax–Wendroff scheme since the calculation of the characteristics is not introduced in the new scheme. Thus, additional computations of characteristics are not necessary. We also extend our method for higher spatial dimensions and illustrate our approach by numerical examples. Copyright © 1999 John Wiley & Sons, Ltd.