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Finite‐difference methods for one‐dimensional hyperbolic conservation laws
Author(s) -
Berkenbosch A. C.,
Kaasschieter E. F.,
ten Thije Boonkkamp J. H. M.
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100207
Subject(s) - conservation law , mathematics , riemann problem , finite difference , flux limiter , hyperbolic partial differential equation , entropy (arrow of time) , riemann hypothesis , finite difference method , scalar (mathematics) , mathematical analysis , nonlinear system , law , partial differential equation , geometry , physics , quantum mechanics , political science
This article contains a survey of some important finite‐difference methods for one‐dimensional hyperbolic conservation laws. Weak solutions of hyperbolic conservation laws are introduced and the concept of entropy stability is discussed. Furthermore, the Riemann problem for hyperbolic conservation laws is solved. An introduction to finite‐difference methods is given for which important concepts such as, e.g., conservativity, stability, and consistency are introduced. Godunov‐type methods are elaborated for general systems of hyperbolic conservation laws. Finally, flux limiter methods are developed for the scalar nonlinear conservation law. © 1994 John Wiley & Sons, Inc.