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Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws

  • Chi-Wang Shu
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1697)

Abstract

In these lecture notes we describe the construction, analysis, and application of ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes for hyperbolic conservation laws and related Hamilton-Jacobi equations. ENO and WENO schemes are high order accurate finite difference schemes designed for problems with piecewise smooth solutions containing discontinuities. The key idea lies at the approximation level, where a nonlinear adaptive procedure is used to automatically choose the locally smoothest stencil, hence avoiding crossing discontinuities in the interpolation procedure as much as possible. ENO and WENO schemes have been quite successful in applications, especially for problems containing both shocks and complicated smooth solution structures, such as compressible turbulence simulations and aeroacoustics.

These lecture notes are basically self-contained. It is our hope that with these notes and with the help of the quoted references, the readers can understand the algorithms and code them up for applications. Sample codes are also available from the author.

Keywords

Vortex Sheet WENO Scheme Numerical Flux Finite Volume Scheme Approximate Riemann Solver 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Chi-Wang Shu
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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