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

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Advanced Numerical Approximation of Nonlinear Hyperbolic Equations

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,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.

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  1. Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    Chi-Wang Shu

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Alfio Quarteroni

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Shu, CW. (1998). Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: Quarteroni, A. (eds) Advanced Numerical Approximation of Nonlinear Hyperbolic Equations. Lecture Notes in Mathematics, vol 1697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096355

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