Efficient implementation of essentially non-oscillatory shock-capturing schemes

In the computation of discontinuous solutions of hyperbolic conservation laws, TVD (total-variation-diminishing), TVB (total-variation-bounded), and the recently developed ENO (essentially non-oscillatory) schemes have proven to be very useful. In this paper two improvements are discussed: a simple...

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Bibliographic Details
Published in:Journal of computational physics 1988-08, Vol.77 (2), p.439-471
Main Authors: Shu, Chi-Wang, Osher, Stanley
Format: Article
Language:English
Subjects:
Compressible flows
shock and detonation phenomena
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Numerical Analysis
Physics
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Summary:In the computation of discontinuous solutions of hyperbolic conservation laws, TVD (total-variation-diminishing), TVB (total-variation-bounded), and the recently developed ENO (essentially non-oscillatory) schemes have proven to be very useful. In this paper two improvements are discussed: a simple TVD Runge-Kutta type time discretization, and an ENO construction procedure based on fluxes rather than on cell averages. These improvements simplify the schemes considerably-especially for multi-dimensional problems with forcing terms. Preliminary numerical results are also given.
ISSN:0021-9991
1090-2716
DOI:10.1016/0021-9991(88)90177-5