Uniformly high order accurate essentially non-oscillatory schemes, III

Journal Article · Sat Feb 01 04:00:00 EST 1997 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1996.5632· OSTI ID:478402

Harten, A ^[1]; Engquist, B; Osher, S ^[2]

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1. Univ of California, Los Angeles, CA (United States)
2. Univ. of California, Los Angeles, CA (United States); and others

We continue the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws. We present an hierarchy of uniformly high-order accurate schemes which generalizes Godunov`s scheme and its second-order accurate MUSCL extension to an arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that, when applied to piecewise smooth data, gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and, consequently, the resulting schemes are highly nonlinear. 32 refs., 20 figs., 2 tabs.

• OSTI ID: 478402
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 131; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
66 PHYSICS
99 GENERAL AND MISCELLANEOUS
ALGORITHMS
CONSERVATION LAWS
FLOW MODELS
GAS FLOW
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS