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A review and comparative study of upwind biased schemes for compressible flow computation. II: 1-D higher-order schemes. (English) Zbl 1012.76046

[For part I see the authors, ibid. 7, No. 1, 19-55 (2000; Zbl 1011.76060).]
Summary: Higher order upwind biased procedures for solving the equations of one-dimensional compressible unsteady flows are surveyed. Approaches based upon the use of either switched artificial viscosity, flux-limiting or slope-limiting are considered and described within a unified framework. The approaches are implemented within the context of an edge-based finite element algorithm, which represents the basis for a future multi-dimensional extension on general grids. The performance of different approaches is illustrated by application to the solution of shock tube problem in different flow regimes.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics

Citations:

Zbl 1011.76060

Software:

HE-E1GODF; SHASTA
PDFBibTeX XMLCite
Full Text: DOI

References:

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