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On the Possible Accuracy of TVD Schemes.

Please always quote using this URN: urn:nbn:de:0297-zib-212
  • The paper presents a detailed analysis of the possible accuracy available for TVD schemes in one dimension with emphasis to the semi-discrete 1-D TVD schemes. The analysis shows that the widely accepted statement [1] of degeneration of accuracy at critical points for TVD schemes should be corrected. We have theorem: TVD schemes using flux limiters $ \varphi $ of the form [1], [2] may be second-order accurate at critical points if $ \varphi $ (3) + $ \varphi $(-1) = 2, but cannot be uniformly second-order accurate in the whole neighborhood of critical point. If $ \varphi $(1) = 1, then the TVD schemes are second-order accurate in the region of smooth solutions sufficiently far from the critical points. Two ways are suggested to improve the accuracy. Numerical example is given. {\bf Keywords:} Semi-discrete schemes, TVD, flux limiter, degeneration of accuracy.

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Author:Wu Huamo
Document Type:ZIB-Report
Tag:TVD; degeneration of accuracy; flux limiter; semi-discrete schemes
Date of first Publication:1989/07/03
Series (Serial Number):ZIB-Report (SC-89-03)
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