## 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.

Author: Wu Huamo ZIB-Report TVD; degeneration of accuracy; flux limiter; semi-discrete schemes 1989/07/03 ZIB-Report (SC-89-03) SC-89-03
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