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 |
|---|---|
| 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) |
| ZIB-Reportnumber: | SC-89-03 |
