@misc{Huamo1989, author = {Huamo, Wu}, title = {On the Possible Accuracy of TVD Schemes.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-212}, number = {SC-89-03}, year = {1989}, abstract = {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.}, language = {en} }