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• 1
Book
Title: On the Possible Accuracy of TVD Schemes. /; Preprint SC 89-03
Author: Huamo, Wu
Year of publication: 1989
Series Statement: Preprint / Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 89-03
ISSN: 0933-7911
Type of Medium: Book
Language: English
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• 2
Book
Title: MmB-A New Class of Accurate High Resolution Schemes for Conservation Laws in Two Dimensions. /; Preprint SC 89-06
Author: Huamo, Wu
Year of publication: 1989
Series Statement: Preprint / Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 89-06
ISSN: 0933-7911
Type of Medium: Book
Language: English
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• 3
Publication Date: 2014-02-26
Description: 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.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
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• 4
Publication Date: 2014-02-26
Description: In this paper we present the MmB schemes, which preserve the local maximum and minimum bounds of the initial data in the smallest union of mesh elements of previous time step containing the domain of dependence of the solution on the mesh element with center at point $P$\ under consideration. In 1-D, the MmB schemes are almost identical with TVD schemes. As well-known, there is no second-order TVD scheme in 2-D, nevertheless, we present here two classes of 2-D second-order accurate MmB-schemes. It is proved that 1-D discrete MmB (or TVD) and 1-D semi-discrete TVD schemes may have second-order accuracy at (nonsonic) critical points, but cannot be of uniformly second-order accurate in the whole neighborhood of the critical points. New accurate high resolution flux limiters are suggested. Numerical results for 1-D and 2-D test problems are given. {\bf Keywords:} Difference scheme, TVD, MmB, flux limiter.
Keywords: ddc:000
Language: English
Type: reportzib , doc-type:preprint
Format: application/pdf
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