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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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