On monotonicity of CABARET scheme approximating the multidimensional scalar conservation law
V.V. Ostapenko, T.V. Protopopova
М.А. Lavrentiev's Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
Keywords: CABARET difference scheme, multidimensional scalar conservation law, monotonicity property
Abstract
The monotonicity of the two-layer with respect to time CABARET scheme approximating the multidimensional scalar conservation law is analyzed. There is proposed a modification of this scheme. This modification of the CABARET scheme retains the monotonicity of the one-dimensional difference solutions in the linear approximation, and, as a result, it provides an increased smoothness during the calculation of the multidimensional discontinuous solutions. The results of test calculations are given. They illustrate the advantages of the modified scheme.
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