Kovyrkina O.   Ostapenko V.  

On Monotonicity of the CABARET Scheme in the Multidimensional Shock Capturing Calculations

Reporter: Kovyrkina O.

Recently, a two-time-level representation of the CABARET scheme [1] has been widely used for the numerical simulation of multidimensional gasdynamic and hydraulic flows. The monotonicity of this scheme in the one-dimensional case was examined in [2]. We analyze its monotonicity in the multidimensional case [3]. In the case of standard correction of flux variables, it is shown that this scheme does not preserve the monotonicity of one-dimensional solutions, that results in noticeable oscillations occurring in the computation of two-dimensional discontinuous solutions. We propose a modification of the two-time-level multidimensional CABARET scheme that preserves the monotonicity of one-dimensional solutions and, as a result, ensures higher smoothness in the computation of multidimensional discontinuous solutions. The results of two dimensional test computations illustrating the advantages of the modified scheme are presented.


  1. V. M. Goloviznin, M. A. Zaitsev, S. A. Karabasov, and I. A. Korotkin, New CFD Algorithms for Multiprocessor Computer Systems (Mosk. Gos. Univ., Moscow, 2013) [in Russian].
  2. O. A. Kovyrkina and V. V. Ostapenko, Math. Model. Comput. Simul. 5 (2), 180–189 (2012).
  3. O. A. Kovyrkina and V. V. Ostapenko, Dokl. Math. 462 (4), 385–390 (2015).

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