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.
REFERENCES
- 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].
- O. A. Kovyrkina and V. V. Ostapenko, Math. Model. Comput. Simul. 5 (2), 180–189 (2012).
- O. A. Kovyrkina and V. V. Ostapenko, Dokl. Math. 462 (4), 385–390 (2015).
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