On the Monotonicity of the CABARET Scheme Approximating a Scalar Conservation Law with an Alternating Characteristic Field and Convex Flux Function


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Abstract

The monotonicity of the CABARET scheme approximating the quasi-linear scalar conservation law with a convex flux is analyzed. The monotonicity conditions for this scheme are obtained in the areas where the propagation velocity of the characteristics has a constant sign, as well as in the areas of sonic lines, sonic bands, and shock waves, where the propagation velocity of the characteristics of the approximated divergent equation changes sign. The test computations are presented that illustrate these properties of the CABARET scheme.

About the authors

N. A. Zyuzina

Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences; Novosibirsk State University

Author for correspondence.
Email: nzyuzina1992@gmail.com
Russian Federation, Siberia; Siberia

O. A. Kovyrkina

Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences

Author for correspondence.
Email: olyana@ngs.ru
Russian Federation, Siberia

V. V. Ostapenko

Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences; Novosibirsk State University

Author for correspondence.
Email: ostapenko_vv@ngs.ru
Russian Federation, Siberia; Siberia

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