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

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 so...

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Bibliographic Details
Published in:Mathematical models and computer simulations 2019, Vol.11 (1), p.46-60
Main Authors: Zyuzina, N. A., Kovyrkina, O. A., Ostapenko, V. V.
Format: Article
Language:English
Subjects:
Approximation
Cabaret
Conservation
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Propagation velocity
Shock wave propagation
Shock waves
Simulation and Modeling
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Summary: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.
ISSN:2070-0482
2070-0490
DOI:10.1134/S2070048219010186