Application of the CABARET Scheme for Calculating Multidimensional Hyperbolic Systems of Conservation Laws

Application of the CABARET Scheme for Calculating Multidimensional Hyperbolic Systems of Conservation Laws Full article

Journal

Computational Mathematics and Mathematical Physics
ISSN: 0965-5425

Output data

Year: 2026, Volume: 66, Number: 7, Pages: 1370-1386 Pages count : 17 DOI: 10.1134/s0965542526700703

Tags

multidimensional hyperbolic system of conservation laws, monotonicity of the CABARET scheme, cylindrical explosion problem for gas dynamics equations

Authors

Kolotilov V.A. ¹ , Ostapenko V.V. ¹

Affiliations

1	Lavrentiev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, pr. akademika Lavrentieva 15, 630090, Novosibirsk, Russia

The method of quasi-invariants is presented for constructing the standard and modified CABARET and CABARETM schemes that approximate the Cauchy problem for a multidimensional quasilinear hyperbolic system of conservation laws. As a specific example, the problem of a cylindrical explosion is considered, which is a two-dimensional Cauchy problem for the equations of nonisentropic gas dynamics with a polytropic equation of state and with special circular piecewise constant initial data. Test calculations have shown that the CABARET scheme is unstable when calculating this problem, while the numerical solution obtained by the CABARETM scheme is stable over a wide range of Courant numbers and localizes all the singularities of the approximated exact solution with high accuracy.

Kolotilov V.A. , Ostapenko V.V.
Application of the CABARET Scheme for Calculating Multidimensional Hyperbolic Systems of Conservation Laws
Computational Mathematics and Mathematical Physics. 2026. V.66. N7. P.1370-1386. DOI: 10.1134/s0965542526700703 WOS Scopus OpenAlex

Submitted:	Oct 29, 2025
Accepted:	Apr 10, 2026
Published print:	Aug 27, 2026

≡ Web of science:	WOS:001862007100011
≡ Scopus:	2-s2.0-105048734786
≡ OpenAlex:	W7204439740