Geodesic
Application of the CABARET scheme for calculating discontinuous solutions of a hyperbolic system of conservation laws
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 62-66.

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A method is proposed for constructing a CABARET scheme that approximates a hyperbolic system of conservation laws that cannot be written in the form of invariants. This technique is based on the method of quasi-invariants and additional flux correction, which ensures monotonization of the difference solution in calculating discontinuous solutions with shock waves and contact discontinuities. As an example, a system of conservation laws for nonisentropic gas dynamics with a polytropic equation of state is considered. Test calculations of the Blast Wave initial-boundary value problem showed that the proposed scheme suppresses nonphysical oscillations leading to the instability of the difference solution in the case when the CABARET scheme is used without additional flux correction.
Keywords: quasi-invariants method, CABARET scheme, equations of gas dynamics, Blast Wave problem. 
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     author = {V. V. Ostapenko and V. A. Kolotilov},
     title = {Application of the {CABARET} scheme for calculating discontinuous solutions of a hyperbolic system of conservation laws},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
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V. V. Ostapenko; V. A. Kolotilov. Application of the CABARET scheme for calculating discontinuous solutions of a hyperbolic system of conservation laws. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 62-66. http://geodesic.mathdoc.fr/item/DANMA_2021_501_a11/

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