Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws

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Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws. / Ostapenko, V. V.; Kolotilov, V. A.

In: Doklady Mathematics, Vol. 104, No. 3, 11.2021, p. 369-373.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{81df2704a0d34741946ea20744522e5a,

title = "Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws",

abstract = "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 = "Blast Wave problem, CABARET scheme, equations of gas dynamics, quasi-invariants method",

author = "Ostapenko, {V. V.} and Kolotilov, {V. A.}",

note = "Funding Information: This work was supported in part by the Russian Foundation for Basic Research and the National Natural Science Foundation of China, project no. 21-51-53012. Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

year = "2021",

month = nov,

doi = "10.1134/S1064562421060120",

language = "English",

volume = "104",

pages = "369--373",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws

AU - Ostapenko, V. V.

AU - Kolotilov, V. A.

N1 - Funding Information: This work was supported in part by the Russian Foundation for Basic Research and the National Natural Science Foundation of China, project no. 21-51-53012. Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

PY - 2021/11

Y1 - 2021/11

N2 - 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.

AB - 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.

KW - Blast Wave problem

KW - CABARET scheme

KW - equations of gas dynamics

KW - quasi-invariants method

UR - http://www.scopus.com/inward/record.url?scp=85127674060&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/811c9797-aa91-376e-b4af-f6518fd3fc21/

U2 - 10.1134/S1064562421060120

DO - 10.1134/S1064562421060120

M3 - Article

AN - SCOPUS:85127674060

VL - 104

SP - 369

EP - 373

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 3

ER -

ID: 35853865