Decay of Unstable Strong Discontinuities in the Case of a Convex-Flux Scalar Conservation Law Approximated by the CABARET Scheme

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Decay of Unstable Strong Discontinuities in the Case of a Convex-Flux Scalar Conservation Law Approximated by the CABARET Scheme. / Zyuzina, N. A.; Ostapenko, V. V.

In: Computational Mathematics and Mathematical Physics, Vol. 58, No. 6, 01.06.2018, p. 950-966.

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

BibTeX

@article{b926861785254e169b4898c4e70aa3e6,

title = "Decay of Unstable Strong Discontinuities in the Case of a Convex-Flux Scalar Conservation Law Approximated by the CABARET Scheme",

abstract = "Abstract: Monotonicity conditions for the CABARET scheme approximating a quasilinear scalar conservation law with a convex flux are obtained. It is shown that the monotonicity of the CABARET scheme for Courant numbers r ∈ (0.5,1] does not ensure the complete decay of unstable strong discontinuities. For the CABARET scheme, a difference analogue of an entropy inequality is derived and a method is proposed ensuring the complete decay of unstable strong discontinuities in the difference solution for any Courant number at which the CABARET scheme is stable. Test computations illustrating these properties of the CABARET scheme are presented.",

keywords = "difference analogue of entropy inequality, monotone CABARET scheme, scalar conservation law, strong discontinuity, CHANGING CHARACTERISTIC FIELD, EQUATIONS, MONOTONICITY, SYSTEMS, SHOCKS",

author = "Zyuzina, {N. A.} and Ostapenko, {V. V.}",

year = "2018",

month = jun,

day = "1",

doi = "10.1134/S0965542518060155",

language = "English",

volume = "58",

pages = "950--966",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "PLEIADES PUBLISHING INC",

number = "6",

}

RIS

TY - JOUR

T1 - Decay of Unstable Strong Discontinuities in the Case of a Convex-Flux Scalar Conservation Law Approximated by the CABARET Scheme

AU - Zyuzina, N. A.

AU - Ostapenko, V. V.

PY - 2018/6/1

Y1 - 2018/6/1

N2 - Abstract: Monotonicity conditions for the CABARET scheme approximating a quasilinear scalar conservation law with a convex flux are obtained. It is shown that the monotonicity of the CABARET scheme for Courant numbers r ∈ (0.5,1] does not ensure the complete decay of unstable strong discontinuities. For the CABARET scheme, a difference analogue of an entropy inequality is derived and a method is proposed ensuring the complete decay of unstable strong discontinuities in the difference solution for any Courant number at which the CABARET scheme is stable. Test computations illustrating these properties of the CABARET scheme are presented.

AB - Abstract: Monotonicity conditions for the CABARET scheme approximating a quasilinear scalar conservation law with a convex flux are obtained. It is shown that the monotonicity of the CABARET scheme for Courant numbers r ∈ (0.5,1] does not ensure the complete decay of unstable strong discontinuities. For the CABARET scheme, a difference analogue of an entropy inequality is derived and a method is proposed ensuring the complete decay of unstable strong discontinuities in the difference solution for any Courant number at which the CABARET scheme is stable. Test computations illustrating these properties of the CABARET scheme are presented.

KW - difference analogue of entropy inequality

KW - monotone CABARET scheme

KW - scalar conservation law

KW - strong discontinuity

KW - CHANGING CHARACTERISTIC FIELD

KW - EQUATIONS

KW - MONOTONICITY

KW - SYSTEMS

KW - SHOCKS

UR - http://www.scopus.com/inward/record.url?scp=85049665559&partnerID=8YFLogxK

U2 - 10.1134/S0965542518060155

DO - 10.1134/S0965542518060155

M3 - Article

AN - SCOPUS:85049665559

VL - 58

SP - 950

EP - 966

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 6

ER -

ID: 14464596