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 d...
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| Autor*in: |
Ostapenko, V. V. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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© Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 3, pp. 369–373. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2021, Vol. 501, pp. 62–66. |
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| Übergeordnetes Werk: |
Enthalten in: Doklady mathematics - Pleiades Publishing, 1995, 104(2021), 3 vom: Nov., Seite 369-373 |
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volume:104 ; year:2021 ; number:3 ; month:11 ; pages:369-373 |
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10.1134/S1064562421060120 |
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| 520 | |a 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. | ||
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10.1134/S1064562421060120 doi (DE-627)OLC2129988547 (DE-He213)S1064562421060120-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ostapenko, V. V. verfasserin aut Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 3, pp. 369–373. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2021, Vol. 501, pp. 62–66. 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. Kolotilov, V. A. aut Enthalten in Doklady mathematics Pleiades Publishing, 1995 104(2021), 3 vom: Nov., Seite 369-373 (DE-627)190923512 (DE-600)1294559-6 (DE-576)051408724 1064-5624 nnns volume:104 year:2021 number:3 month:11 pages:369-373 https://doi.org/10.1134/S1064562421060120 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 104 2021 3 11 369-373 |
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10.1134/S1064562421060120 doi (DE-627)OLC2129988547 (DE-He213)S1064562421060120-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ostapenko, V. V. verfasserin aut Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 3, pp. 369–373. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2021, Vol. 501, pp. 62–66. 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. Kolotilov, V. A. aut Enthalten in Doklady mathematics Pleiades Publishing, 1995 104(2021), 3 vom: Nov., Seite 369-373 (DE-627)190923512 (DE-600)1294559-6 (DE-576)051408724 1064-5624 nnns volume:104 year:2021 number:3 month:11 pages:369-373 https://doi.org/10.1134/S1064562421060120 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 104 2021 3 11 369-373 |
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10.1134/S1064562421060120 doi (DE-627)OLC2129988547 (DE-He213)S1064562421060120-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ostapenko, V. V. verfasserin aut Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 3, pp. 369–373. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2021, Vol. 501, pp. 62–66. 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. Kolotilov, V. A. aut Enthalten in Doklady mathematics Pleiades Publishing, 1995 104(2021), 3 vom: Nov., Seite 369-373 (DE-627)190923512 (DE-600)1294559-6 (DE-576)051408724 1064-5624 nnns volume:104 year:2021 number:3 month:11 pages:369-373 https://doi.org/10.1134/S1064562421060120 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT AR 104 2021 3 11 369-373 |
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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. © Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 3, pp. 369–373. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2021, Vol. 501, pp. 62–66. |
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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. © Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 3, pp. 369–373. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2021, Vol. 501, pp. 62–66. |
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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. © Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 3, pp. 369–373. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2021, Vol. 501, pp. 62–66. |
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V.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Application of the CABARET Scheme for Calculating Discontinuous Solutions of a Hyperbolic System of Conservation Laws</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Pleiades Publishing, Ltd. 2021. 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