An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids
Abstract Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. For solutions with discontinuities appearing in such as conservation laws, a certain limiter has...
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Gespeichert in:
| Autor*in: |
Chen, Li [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of scientific computing - Springer US, 1986, 68(2016), 3 vom: 11. Feb., Seite 1172-1197 |
|---|---|
| Übergeordnetes Werk: |
volume:68 ; year:2016 ; number:3 ; day:11 ; month:02 ; pages:1172-1197 |
| Links: |
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| DOI / URN: |
10.1007/s10915-016-0173-1 |
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OLC2073315658 |
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| 520 | |a Abstract Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. For solutions with discontinuities appearing in such as conservation laws, a certain limiter has to be applied to the predicted gradient to prevent numerical oscillations. We propose in this paper a new formulation for linear reconstruction on unstructured grids, which integrates the prediction of the gradient and the limiter together. By solving on each cell a tiny linear programming problem without any parameters, the gradient is directly obtained which satisfies the monotonicity condition. It can be shown that the resulting numerical scheme with our new method fulfils a discrete maximum principle with fair relaxed geometric constraints on grids. Numerical results demonstrate that our method achieves satisfactory numerical accuracy with theoretical guarantee of local discrete maximum principle. | ||
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10.1007/s10915-016-0173-1 doi (DE-627)OLC2073315658 (DE-He213)s10915-016-0173-1-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Chen, Li verfasserin aut An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. For solutions with discontinuities appearing in such as conservation laws, a certain limiter has to be applied to the predicted gradient to prevent numerical oscillations. We propose in this paper a new formulation for linear reconstruction on unstructured grids, which integrates the prediction of the gradient and the limiter together. By solving on each cell a tiny linear programming problem without any parameters, the gradient is directly obtained which satisfies the monotonicity condition. It can be shown that the resulting numerical scheme with our new method fulfils a discrete maximum principle with fair relaxed geometric constraints on grids. Numerical results demonstrate that our method achieves satisfactory numerical accuracy with theoretical guarantee of local discrete maximum principle. Linear reconstruction Finite volume method Simplex method Linear programming Li, Ruo aut Enthalten in Journal of scientific computing Springer US, 1986 68(2016), 3 vom: 11. Feb., Seite 1172-1197 (DE-627)129217549 (DE-600)56055-8 (DE-576)065121945 0885-7474 nnns volume:68 year:2016 number:3 day:11 month:02 pages:1172-1197 https://doi.org/10.1007/s10915-016-0173-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 68 2016 3 11 02 1172-1197 |
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10.1007/s10915-016-0173-1 doi (DE-627)OLC2073315658 (DE-He213)s10915-016-0173-1-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Chen, Li verfasserin aut An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. For solutions with discontinuities appearing in such as conservation laws, a certain limiter has to be applied to the predicted gradient to prevent numerical oscillations. We propose in this paper a new formulation for linear reconstruction on unstructured grids, which integrates the prediction of the gradient and the limiter together. By solving on each cell a tiny linear programming problem without any parameters, the gradient is directly obtained which satisfies the monotonicity condition. It can be shown that the resulting numerical scheme with our new method fulfils a discrete maximum principle with fair relaxed geometric constraints on grids. Numerical results demonstrate that our method achieves satisfactory numerical accuracy with theoretical guarantee of local discrete maximum principle. Linear reconstruction Finite volume method Simplex method Linear programming Li, Ruo aut Enthalten in Journal of scientific computing Springer US, 1986 68(2016), 3 vom: 11. Feb., Seite 1172-1197 (DE-627)129217549 (DE-600)56055-8 (DE-576)065121945 0885-7474 nnns volume:68 year:2016 number:3 day:11 month:02 pages:1172-1197 https://doi.org/10.1007/s10915-016-0173-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 68 2016 3 11 02 1172-1197 |
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10.1007/s10915-016-0173-1 doi (DE-627)OLC2073315658 (DE-He213)s10915-016-0173-1-p DE-627 ger DE-627 rakwb eng 004 VZ 11 ssgn Chen, Li verfasserin aut An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2016 Abstract Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. For solutions with discontinuities appearing in such as conservation laws, a certain limiter has to be applied to the predicted gradient to prevent numerical oscillations. We propose in this paper a new formulation for linear reconstruction on unstructured grids, which integrates the prediction of the gradient and the limiter together. By solving on each cell a tiny linear programming problem without any parameters, the gradient is directly obtained which satisfies the monotonicity condition. It can be shown that the resulting numerical scheme with our new method fulfils a discrete maximum principle with fair relaxed geometric constraints on grids. Numerical results demonstrate that our method achieves satisfactory numerical accuracy with theoretical guarantee of local discrete maximum principle. Linear reconstruction Finite volume method Simplex method Linear programming Li, Ruo aut Enthalten in Journal of scientific computing Springer US, 1986 68(2016), 3 vom: 11. Feb., Seite 1172-1197 (DE-627)129217549 (DE-600)56055-8 (DE-576)065121945 0885-7474 nnns volume:68 year:2016 number:3 day:11 month:02 pages:1172-1197 https://doi.org/10.1007/s10915-016-0173-1 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 68 2016 3 11 02 1172-1197 |
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Abstract Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. For solutions with discontinuities appearing in such as conservation laws, a certain limiter has to be applied to the predicted gradient to prevent numerical oscillations. We propose in this paper a new formulation for linear reconstruction on unstructured grids, which integrates the prediction of the gradient and the limiter together. By solving on each cell a tiny linear programming problem without any parameters, the gradient is directly obtained which satisfies the monotonicity condition. It can be shown that the resulting numerical scheme with our new method fulfils a discrete maximum principle with fair relaxed geometric constraints on grids. Numerical results demonstrate that our method achieves satisfactory numerical accuracy with theoretical guarantee of local discrete maximum principle. © Springer Science+Business Media New York 2016 |
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Abstract Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. For solutions with discontinuities appearing in such as conservation laws, a certain limiter has to be applied to the predicted gradient to prevent numerical oscillations. We propose in this paper a new formulation for linear reconstruction on unstructured grids, which integrates the prediction of the gradient and the limiter together. By solving on each cell a tiny linear programming problem without any parameters, the gradient is directly obtained which satisfies the monotonicity condition. It can be shown that the resulting numerical scheme with our new method fulfils a discrete maximum principle with fair relaxed geometric constraints on grids. Numerical results demonstrate that our method achieves satisfactory numerical accuracy with theoretical guarantee of local discrete maximum principle. © Springer Science+Business Media New York 2016 |
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Abstract Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. For solutions with discontinuities appearing in such as conservation laws, a certain limiter has to be applied to the predicted gradient to prevent numerical oscillations. We propose in this paper a new formulation for linear reconstruction on unstructured grids, which integrates the prediction of the gradient and the limiter together. By solving on each cell a tiny linear programming problem without any parameters, the gradient is directly obtained which satisfies the monotonicity condition. It can be shown that the resulting numerical scheme with our new method fulfils a discrete maximum principle with fair relaxed geometric constraints on grids. Numerical results demonstrate that our method achieves satisfactory numerical accuracy with theoretical guarantee of local discrete maximum principle. © Springer Science+Business Media New York 2016 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2073315658</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503144851.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200819s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10915-016-0173-1</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2073315658</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s10915-016-0173-1-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">11</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chen, Li</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</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">© Springer Science+Business Media New York 2016</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. 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