Very-high-order weno schemes
We study weno(2 r − 1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping ( wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-esse...
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| creator | Gerolymos, G.A. Sénéchal, D. Vallet, I. |
| description | We study
weno(2
r
−
1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving
weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (
wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to
weno17
(
r
=
9
)
. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent
cfl limitation
(
cfl
∈
[
0.8
,
1
]
)
, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent
p
β
in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted
eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as
p
β
=
r
, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of
p
β
=
2
(this is valid both for
weno and
wenom reconstructions), although the optimal value of the exponent is probably
p
β
(
r
)
∈
[
2
,
r
]
. Then, we apply the family of very-high-order
wenom
p
β
=
r
reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes
iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (
ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed
ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume
weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding
rorwenom
p
β
=
r
schemes are essentially nonoscillatory, as
Δ
x
→
0
, up to
r
=
9
, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases. |
| doi_str_mv | 10.1016/j.jcp.2009.07.039 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1786159033</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0021999109003908</els_id><sourcerecordid>1786159033</sourcerecordid><originalsourceid>FETCH-LOGICAL-c393t-a06d16d49f42c83ba56842803e89459afe5fdfae7b59febbc6af1c4105471ddb3</originalsourceid><addsrcrecordid>eNqFkE1LAzEURYMoWKs_QHDRjeBmxveSTGaCKyl-QcGNug2ZzIvNMO3UpFX67x1pcamruzn3XjiMnSPkCKiu27x1q5wD6BzKHIQ-YCMEDRkvUR2yEQDHTGuNx-wkpRYAqkJWI3bxRnGbzcP7POtjQ3HyRct-ktycFpRO2ZG3XaKzfY7Z6_3dy_Qxmz0_PE1vZ5kTWqwzC6pB1UjtJXeVqG2hKskrEFRpWWjrqfCNt1TWhfZU105Zj04iFLLEpqnFmF3tdlex_9hQWptFSI66zi6p3ySDZaWw0CDE_yhXqpRSoB5Q3KEu9ilF8mYVw8LGrUEwP9JMawZp5keagdIM0obO5X7eJmc7H-3ShfRb5HxwyoEP3M2Oo0HLZ6Bokgu0dNSESG5tmj788fIN1GZ_ng</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1266744319</pqid></control><display><type>article</type><title>Very-high-order weno schemes</title><source>Elsevier ScienceDirect Journals</source><creator>Gerolymos, G.A. ; Sénéchal, D. ; Vallet, I.</creator><creatorcontrib>Gerolymos, G.A. ; Sénéchal, D. ; Vallet, I.</creatorcontrib><description>We study
weno(2
r
−
1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving
weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (
wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to
weno17
(
r
=
9
)
. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent
cfl limitation
(
cfl
∈
[
0.8
,
1
]
)
, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent
p
β
in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted
eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as
p
β
=
r
, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of
p
β
=
2
(this is valid both for
weno and
wenom reconstructions), although the optimal value of the exponent is probably
p
β
(
r
)
∈
[
2
,
r
]
. Then, we apply the family of very-high-order
wenom
p
β
=
r
reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes
iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (
ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed
ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume
weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding
rorwenom
p
β
=
r
schemes are essentially nonoscillatory, as
Δ
x
→
0
, up to
r
=
9
, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2009.07.039</identifier><identifier>CODEN: JCTPAH</identifier><language>eng</language><publisher>Kidlington: Elsevier Inc</publisher><subject>Adjustable ; Algorithms ; Computational techniques ; Conservation laws ; Euler equations ; Exact sciences and technology ; Exponents ; High-order schemes ; Hyperbolic conservation laws ; Mathematical methods in physics ; Nonlinearity ; Optimization ; Physics ; Reconstruction ; Scalars ; Smoothness indicators ; weno schemes</subject><ispartof>Journal of computational physics, 2009-12, Vol.228 (23), p.8481-8524</ispartof><rights>2009 Elsevier Inc.</rights><rights>2009 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c393t-a06d16d49f42c83ba56842803e89459afe5fdfae7b59febbc6af1c4105471ddb3</citedby><cites>FETCH-LOGICAL-c393t-a06d16d49f42c83ba56842803e89459afe5fdfae7b59febbc6af1c4105471ddb3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0021999109003908$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22109202$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Gerolymos, G.A.</creatorcontrib><creatorcontrib>Sénéchal, D.</creatorcontrib><creatorcontrib>Vallet, I.</creatorcontrib><title>Very-high-order weno schemes</title><title>Journal of computational physics</title><description>We study
weno(2
r
−
1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving
weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (
wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to
weno17
(
r
=
9
)
. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent
cfl limitation
(
cfl
∈
[
0.8
,
1
]
)
, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent
p
β
in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted
eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as
p
β
=
r
, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of
p
β
=
2
(this is valid both for
weno and
wenom reconstructions), although the optimal value of the exponent is probably
p
β
(
r
)
∈
[
2
,
r
]
. Then, we apply the family of very-high-order
wenom
p
β
=
r
reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes
iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (
ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed
ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume
weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding
rorwenom
p
β
=
r
schemes are essentially nonoscillatory, as
Δ
x
→
0
, up to
r
=
9
, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.</description><subject>Adjustable</subject><subject>Algorithms</subject><subject>Computational techniques</subject><subject>Conservation laws</subject><subject>Euler equations</subject><subject>Exact sciences and technology</subject><subject>Exponents</subject><subject>High-order schemes</subject><subject>Hyperbolic conservation laws</subject><subject>Mathematical methods in physics</subject><subject>Nonlinearity</subject><subject>Optimization</subject><subject>Physics</subject><subject>Reconstruction</subject><subject>Scalars</subject><subject>Smoothness indicators</subject><subject>weno schemes</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNqFkE1LAzEURYMoWKs_QHDRjeBmxveSTGaCKyl-QcGNug2ZzIvNMO3UpFX67x1pcamruzn3XjiMnSPkCKiu27x1q5wD6BzKHIQ-YCMEDRkvUR2yEQDHTGuNx-wkpRYAqkJWI3bxRnGbzcP7POtjQ3HyRct-ktycFpRO2ZG3XaKzfY7Z6_3dy_Qxmz0_PE1vZ5kTWqwzC6pB1UjtJXeVqG2hKskrEFRpWWjrqfCNt1TWhfZU105Zj04iFLLEpqnFmF3tdlex_9hQWptFSI66zi6p3ySDZaWw0CDE_yhXqpRSoB5Q3KEu9ilF8mYVw8LGrUEwP9JMawZp5keagdIM0obO5X7eJmc7H-3ShfRb5HxwyoEP3M2Oo0HLZ6Bokgu0dNSESG5tmj788fIN1GZ_ng</recordid><startdate>20091210</startdate><enddate>20091210</enddate><creator>Gerolymos, G.A.</creator><creator>Sénéchal, D.</creator><creator>Vallet, I.</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20091210</creationdate><title>Very-high-order weno schemes</title><author>Gerolymos, G.A. ; Sénéchal, D. ; Vallet, I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c393t-a06d16d49f42c83ba56842803e89459afe5fdfae7b59febbc6af1c4105471ddb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Adjustable</topic><topic>Algorithms</topic><topic>Computational techniques</topic><topic>Conservation laws</topic><topic>Euler equations</topic><topic>Exact sciences and technology</topic><topic>Exponents</topic><topic>High-order schemes</topic><topic>Hyperbolic conservation laws</topic><topic>Mathematical methods in physics</topic><topic>Nonlinearity</topic><topic>Optimization</topic><topic>Physics</topic><topic>Reconstruction</topic><topic>Scalars</topic><topic>Smoothness indicators</topic><topic>weno schemes</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gerolymos, G.A.</creatorcontrib><creatorcontrib>Sénéchal, D.</creatorcontrib><creatorcontrib>Vallet, I.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gerolymos, G.A.</au><au>Sénéchal, D.</au><au>Vallet, I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Very-high-order weno schemes</atitle><jtitle>Journal of computational physics</jtitle><date>2009-12-10</date><risdate>2009</risdate><volume>228</volume><issue>23</issue><spage>8481</spage><epage>8524</epage><pages>8481-8524</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><coden>JCTPAH</coden><abstract>We study
weno(2
r
−
1) reconstruction [D.S. Balsara, C.W. Shu, Monotonicity prserving
weno schemes with increasingly high-order of accuracy, J. Comput. Phys. 160 (2000) 405–452], with the mapping (
wenom) procedure of the nonlinear weights [A.K. Henrick, T.D. Aslam, J.M. Powers, Mapped weighted-essentially-non-oscillatory schemes: achieving optimal order near critical points, J. Comput. Phys. 207 (2005) 542–567], which we extend up to
weno17
(
r
=
9
)
. We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent
cfl limitation
(
cfl
∈
[
0.8
,
1
]
)
, for scalar hyperbolic problems (both linear and scalar conservation laws), provided that the exponent
p
β
in the definition of the Jiang–Shu [G.S. Jiang, C.W. Shu, Efficient implementation of weighted
eno schemes, J. Comput. Phys. 126 (1996) 202–228] nonlinear weights be taken as
p
β
=
r
, as originally proposed by Liu et al. [X.D. Liu, S. Osher, T. Chan, Weighted essentially nonoscillatory schemes, J. Comput. Phys. 115 (1994) 200–212], instead of
p
β
=
2
(this is valid both for
weno and
wenom reconstructions), although the optimal value of the exponent is probably
p
β
(
r
)
∈
[
2
,
r
]
. Then, we apply the family of very-high-order
wenom
p
β
=
r
reconstructions to the Euler equations of gasdynamics, by combining local characteristic decomposition [A. Harten, B. Engquist, S. Osher, S.R. Chakravarthy, Uniformly high-order accurate essentially nonoscillatory schemes
iii, J. Comput. Phys. 71 (1987) 231–303], with recursive-order-reduction (
ror) aiming at aleviating the problems induced by the nonlinear interactions of characteristic fields within the stencil. The proposed
ror algorithm, which generalizes the algorithm of Titarev and Toro [V.A. Titarev, E.F. Toro, Finite-volume
weno schemes for 3-D conservation laws, J. Comput. Phys. 201 (2004) 238–260], is free of adjustable parameters, and the corresponding
rorwenom
p
β
=
r
schemes are essentially nonoscillatory, as
Δ
x
→
0
, up to
r
=
9
, for all of the test-cases studied. Finally, the unsplit linewise 2-D extension of the schemes is evaluated for several test-cases.</abstract><cop>Kidlington</cop><pub>Elsevier Inc</pub><doi>10.1016/j.jcp.2009.07.039</doi><tpages>44</tpages></addata></record> |
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| source | Elsevier ScienceDirect Journals |
| subjects | Adjustable Algorithms Computational techniques Conservation laws Euler equations Exact sciences and technology Exponents High-order schemes Hyperbolic conservation laws Mathematical methods in physics Nonlinearity Optimization Physics Reconstruction Scalars Smoothness indicators weno schemes |
| title | Very-high-order weno schemes |
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