Comparison of very high order (O3–18) flux and Crowley flux, and (O3–17) WENO flux schemes with a 2D nonlinear test problem
Two‐dimensional, nonlinear diffusion‐limited colliding plumes simulations were used to demonstrate the improved solution accuracy with very high order O9–18 flux schemes, including upwind‐biased and even‐centred constant grid flux and Crowley constant grid flux schemes, and odd order weighted essent...
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| creator | Straka, Jerry M. Kanak, Katharine M. Williams, Paul D. |
| description | Two‐dimensional, nonlinear diffusion‐limited colliding plumes simulations were used to demonstrate the improved solution accuracy with very high order O9–18 flux schemes, including upwind‐biased and even‐centred constant grid flux and Crowley constant grid flux schemes, and odd order weighted essentially non‐oscillatory (WENO) flux schemes, along with variations and hybrids of these. All schemes were coupled with comparably high order even‐centred Lagrangian interpolations and pressure gradient/divergence approximations, and O18 spatial filtering. Subgrid‐scale (SGS) turbulent flux calculations, with a constant eddy‐mixing coefficient, were made with O2 spatial approximations (O4–20 accurate SGS turbulent fluxes had little impact). Using a range of resolutions from Δx = Δz = 25–166.66… m for all schemes comparisons against an O17 flux, 25 m resolution reference solution showed solutions made with ≥O9 fluxes produced (often substantially) improved solutions, both visually and usually objectively, compared to solutions produced with lower order ( |
| doi_str_mv | 10.1002/qj.4579 |
| format | Article |
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Summary of key findings: Very high order odd and even order flux and Crowley flux, and odd order WENO flux schemes were evaluated for orders of accuracy that ranged from order 3 to 20 and resolutions that varied by a factor of six, using simulations of nonlinear 2D colliding plumes. At intermediate resolutions, which only marginally resolved important flow structures, the best solutions were obtained with ≥O13/14 flux, Crowley flux, and O13–17 WENO flux. For a given resolution, the Crowley solutions were least computationally intensive. Parts of the nonlinear 2D colliding plumes solutions, especially near the stronger rotors were best simulated, using odd order 5 and 17 Crowley, odd/even order 5/6 and 17/18 order Flux, and odd order 5 and 17 WENO flux.</description><identifier>ISSN: 0035-9009</identifier><identifier>EISSN: 1477-870X</identifier><identifier>DOI: 10.1002/qj.4579</identifier><language>eng</language><publisher>Chichester, UK: John Wiley & Sons, Ltd</publisher><subject>Accuracy ; Approximation ; colliding plumes ; Crowley ; Fluctuations ; high order numerical approximations ; high order upwind and centred fluxes ; Hybrids ; Plumes ; Prediction models ; Pressure gradients ; Turbulent fluxes ; Weather forecasting ; WENO</subject><ispartof>Quarterly journal of the Royal Meteorological Society, 2023-10, Vol.149 (757), p.3669-3710</ispartof><rights>2023 Royal Meteorological Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2849-a44f9f293b58c0f5edc9fbf3c32931ca8dd57493449967aaa2510cbe48a5d25f3</cites><orcidid>0000-0003-3672-5858 ; 0000-0002-9713-9820 ; 0000-0003-3479-9669</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fqj.4579$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fqj.4579$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Straka, Jerry M.</creatorcontrib><creatorcontrib>Kanak, Katharine M.</creatorcontrib><creatorcontrib>Williams, Paul D.</creatorcontrib><title>Comparison of very high order (O3–18) flux and Crowley flux, and (O3–17) WENO flux schemes with a 2D nonlinear test problem</title><title>Quarterly journal of the Royal Meteorological Society</title><description>Two‐dimensional, nonlinear diffusion‐limited colliding plumes simulations were used to demonstrate the improved solution accuracy with very high order O9–18 flux schemes, including upwind‐biased and even‐centred constant grid flux and Crowley constant grid flux schemes, and odd order weighted essentially non‐oscillatory (WENO) flux schemes, along with variations and hybrids of these. All schemes were coupled with comparably high order even‐centred Lagrangian interpolations and pressure gradient/divergence approximations, and O18 spatial filtering. Subgrid‐scale (SGS) turbulent flux calculations, with a constant eddy‐mixing coefficient, were made with O2 spatial approximations (O4–20 accurate SGS turbulent fluxes had little impact). Using a range of resolutions from Δx = Δz = 25–166.66… m for all schemes comparisons against an O17 flux, 25 m resolution reference solution showed solutions made with ≥O9 fluxes produced (often substantially) improved solutions, both visually and usually objectively, compared to solutions produced with lower order (<O9/10) fluxes, especially at intermediate resolutions (33.33–100 m). Expectedly, odd order solutions were increasingly damped as accuracy was decreased, especially from O9 to O3, especially for WENO solutions, while even order solutions were increasingly contaminated with dispersion and aliasing errors as accuracy was decreased, especially from O10 to O4. Odd order schemes also produced better solutions than even order schemes for <O9/10 fluxes, while the highest order (≥O13/14) schemes produced the best solutions, for any given resolution. Even order flux and Crowley flux (WENO) solutions were the least (most) computationally expensive, based on either floating‐point operations (FPO) or CPU times. Efficient WENO‐Sine and proposed hybrid Crowley‐WENO(‐Sine) schemes required fewer FPOs to produce more accurate solutions than traditional WENO schemes. We are encouraged by the often much improved visual and objective accuracy of very high order (≥O9) fluxes in simulations of a complex problem, and encourage further testing in numerical weather prediction models.
Summary of key findings: Very high order odd and even order flux and Crowley flux, and odd order WENO flux schemes were evaluated for orders of accuracy that ranged from order 3 to 20 and resolutions that varied by a factor of six, using simulations of nonlinear 2D colliding plumes. At intermediate resolutions, which only marginally resolved important flow structures, the best solutions were obtained with ≥O13/14 flux, Crowley flux, and O13–17 WENO flux. For a given resolution, the Crowley solutions were least computationally intensive. Parts of the nonlinear 2D colliding plumes solutions, especially near the stronger rotors were best simulated, using odd order 5 and 17 Crowley, odd/even order 5/6 and 17/18 order Flux, and odd order 5 and 17 WENO flux.</description><subject>Accuracy</subject><subject>Approximation</subject><subject>colliding plumes</subject><subject>Crowley</subject><subject>Fluctuations</subject><subject>high order numerical approximations</subject><subject>high order upwind and centred fluxes</subject><subject>Hybrids</subject><subject>Plumes</subject><subject>Prediction models</subject><subject>Pressure gradients</subject><subject>Turbulent fluxes</subject><subject>Weather forecasting</subject><subject>WENO</subject><issn>0035-9009</issn><issn>1477-870X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp10N9KwzAUBvAgCs4pvkLACx3amaSJaS6lzn8Mh6DoXUnTxLa0zZZszl3pO_iGPond6q1XBz5-nHP4ADjEaIgRIuezckgZF1ughynnQcTR6zboIRSyQCAkdsGe9yVCiHHCe-AztvVUusLbBloD37Vbwbx4y6F1mXbwZBL-fH3jaABNtfiAsslg7Oyy0qtNcLZJ_hAfwJfRw6STXuW61h4ui3kOJSRXsLFNVTRaOjjXfg6nzqaVrvfBjpGV1wd_sw-er0dP8W0wntzcxZfjQJGIikBSaoQhIkxZpJBhOlPCpCZUYZthJaMsY5yKkFIhLriUkjCMVKppJFlGmAn74Kjb296dLdoHktIuXNOeTEhbC8YR4VGrjjulnPXeaZNMXVFLt0owStbtJrMyWbfbytNOLou2jP9Y8ni_0b_a8noq</recordid><startdate>202310</startdate><enddate>202310</enddate><creator>Straka, Jerry M.</creator><creator>Kanak, Katharine M.</creator><creator>Williams, Paul D.</creator><general>John Wiley & Sons, Ltd</general><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TG</scope><scope>7TN</scope><scope>F1W</scope><scope>H96</scope><scope>KL.</scope><scope>L.G</scope><orcidid>https://orcid.org/0000-0003-3672-5858</orcidid><orcidid>https://orcid.org/0000-0002-9713-9820</orcidid><orcidid>https://orcid.org/0000-0003-3479-9669</orcidid></search><sort><creationdate>202310</creationdate><title>Comparison of very high order (O3–18) flux and Crowley flux, and (O3–17) WENO flux schemes with a 2D nonlinear test problem</title><author>Straka, Jerry M. ; Kanak, Katharine M. ; Williams, Paul D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2849-a44f9f293b58c0f5edc9fbf3c32931ca8dd57493449967aaa2510cbe48a5d25f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Accuracy</topic><topic>Approximation</topic><topic>colliding plumes</topic><topic>Crowley</topic><topic>Fluctuations</topic><topic>high order numerical approximations</topic><topic>high order upwind and centred fluxes</topic><topic>Hybrids</topic><topic>Plumes</topic><topic>Prediction models</topic><topic>Pressure gradients</topic><topic>Turbulent fluxes</topic><topic>Weather forecasting</topic><topic>WENO</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Straka, Jerry M.</creatorcontrib><creatorcontrib>Kanak, Katharine M.</creatorcontrib><creatorcontrib>Williams, Paul D.</creatorcontrib><collection>CrossRef</collection><collection>Meteorological & Geoastrophysical Abstracts</collection><collection>Oceanic Abstracts</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>Meteorological & Geoastrophysical Abstracts - Academic</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><jtitle>Quarterly journal of the Royal Meteorological Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Straka, Jerry M.</au><au>Kanak, Katharine M.</au><au>Williams, Paul D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Comparison of very high order (O3–18) flux and Crowley flux, and (O3–17) WENO flux schemes with a 2D nonlinear test problem</atitle><jtitle>Quarterly journal of the Royal Meteorological Society</jtitle><date>2023-10</date><risdate>2023</risdate><volume>149</volume><issue>757</issue><spage>3669</spage><epage>3710</epage><pages>3669-3710</pages><issn>0035-9009</issn><eissn>1477-870X</eissn><abstract>Two‐dimensional, nonlinear diffusion‐limited colliding plumes simulations were used to demonstrate the improved solution accuracy with very high order O9–18 flux schemes, including upwind‐biased and even‐centred constant grid flux and Crowley constant grid flux schemes, and odd order weighted essentially non‐oscillatory (WENO) flux schemes, along with variations and hybrids of these. All schemes were coupled with comparably high order even‐centred Lagrangian interpolations and pressure gradient/divergence approximations, and O18 spatial filtering. Subgrid‐scale (SGS) turbulent flux calculations, with a constant eddy‐mixing coefficient, were made with O2 spatial approximations (O4–20 accurate SGS turbulent fluxes had little impact). Using a range of resolutions from Δx = Δz = 25–166.66… m for all schemes comparisons against an O17 flux, 25 m resolution reference solution showed solutions made with ≥O9 fluxes produced (often substantially) improved solutions, both visually and usually objectively, compared to solutions produced with lower order (<O9/10) fluxes, especially at intermediate resolutions (33.33–100 m). Expectedly, odd order solutions were increasingly damped as accuracy was decreased, especially from O9 to O3, especially for WENO solutions, while even order solutions were increasingly contaminated with dispersion and aliasing errors as accuracy was decreased, especially from O10 to O4. Odd order schemes also produced better solutions than even order schemes for <O9/10 fluxes, while the highest order (≥O13/14) schemes produced the best solutions, for any given resolution. Even order flux and Crowley flux (WENO) solutions were the least (most) computationally expensive, based on either floating‐point operations (FPO) or CPU times. Efficient WENO‐Sine and proposed hybrid Crowley‐WENO(‐Sine) schemes required fewer FPOs to produce more accurate solutions than traditional WENO schemes. We are encouraged by the often much improved visual and objective accuracy of very high order (≥O9) fluxes in simulations of a complex problem, and encourage further testing in numerical weather prediction models.
Summary of key findings: Very high order odd and even order flux and Crowley flux, and odd order WENO flux schemes were evaluated for orders of accuracy that ranged from order 3 to 20 and resolutions that varied by a factor of six, using simulations of nonlinear 2D colliding plumes. At intermediate resolutions, which only marginally resolved important flow structures, the best solutions were obtained with ≥O13/14 flux, Crowley flux, and O13–17 WENO flux. For a given resolution, the Crowley solutions were least computationally intensive. Parts of the nonlinear 2D colliding plumes solutions, especially near the stronger rotors were best simulated, using odd order 5 and 17 Crowley, odd/even order 5/6 and 17/18 order Flux, and odd order 5 and 17 WENO flux.</abstract><cop>Chichester, UK</cop><pub>John Wiley & Sons, Ltd</pub><doi>10.1002/qj.4579</doi><tpages>42</tpages><orcidid>https://orcid.org/0000-0003-3672-5858</orcidid><orcidid>https://orcid.org/0000-0002-9713-9820</orcidid><orcidid>https://orcid.org/0000-0003-3479-9669</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Accuracy Approximation colliding plumes Crowley Fluctuations high order numerical approximations high order upwind and centred fluxes Hybrids Plumes Prediction models Pressure gradients Turbulent fluxes Weather forecasting WENO |
| title | Comparison of very high order (O3–18) flux and Crowley flux, and (O3–17) WENO flux schemes with a 2D nonlinear test problem |
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