{"id":"https://openalex.org/W3158537637","doi":"https://doi.org/10.1016/j.jcp.2021.110868","title":"A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains","display_name":"A mass-, kinetic energy- and helicity-conserving mimetic dual-field discretization for three-dimensional incompressible Navier-Stokes equations, part I: Periodic domains","publication_year":2021,"publication_date":"2021-11-26","ids":{"openalex":"https://openalex.org/W3158537637","doi":"https://doi.org/10.1016/j.jcp.2021.110868","mag":"3158537637"},"language":"en","primary_location":{"id":"doi:10.1016/j.jcp.2021.110868","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jcp.2021.110868","pdf_url":"https://www.sciencedirect.com/science/article/am/pii/S0021999121007634?via%3Dihub","source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.sciencedirect.com/science/article/am/pii/S0021999121007634?via%3Dihub","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101926151","display_name":"Yi Zhang","orcid":"https://orcid.org/0009-0003-4394-3447"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Yi Zhang","raw_affiliation_strings":["Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, the Netherlands","Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, The Netherlands#TAB#"],"affiliations":[{"raw_affiliation_string":"Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, the Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, The Netherlands#TAB#","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066967170","display_name":"Artur Palha","orcid":"https://orcid.org/0000-0002-3217-0747"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Artur Palha","raw_affiliation_strings":["Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, the Netherlands","Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, The Netherlands#TAB#"],"affiliations":[{"raw_affiliation_string":"Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, the Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, The Netherlands#TAB#","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017322298","display_name":"Marc Gerritsma","orcid":"https://orcid.org/0000-0003-2539-642X"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Marc Gerritsma","raw_affiliation_strings":["Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, the Netherlands","Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, The Netherlands#TAB#"],"affiliations":[{"raw_affiliation_string":"Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, the Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Delft University of Technology, Faculty of Aerospace Engineering, Kluyverweg 1, 2629 HS Delft, The Netherlands#TAB#","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028355904","display_name":"Leo G. Rebholz","orcid":"https://orcid.org/0000-0002-5173-5731"},"institutions":[{"id":"https://openalex.org/I8078737","display_name":"Clemson University","ror":"https://ror.org/037s24f05","country_code":"US","type":"education","lineage":["https://openalex.org/I8078737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leo G. Rebholz","raw_affiliation_strings":["Clemson University, 105 Sikes Hall, Clemson, SC 29634, United States"],"affiliations":[{"raw_affiliation_string":"Clemson University, 105 Sikes Hall, Clemson, SC 29634, United States","institution_ids":["https://openalex.org/I8078737"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101926151"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":{"value":3750,"currency":"USD","value_usd":3750},"apc_paid":{"value":3750,"currency":"USD","value_usd":3750},"fwci":0.3103,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50989654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"451","issue":null,"first_page":"110868","last_page":"110868"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8932042121887207},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.6897836923599243},{"id":"https://openalex.org/keywords/helicity","display_name":"Helicity","score":0.6069936156272888},{"id":"https://openalex.org/keywords/kinetic-energy","display_name":"Kinetic energy","score":0.5755681991577148},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5338553190231323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4980294704437256},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.4921204447746277},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4916096329689026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4587675631046295},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4542666971683502},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.440904825925827},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.41899916529655457},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36931800842285156},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2260608673095703},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0754876434803009}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8932042121887207},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.6897836923599243},{"id":"https://openalex.org/C2775859700","wikidata":"https://www.wikidata.org/wiki/Q568855","display_name":"Helicity","level":2,"score":0.6069936156272888},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.5755681991577148},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5338553190231323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4980294704437256},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4921204447746277},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4916096329689026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4587675631046295},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4542666971683502},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.440904825925827},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.41899916529655457},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36931800842285156},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2260608673095703},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0754876434803009}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/j.jcp.2021.110868","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jcp.2021.110868","pdf_url":"https://www.sciencedirect.com/science/article/am/pii/S0021999121007634?via%3Dihub","source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},{"id":"mag:3158537637","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2104.13023.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:tudelft.nl:uuid:365b262d-347d-4e0f-b786-0358f5f09763","is_oa":false,"landing_page_url":"http://resolver.tudelft.nl/uuid:365b262d-347d-4e0f-b786-0358f5f09763","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"},{"id":"doi:10.48550/arxiv.2104.13023","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2104.13023","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1016/j.jcp.2021.110868","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.jcp.2021.110868","pdf_url":"https://www.sciencedirect.com/science/article/am/pii/S0021999121007634?via%3Dihub","source":{"id":"https://openalex.org/S148709879","display_name":"Journal of Computational Physics","issn_l":"0021-9991","issn":["0021-9991","1090-2716"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1426318481","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G2228512978","display_name":null,"funder_award_id":"2011490","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3977936395","display_name":null,"funder_award_id":"201607720010","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G5921281487","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7633583304","display_name":null,"funder_award_id":"DMS2011490","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8589651859","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3158537637.pdf","grobid_xml":"https://content.openalex.org/works/W3158537637.grobid-xml"},"referenced_works_count":114,"referenced_works":["https://openalex.org/W52307013","https://openalex.org/W75121779","https://openalex.org/W111618586","https://openalex.org/W136185420","https://openalex.org/W221613585","https://openalex.org/W603762250","https://openalex.org/W850234113","https://openalex.org/W1491317504","https://openalex.org/W1529056661","https://openalex.org/W1544770838","https://openalex.org/W1570976541","https://openalex.org/W1572413092","https://openalex.org/W1591380302","https://openalex.org/W1716828076","https://openalex.org/W1966158133","https://openalex.org/W1966250575","https://openalex.org/W1991111638","https://openalex.org/W1992935563","https://openalex.org/W1997633759","https://openalex.org/W1999038482","https://openalex.org/W2011356442","https://openalex.org/W2012393256","https://openalex.org/W2018042073","https://openalex.org/W2026825964","https://openalex.org/W2028246274","https://openalex.org/W2028811441","https://openalex.org/W2028916079","https://openalex.org/W2029687326","https://openalex.org/W2031013279","https://openalex.org/W2034039186","https://openalex.org/W2035025901","https://openalex.org/W2036895361","https://openalex.org/W2059413295","https://openalex.org/W2060136573","https://openalex.org/W2060890023","https://openalex.org/W2062618977","https://openalex.org/W2064857459","https://openalex.org/W2073685945","https://openalex.org/W2077674352","https://openalex.org/W2078133941","https://openalex.org/W2083796813","https://openalex.org/W2088305381","https://openalex.org/W2099803355","https://openalex.org/W2100520873","https://openalex.org/W2100972184","https://openalex.org/W2105146991","https://openalex.org/W2114649799","https://openalex.org/W2119306252","https://openalex.org/W2120103450","https://openalex.org/W2128884148","https://openalex.org/W2130686389","https://openalex.org/W2131341034","https://openalex.org/W2137075874","https://openalex.org/W2137497682","https://openalex.org/W2138486270","https://openalex.org/W2141094169","https://openalex.org/W2150991141","https://openalex.org/W2155718237","https://openalex.org/W2157822890","https://openalex.org/W2158749668","https://openalex.org/W2160852351","https://openalex.org/W2170039048","https://openalex.org/W2171638448","https://openalex.org/W2181277443","https://openalex.org/W2226760786","https://openalex.org/W2297792911","https://openalex.org/W2298872691","https://openalex.org/W2320717124","https://openalex.org/W2407958413","https://openalex.org/W2410416051","https://openalex.org/W2734964235","https://openalex.org/W2766780695","https://openalex.org/W2788566950","https://openalex.org/W2885312701","https://openalex.org/W2889174971","https://openalex.org/W2901886765","https://openalex.org/W2906022956","https://openalex.org/W2912271984","https://openalex.org/W2947056241","https://openalex.org/W2954244018","https://openalex.org/W2963462928","https://openalex.org/W2969109886","https://openalex.org/W2972465740","https://openalex.org/W2978600120","https://openalex.org/W3007837603","https://openalex.org/W3024662081","https://openalex.org/W3038698521","https://openalex.org/W3096136884","https://openalex.org/W3096278902","https://openalex.org/W3099687355","https://openalex.org/W3102475271","https://openalex.org/W3102477591","https://openalex.org/W3103476862","https://openalex.org/W3104861780","https://openalex.org/W3118603651","https://openalex.org/W3135807520","https://openalex.org/W3141401227","https://openalex.org/W4251865999","https://openalex.org/W6602146151","https://openalex.org/W6603079820","https://openalex.org/W6604536441","https://openalex.org/W6605476129","https://openalex.org/W6608822307","https://openalex.org/W6634127885","https://openalex.org/W6634215410","https://openalex.org/W6650107179","https://openalex.org/W6655157322","https://openalex.org/W6657474332","https://openalex.org/W6684895831","https://openalex.org/W6702358223","https://openalex.org/W6720526450","https://openalex.org/W6758478150","https://openalex.org/W6766832440","https://openalex.org/W6767323795"],"related_works":["https://openalex.org/W2320717124","https://openalex.org/W2148961665","https://openalex.org/W3013932105","https://openalex.org/W2791871591","https://openalex.org/W2127439711","https://openalex.org/W2187142289","https://openalex.org/W3087068748","https://openalex.org/W2033380043","https://openalex.org/W3043321978","https://openalex.org/W2050437114","https://openalex.org/W2963099921","https://openalex.org/W3103237299","https://openalex.org/W3042395950","https://openalex.org/W2060285201","https://openalex.org/W3105140558","https://openalex.org/W2139132325","https://openalex.org/W2278821917","https://openalex.org/W2905005304","https://openalex.org/W2711188637","https://openalex.org/W1521454588"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,23,88],"mimetic":[3,77],"dual-field":[4,25],"discretization":[5,19,75],"which":[6,51],"conserves":[7],"mass,":[8,95],"kinetic":[9,96,116],"energy":[10,97,117],"and":[11,37,56,69,98,118],"helicity":[12,99,119],"for":[13,45],"three-dimensional":[14],"incompressible":[15],"Navier-Stokes":[16],"equations.":[17],"The":[18,73],"makes":[20],"use":[21],"of":[22,33,40,94,103,115],"conservative":[24],"mixed":[26],"weak":[27],"formulation":[28],"where":[29],"two":[30],"evolution":[31,54],"equations":[32,55],"velocity":[34],"are":[35,43,67,124,132],"employed":[36],"dual":[38],"representations":[39],"the":[41,53,58,62,79,82,101,109,121,130],"solution":[42],"sought":[44],"each":[46],"variable.":[47],"A":[48],"temporal":[49],"discretization,":[50],"staggers":[52],"handles":[57],"nonlinearity":[59],"such":[60],"that":[61,81],"resulting":[63],"discrete":[64,89,110],"algebraic":[65],"systems":[66],"linear":[68],"decoupled,":[70],"is":[71,76,106],"constructed.":[72],"spatial":[74],"in":[78,100,120],"sense":[80],"finite":[83],"dimensional":[84],"function":[85],"spaces":[86],"form":[87],"de":[90],"Rham":[91],"complex.":[92],"Conservation":[93],"absence":[102],"dissipative":[104],"terms":[105],"proven":[107],"at":[108],"level.":[111],"Proper":[112],"dissipation":[113],"rates":[114],"viscous":[122],"case":[123],"also":[125],"proven.":[126],"Numerical":[127],"tests":[128],"supporting":[129],"method":[131],"provided.":[133]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}