{"id":"https://openalex.org/W1977297792","doi":"https://doi.org/10.1137/070692182","title":"Symmetric Positive Definite Flux-Continuous Full-Tensor Finite-Volume Schemes on Unstructured Cell-Centered Triangular Grids","display_name":"Symmetric Positive Definite Flux-Continuous Full-Tensor Finite-Volume Schemes on Unstructured Cell-Centered Triangular Grids","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1977297792","doi":"https://doi.org/10.1137/070692182","mag":"1977297792"},"language":"en","primary_location":{"id":"doi:10.1137/070692182","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070692182","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007586511","display_name":"Helmer Andr\u00e9 Friis","orcid":"https://orcid.org/0000-0003-2462-1381"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Helmer Andr\u00e9 Friis","raw_affiliation_strings":["HelmerAndre.Friis@iris.no#TAB#"],"affiliations":[{"raw_affiliation_string":"HelmerAndre.Friis@iris.no#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039120348","display_name":"Michael G. Edwards","orcid":"https://orcid.org/0000-0003-2948-4101"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael G. Edwards","raw_affiliation_strings":["m.g.edwards@swansea.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"m.g.edwards@swansea.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058498863","display_name":"Johannes Mykkeltveit","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Johannes Mykkeltveit","raw_affiliation_strings":["Johannes.Mykkeltveit@iris.no#TAB#"],"affiliations":[{"raw_affiliation_string":"Johannes.Mykkeltveit@iris.no#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5007586511"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.0273,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.96767671,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"31","issue":"2","first_page":"1192","last_page":"1220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9987999796867371,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9950000047683716,"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/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.8465094566345215},{"id":"https://openalex.org/keywords/positive-definiteness","display_name":"Positive definiteness","score":0.8453236818313599},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7846737504005432},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7582456469535828},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.636134147644043},{"id":"https://openalex.org/keywords/unstructured-grid","display_name":"Unstructured grid","score":0.5807721614837646},{"id":"https://openalex.org/keywords/regular-grid","display_name":"Regular grid","score":0.547041118144989},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5466880202293396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5403016805648804},{"id":"https://openalex.org/keywords/symmetric-tensor","display_name":"Symmetric tensor","score":0.5330321788787842},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.49416783452033997},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4825522303581238},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4746732711791992},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38730373978614807},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.28846848011016846},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13281631469726562},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.11855319142341614},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09307628870010376},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08456209301948547},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.07640400528907776}],"concepts":[{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.8465094566345215},{"id":"https://openalex.org/C2778265155","wikidata":"https://www.wikidata.org/wiki/Q7233276","display_name":"Positive definiteness","level":4,"score":0.8453236818313599},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7846737504005432},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7582456469535828},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.636134147644043},{"id":"https://openalex.org/C134620963","wikidata":"https://www.wikidata.org/wiki/Q17078677","display_name":"Unstructured grid","level":3,"score":0.5807721614837646},{"id":"https://openalex.org/C43173174","wikidata":"https://www.wikidata.org/wiki/Q2646942","display_name":"Regular grid","level":3,"score":0.547041118144989},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5466880202293396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5403016805648804},{"id":"https://openalex.org/C20178491","wikidata":"https://www.wikidata.org/wiki/Q2204117","display_name":"Symmetric tensor","level":3,"score":0.5330321788787842},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.49416783452033997},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4825522303581238},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4746732711791992},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38730373978614807},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28846848011016846},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13281631469726562},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.11855319142341614},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09307628870010376},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08456209301948547},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.07640400528907776},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070692182","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070692182","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4300000071525574,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W5373060","https://openalex.org/W79611936","https://openalex.org/W1528192786","https://openalex.org/W1530030810","https://openalex.org/W1545095299","https://openalex.org/W1964392553","https://openalex.org/W1976718653","https://openalex.org/W1979821272","https://openalex.org/W1982908458","https://openalex.org/W1983124639","https://openalex.org/W1995682074","https://openalex.org/W1995848272","https://openalex.org/W2014952856","https://openalex.org/W2020862018","https://openalex.org/W2034170310","https://openalex.org/W2035728289","https://openalex.org/W2036846784","https://openalex.org/W2038777987","https://openalex.org/W2067510987","https://openalex.org/W2068915986","https://openalex.org/W2071582219","https://openalex.org/W2074387770","https://openalex.org/W2076014276","https://openalex.org/W2078538975","https://openalex.org/W2080272847","https://openalex.org/W2080624765","https://openalex.org/W2083087132","https://openalex.org/W2100520873","https://openalex.org/W2118131776","https://openalex.org/W2145062249","https://openalex.org/W2153407748","https://openalex.org/W2160373090"],"related_works":["https://openalex.org/W2369793817","https://openalex.org/W2364489971","https://openalex.org/W2361979571","https://openalex.org/W4205226845","https://openalex.org/W3208377712","https://openalex.org/W2043819621","https://openalex.org/W2373372131","https://openalex.org/W2147922812","https://openalex.org/W2063005030","https://openalex.org/W1977297792"],"abstract_inverted_index":{"Novel":[0],"cell-centered":[1],"full-tensor":[2],"finite-volume":[3],"methods":[4,68,138],"are":[5,18,37,69,78,93,107],"presented":[6,94],"for":[7,53,80,95],"general":[8],"unstructured":[9,96],"grids":[10,98],"in":[11,26,148],"two":[12],"spatial":[13],"dimensions.":[14],"The":[15,105],"numerical":[16],"schemes":[17,106],"flux-continuous":[19],"and":[20,65,87,123],"based":[21],"on":[22],"computing":[23],"the":[24,42,66,84,103,110,137,142],"transmissibilities":[25],"a":[27,40],"local":[28,34],"subcell":[29,88],"transform":[30],"space,":[31],"ensuring":[32],"that":[33],"flux":[35,113],"matrices":[36],"symmetric.":[38],"As":[39],"result":[41],"global":[43],"discretization":[44],"matrix":[45],"is":[46,62,139],"shown":[47,70],"to":[48,71],"be":[49,72],"symmetric":[50,58,67],"positive":[51,81],"definite":[52],"any":[54],"grid":[55],"type.":[56],"A":[57],"physical":[59,85],"space":[60,86,89],"method":[61],"also":[63],"introduced,":[64],"closely":[73],"related.":[74],"Discrete":[75],"ellipticity":[76],"conditions":[77],"derived":[79],"definiteness":[82],"of":[83,102],"schemes.":[90],"Computational":[91],"examples":[92],"triangular":[97],"demonstrating":[99],"good":[100],"performance":[101],"scheme.":[104],"compared":[108],"with":[109],"so-called":[111],"multipoint":[112],"approximation":[114],"(MPFA)":[115],"O-method":[116],"[I.":[117],"Aavatsmark,":[118],"T.":[119,124],"Barkve,":[120],"\u00d8.":[121],"B\u00f8e,":[122],"Mannseth,":[125],"SIAM":[126],"J.":[127],"Sci.":[128],"Comput.,":[129],"19":[130],"(1998),":[131],"pp.":[132],"1700\u20131716].":[133],"Good":[134],"agreement":[135],"between":[136],"obtained,":[140],"but":[141],"new":[143],"scheme":[144],"shows":[145],"improved":[146],"behavior":[147],"challenging":[149],"cases.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}