{"id":"https://openalex.org/W2033197745","doi":"https://doi.org/10.1017/s0962492914000099","title":"Numerical methods with controlled dissipation for small-scale dependent shocks","display_name":"Numerical methods with controlled dissipation for small-scale dependent shocks","publication_year":2014,"publication_date":"2014-05-01","ids":{"openalex":"https://openalex.org/W2033197745","doi":"https://doi.org/10.1017/s0962492914000099","mag":"2033197745"},"language":"en","primary_location":{"id":"doi:10.1017/s0962492914000099","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0962492914000099","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/69956E5DD54B36728E92D5E9522B6D70/S0962492914000099a.pdf/div-class-title-numerical-methods-with-controlled-dissipation-for-small-scale-dependent-shocks-a-href-fn01-ref-type-fn-span-class-sup-span-a-div.pdf","source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/69956E5DD54B36728E92D5E9522B6D70/S0962492914000099a.pdf/div-class-title-numerical-methods-with-controlled-dissipation-for-small-scale-dependent-shocks-a-href-fn01-ref-type-fn-span-class-sup-span-a-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035830456","display_name":"Philippe G. LeFloch","orcid":"https://orcid.org/0000-0002-9546-0784"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Philippe G. LeFloch","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions, Centre National de la Recherche Scientifique, Universit\u00e9 Pierre et Marie Curie, 4 Place Jussieu, 75258 Paris, France, E-mail:"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, Centre National de la Recherche Scientifique, Universit\u00e9 Pierre et Marie Curie, 4 Place Jussieu, 75258 Paris, France, E-mail:","institution_ids":["https://openalex.org/I4210158291","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082251879","display_name":"Siddhartha Kumar Mishra","orcid":"https://orcid.org/0000-0003-1627-1377"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siddhartha Mishra","raw_affiliation_strings":["Seminar for Applied Mathematics, D-Math, Eidgen\u00f6ssische Technische Hochschule, HG Raemistrasse, Z\u00fcrich\u20138092, Switzerland, E-mail:"],"affiliations":[{"raw_affiliation_string":"Seminar for Applied Mathematics, D-Math, Eidgen\u00f6ssische Technische Hochschule, HG Raemistrasse, Z\u00fcrich\u20138092, Switzerland, E-mail:","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5035830456"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":4.1841,"has_fulltext":true,"cited_by_count":28,"citation_normalized_percentile":{"value":0.9362705,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":null,"first_page":"743","last_page":"816"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.49140000343322754,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.49140000343322754,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.3578000068664551,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.08229999989271164,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.7477074861526489},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5950729846954346},{"id":"https://openalex.org/keywords/shock-wave","display_name":"Shock wave","score":0.5434849262237549},{"id":"https://openalex.org/keywords/shock-front","display_name":"Shock front","score":0.5310174822807312},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5049265027046204},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4998912811279297},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.4784795641899109},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4598809480667114},{"id":"https://openalex.org/keywords/shock","display_name":"Shock (circulatory)","score":0.45551884174346924},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.41975340247154236},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.41113048791885376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3800601363182068},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36126551032066345},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3099898099899292},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29135286808013916},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.14770135283470154}],"concepts":[{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.7477074861526489},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5950729846954346},{"id":"https://openalex.org/C70477161","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock wave","level":2,"score":0.5434849262237549},{"id":"https://openalex.org/C2991680060","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock front","level":3,"score":0.5310174822807312},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5049265027046204},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4998912811279297},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.4784795641899109},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4598809480667114},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.45551884174346924},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41975340247154236},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.41113048791885376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3800601363182068},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36126551032066345},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3099898099899292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29135286808013916},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.14770135283470154},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0962492914000099","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0962492914000099","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/69956E5DD54B36728E92D5E9522B6D70/S0962492914000099a.pdf/div-class-title-numerical-methods-with-controlled-dissipation-for-small-scale-dependent-shocks-a-href-fn01-ref-type-fn-span-class-sup-span-a-div.pdf","source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1312.1280","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1312.1280","pdf_url":"https://arxiv.org/pdf/1312.1280","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":"","raw_type":"text"},{"id":"pmh:doi:10.3929/ethz-b-000413365","is_oa":false,"landing_page_url":"http://hdl.handle.net/20.500.11850/164239","pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1017/s0962492914000099","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0962492914000099","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/69956E5DD54B36728E92D5E9522B6D70/S0962492914000099a.pdf/div-class-title-numerical-methods-with-controlled-dissipation-for-small-scale-dependent-shocks-a-href-fn01-ref-type-fn-span-class-sup-span-a-div.pdf","source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5299999713897705,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G7758152977","display_name":null,"funder_award_id":"support","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2033197745.pdf","grobid_xml":"https://content.openalex.org/works/W2033197745.grobid-xml"},"referenced_works_count":199,"referenced_works":["https://openalex.org/W40395561","https://openalex.org/W115528814","https://openalex.org/W139467979","https://openalex.org/W285505819","https://openalex.org/W978740096","https://openalex.org/W1488954673","https://openalex.org/W1508067158","https://openalex.org/W1533568430","https://openalex.org/W1567809041","https://openalex.org/W1570562155","https://openalex.org/W1596823068","https://openalex.org/W1601100443","https://openalex.org/W1611885289","https://openalex.org/W1640432653","https://openalex.org/W1647090223","https://openalex.org/W1650943937","https://openalex.org/W1963544899","https://openalex.org/W1963871232","https://openalex.org/W1965653881","https://openalex.org/W1967085850","https://openalex.org/W1967749918","https://openalex.org/W1969402902","https://openalex.org/W1971166309","https://openalex.org/W1971770117","https://openalex.org/W1972407423","https://openalex.org/W1972924431","https://openalex.org/W1974284693","https://openalex.org/W1974523068","https://openalex.org/W1975772261","https://openalex.org/W1976197236","https://openalex.org/W1977119274","https://openalex.org/W1979571344","https://openalex.org/W1979936814","https://openalex.org/W1980014272","https://openalex.org/W1980443091","https://openalex.org/W1982227924","https://openalex.org/W1982535370","https://openalex.org/W1984429549","https://openalex.org/W1985570727","https://openalex.org/W1985631557","https://openalex.org/W1985715533","https://openalex.org/W1986675731","https://openalex.org/W1988206114","https://openalex.org/W1989037733","https://openalex.org/W1989065835","https://openalex.org/W1990596161","https://openalex.org/W1992470350","https://openalex.org/W1994958147","https://openalex.org/W1996290095","https://openalex.org/W1996336488","https://openalex.org/W1996584940","https://openalex.org/W1997688945","https://openalex.org/W1998887941","https://openalex.org/W2000012390","https://openalex.org/W2001884093","https://openalex.org/W2002544802","https://openalex.org/W2003885580","https://openalex.org/W2005619236","https://openalex.org/W2006842987","https://openalex.org/W2007031446","https://openalex.org/W2008685881","https://openalex.org/W2008855265","https://openalex.org/W2011097024","https://openalex.org/W2011669849","https://openalex.org/W2012153215","https://openalex.org/W2012312399","https://openalex.org/W2014190507","https://openalex.org/W2015990534","https://openalex.org/W2016002683","https://openalex.org/W2016244524","https://openalex.org/W2017935165","https://openalex.org/W2018478522","https://openalex.org/W2020168202","https://openalex.org/W2021017610","https://openalex.org/W2025411653","https://openalex.org/W2028784283","https://openalex.org/W2028808993","https://openalex.org/W2029541243","https://openalex.org/W2029811565","https://openalex.org/W2030235174","https://openalex.org/W2035842003","https://openalex.org/W2036724266","https://openalex.org/W2038446814","https://openalex.org/W2039143230","https://openalex.org/W2039734675","https://openalex.org/W2041983391","https://openalex.org/W2045355674","https://openalex.org/W2046494788","https://openalex.org/W2048066720","https://openalex.org/W2048459778","https://openalex.org/W2049025708","https://openalex.org/W2049266244","https://openalex.org/W2051227185","https://openalex.org/W2051524346","https://openalex.org/W2053050217","https://openalex.org/W2053260985","https://openalex.org/W2053715298","https://openalex.org/W2054020215","https://openalex.org/W2054480293","https://openalex.org/W2054815866","https://openalex.org/W2056044633","https://openalex.org/W2056092599","https://openalex.org/W2056326859","https://openalex.org/W2057280774","https://openalex.org/W2059603117","https://openalex.org/W2060586876","https://openalex.org/W2061726168","https://openalex.org/W2062082273","https://openalex.org/W2062183655","https://openalex.org/W2062786708","https://openalex.org/W2062845250","https://openalex.org/W2064872109","https://openalex.org/W2066625432","https://openalex.org/W2066708285","https://openalex.org/W2067669167","https://openalex.org/W2069973298","https://openalex.org/W2070543376","https://openalex.org/W2072226973","https://openalex.org/W2072434763","https://openalex.org/W2073054365","https://openalex.org/W2075610411","https://openalex.org/W2077061939","https://openalex.org/W2078665336","https://openalex.org/W2079075889","https://openalex.org/W2079155211","https://openalex.org/W2079511661","https://openalex.org/W2081854106","https://openalex.org/W2083072109","https://openalex.org/W2085839771","https://openalex.org/W2088655341","https://openalex.org/W2089174520","https://openalex.org/W2090076044","https://openalex.org/W2091943789","https://openalex.org/W2092177491","https://openalex.org/W2092435235","https://openalex.org/W2092889806","https://openalex.org/W2094864716","https://openalex.org/W2100669199","https://openalex.org/W2101796778","https://openalex.org/W2105137108","https://openalex.org/W2105446689","https://openalex.org/W2106787187","https://openalex.org/W2107292223","https://openalex.org/W2108503507","https://openalex.org/W2111057149","https://openalex.org/W2111072571","https://openalex.org/W2112150873","https://openalex.org/W2122633166","https://openalex.org/W2131659230","https://openalex.org/W2136371269","https://openalex.org/W2136592480","https://openalex.org/W2137742686","https://openalex.org/W2138746820","https://openalex.org/W2140458275","https://openalex.org/W2141734987","https://openalex.org/W2142274843","https://openalex.org/W2142985546","https://openalex.org/W2143752850","https://openalex.org/W2149201500","https://openalex.org/W2151634058","https://openalex.org/W2154441987","https://openalex.org/W2155297095","https://openalex.org/W2163538104","https://openalex.org/W2165182409","https://openalex.org/W2166873416","https://openalex.org/W2166938161","https://openalex.org/W2167278920","https://openalex.org/W2171673861","https://openalex.org/W2334606364","https://openalex.org/W2402588148","https://openalex.org/W2490862251","https://openalex.org/W2525266113","https://openalex.org/W2566514124","https://openalex.org/W2566787454","https://openalex.org/W2963438484","https://openalex.org/W2963773710","https://openalex.org/W2963889733","https://openalex.org/W2963943378","https://openalex.org/W2963991582","https://openalex.org/W2964126157","https://openalex.org/W3100575910","https://openalex.org/W3101554515","https://openalex.org/W4231711300","https://openalex.org/W4236965075","https://openalex.org/W4242340130","https://openalex.org/W4242785922","https://openalex.org/W4250741917","https://openalex.org/W4255388216","https://openalex.org/W4298232918","https://openalex.org/W4298426431","https://openalex.org/W4388310150","https://openalex.org/W6648596503","https://openalex.org/W6653586565","https://openalex.org/W6660985705","https://openalex.org/W6669991307","https://openalex.org/W6674572245","https://openalex.org/W6758621779","https://openalex.org/W6776516040","https://openalex.org/W6804391582"],"related_works":["https://openalex.org/W2077594309","https://openalex.org/W2142615002","https://openalex.org/W2750586119","https://openalex.org/W2050933238","https://openalex.org/W2320760145","https://openalex.org/W3172357549","https://openalex.org/W1558992124","https://openalex.org/W2170911774","https://openalex.org/W1994050760","https://openalex.org/W2082030652"],"abstract_inverted_index":{"We":[0,31,51,100],"provide":[1,101],"a":[2,86,89,102],"\u2018user":[3],"guide\u2019":[4],"to":[5,21,69,150],"the":[6,9,14,53,62,117,121,124,132,140],"literature":[7],"of":[8,18,35,91,104,123,129],"past":[10],"twenty":[11],"years":[12],"concerning":[13],"modelling":[15],"and":[16,37,47,60],"approximation":[17],"discontinuous":[19],"solutions":[20,82,155],"nonlinear":[22],"hyperbolic":[23,42],"systems":[24,43],"that":[25,65],"admit":[26],"small-scale":[27,71,80],"dependent":[28,72,81],"shock":[29,157],"waves.":[30,158],"cover":[32],"several":[33],"classes":[34],"problems":[36],"solutions:":[38],"nonclassical":[39],"undercompressive":[40],"shocks,":[41],"in":[44,57,131],"nonconservative":[45],"form,":[46],"boundary":[48,97],"layer":[49],"problems.":[50],"review":[52,103],"relevant":[54,152],"models":[55],"arising":[56],"continuum":[58],"physics":[59],"describe":[61],"numerical":[63,105],"methods":[64,106],"have":[66],"been":[67],"proposed":[68],"capture":[70],"solutions.":[73],"In":[74],"agreement":[75],"with":[76,144],"general":[77],"well-posedness":[78],"theory,":[79],"are":[83],"characterized":[84],"by":[85,139],"kinetic":[87],"relation,":[88],"family":[90],"paths":[92],",":[93],"or":[94],"an":[95],"admissible":[96],"set":[98],".":[99],"(front-tracking":[107],"schemes,":[108,111,146],"finite":[109,112],"difference":[110],"volume":[113],"schemes),":[114],"which,":[115],"at":[116],"discrete":[118,145],"level,":[119],"reproduce":[120],"effect":[122],"physically":[125],"meaningful":[126],"dissipation":[127],"mechanisms":[128],"interest":[130],"applications.":[133],"An":[134],"essential":[135],"role":[136],"is":[137,148],"played":[138],"equivalent":[141],"equation":[142],"associated":[143],"which":[147],"found":[149],"be":[151],"even":[153],"for":[154],"containing":[156]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-12T07:58:50.170612","created_date":"2025-10-10T00:00:00"}