[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118386-en":3,"doc-seo-118386-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118386,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Code integration and validation of a machine learning based RANS model - Thesis","Turbulence modeling in fluid dynamics is addressed by integrating machine learning into Reynolds-averaged Navier–Stokes (RANS) closure frameworks. The thesis proposes and validates both high- and low-Reynolds neuronal models on canonical turbulent channel-flow conditions, comparing neural predictions against standard k–ε closures. Preliminary experiments injecting explicit Reynolds stresses from DNS into the RANS equations highlight ill-conditioning issues. High-Re neuronal k–ε performance matches the standard model but with more than twice the computational cost, while low-Re neuronal models better predict Reynolds stress anisotropy than analytical closures, clarifying prior ambiguities. Code integration in the TRUST/TrioCFD solver supports practical academic and industrial use, advancing RANS reliability.","Code integration and validation of a machine learning based RANS model  \nTesi di Laurea Magistrale in  \nMathematical Engineering-Ingegneria Matematica  \nAuthor: Davide Repetto  \nStudent ID: 990543  \nPolitecnico di Milano Advisor: Prof. Marco Verani  \nSorbonne Université Advisor: Prof. Corrado Maurini  \nCEA/CNRS Advisors: Pierre-Emmanuel Angeli, Didier Lucor Academic Year: 2022-23  \ni  \nAbstract  \nTurbulence presents a complex modeling challenge in fluid dynamics simulations. Traditional approaches rely on Reynolds-averaged Navier-Stokes (RANS) equations paired with closure models, but often lack accuracy and universality. This thesis investigates integrating machine learning into RANS frameworks to enhance turbulence modeling.  \nBoth high-Reynolds and low-Reynolds neuronal models are proposed and validated on the canonical turbulent channel flow configuration. Preliminary tests injecting explicit Reynolds stresses from direct numerical simulations (DNS) into RANS equations reveal ill-conditioning concerns. The high-Reynolds neuronal k − ε model demonstrates comparable performance to the standard k − ε model, while requiring over twice the computational expense. However, the low-Reynolds neuronal models exhibit promising capabilities, with neural network outputs significantly outperforming analytical closures in predicting Reynolds stress anisotropy.  \nThis research clarifies ambiguities in prior approaches and validates a generalized tensor formulation to address limitations. Code integration in the TRUST/TrioCFD solver enables practical usage for academic and industrial simulations. Overall, the physicsinformed machine learning techniques presented strong potential to enhance turbulence modeling. Although limitations exist, the improved accuracy and reliability constitute valuable contributions towards advancing RANS capabilities.  \nKeywords: CFD, RANS, Turbulence, Machine Learning, k − ε models, Low-Reynolds models.  \niii  \nAbstract in lingua italiana  \nLa turbolenza rappresenta una sfida complessa nella modellistica delle simulazioni didinamica dei fluidi. Gli approcci tradizionali si basano sulle equazioni Reynolds-Averaged Navier-Stokes (RANS) abbinati a modelli di chiusura del tensore di Reynolds, ma spesso presentano problemi di precisione e universalità . Questa tesi investiga l’integrazione del machine learning nei modelli di chiusura delle RANS per migliorare la modellazione della turbolenza.  \nVengono proposti e validati modelli neurali sia ad alto che basso numero di Reynolds sulla configurazione di flusso turbolento in un canale piano. I test preliminari in cui il tensore Reynolds è trattato esplicitamente mostrano problemi dovuti al cattivo condizionamento delle equazioni RANS. Il modello neuronale k − ε ad alto numero di Reynolds dimostra una performance comparabile al modello standard k − ε, richiedendo però oltre il doppio del costo computazionale. D’altra parte, i modelli neurali a basso numero di Reynolds mostrano capacità promettenti. In particolare gli output della rete neurale sonosignificativamente migliori dei valori relativi alle stesse grandezze ottenuti dai modellitradizionali.  \nL’integrazione del codice nel solver TRUST/TrioCFD consente un utilizzo del modello neuronale a basso Reynolds per simulazioni accademiche e industriali. Nel complesso, letecniche di apprendimento automatico presentano un forte potenziale per migliorare lamodellazione della turbolenza. Nonostante le limitazioni, l’aumentata precisione e affidabilità costituiscono contributi preziosi per l’avanzamento delle capacità RANS.  \nParole chiave: Fluidodinamica Computazionale, RANS, Turbolenza, Machine Learning, Modelli k − ε, Modelli a basso numero di Reynolds.  \nResumé en français  \nLa turbulence représente un défi complexe dans la modélisation des simulations de dynamique des fluides. Les approches traditionnelles sont basées sur les équations de NavierStokes moyennées dans le temps (RANS) associées à des modèles de fermeture du t","cbCaim828nFW6Dxy","https://ap.wps.com/l/cbCaim828nFW6Dxy","pdf",3086602,1,102,"English","en",105,"# Contents\n## Context of Study\n## Navier-Stokes equations for incompressible fluids\n## Computational modeling\n## DNS modeling\n## RANS modeling\n## Turbulence Models based on LEVM\n## Mixing length model","[{\"question\":\"What is the main goal of the thesis?\",\"answer\":\"To integrate machine learning into RANS closure models to improve turbulence modeling accuracy and generality.\"},{\"question\":\"How are the neuronal models evaluated?\",\"answer\":\"They are proposed and validated on canonical turbulent channel flow, comparing neural outputs with standard analytical closures.\"},{\"question\":\"What issue arises when injecting explicit Reynolds stresses from DNS into RANS equations?\",\"answer\":\"The RANS equations show ill-conditioning concerns, making the explicit-stress injection problematic.\"}]","Code integration and validation of a machine learning based RANS model - Thesis | PDF",1785683372,257,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"code-integration-and-validation-of-a-machine-learning-based-rans-model-thesis","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/code-integration-and-validation-of-a-machine-learning-based-rans-model-thesis/118386/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is the main goal of the thesis?","Question",{"text":75,"@type":76},"To integrate machine learning into RANS closure models to improve turbulence modeling accuracy and generality.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are the neuronal models evaluated?",{"text":80,"@type":76},"They are proposed and validated on canonical turbulent channel flow, comparing neural outputs with standard analytical closures.",{"name":82,"@type":73,"acceptedAnswer":83},"What issue arises when injecting explicit Reynolds stresses from DNS into RANS equations?",{"text":84,"@type":76},"The RANS equations show ill-conditioning concerns, making the explicit-stress injection problematic.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]