[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120414-en":3,"doc-seo-120414-105":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":20,"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},120414,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Mimetic Methods And Machine Learning For Turbulent Flows - Dissertation","This dissertation develops mimetic difference methods and integrates them with turbulence modeling using machine learning. It formulates mimetic operators for spatial discretization, analyzes identities, and demonstrates high-order implementations for key PDE operators such as gradient and divergence, then applies the framework to Navier–Stokes equations with structure-preserving time integration. Turbulence challenges are reviewed through DNS, RANS, LES, filtering, and closure strategies. Finally, data-driven SGS closure models using neural networks are trained and evaluated through multiple numerical examples for turbulent flows.","UC Irvine  \nUC Irvine Electronic Theses and Dissertations  \nTitle  \nMimetic Methods And Machine Learning For Turbulent Flows  \nPermalink  \n[https://escholarship.org/uc/item/336522dq](https://escholarship.org/uc/item/336522dq)  \nAuthor  \nSrinivasan, Anand  \nPublication Date  \n2025  \nCopyright Information  \nThis work is made available under the terms of a Creative Commons AttributionNonCommercial-NoDerivatives License, available at [https://creativecommons.org/licenses/by-nc-nd/4.0/](https://creativecommons.org/licenses/by-nc-nd/4.0/)  \n[Peer reviewed|Thesis/dissertation](Peer reviewed|Thesis/dissertation)  \n[eScholarship.org](eScholarship.org) Powered by the California Digital Library  \nUniversity of California  \nSAN DIEGO STATE UNIVERSITY &  \nUNIVERSITY OF CALIFORNIA, IRVINE  \nMimetic Methods And Machine Learning For Turbulent Flows  \nDISSERTATION  \nsubmitted in partial satisfaction of the requirements  \nfor the degree of  \nDOCTOR OF PHILOSOPHY  \nin Computational Science  \nby  \nAnand Srinivasan  \nDissertation Committee:  \nProfessor Jos´e E. Castillo (SDSU), Chair  \nAssistant Professor Perry Johnson (UCI), Co-Advisor Professor Eric Mjolsness (UCI)  \nAssistant Professor Qi Wang (SDSU) Associate Professor Tirtha Banerjee (UCI)  \n© 2025 Anand Srinivasan  \nDEDICATION  \nTo Amma and Appa for their unwavering support and encouragement.  \nTABLE OF CONTENTS  \nPage  \nLIST OF FIGURES v  \nLIST OF TABLES vii  \nACKNOWLEDGMENTS viii  \nVITA ix  \nABSTRACT OF THE DISSERTATION xi  \n1 Introduction 1  \n1.1 Organization Of This Dissertation ........................ 4  \n2 Mimetic Difference Methods And Spatial Discretization 6  \n2.1 Mimetic Methods ................................. 8  \n2.2 Identities ...................................... 11  \n2.3 High Order Mimetic Operators ......................... 13  \n2.4 Numerical Examples ............................... 16  \n2.4.1 Gradient .................................. 17  \n2.4.2 Divergence ................................. 18  \n2.4.3 One Dimensional Convection-Diffusion Equation ............ 19  \n2.5 Chapter Summary And Outlook ......................... 20  \n3 Fluid Flows And Navier Stokes Equations 22  \n3.1 Navier Stokes Equations ............................. 23  \n3.1.1 Conservation Property For The NS Equations ............. 24  \n3.1.2 Skew-Symmetric Form And Energy Conservation ........... 26  \n3.2 Mimetic Formulation Of The NS-Equations ................... 27  \n3.3 Semi-Discrete Numerical Integration Of The NS-Equations .......... 30  \n3.3.1 Pseudo Symplectic Runge Kutta Methods ............... 32  \n3.4 Semi-Discrete Mimetic Pseudo Symplectic Implementation .......... 34  \n3.5 Chapter Summary And Outlook ......................... 36  \n4 Numerical Simulation Of Incompressible NS-Equations 37  \n4.1 Two Dimensional Lid Driven Cavity Problem ................. 37  \n4.2 Three Dimensional Lid Driven Cavity Problem ................. 38  \n4.3 Two dimensional Taylor Green Vortex ..................... 39  \n4.4 Two dimensional Turbulent Taylor Green Problem ............... 41  \n4.5 Three dimensional Taylor-Green Vortex ..................... 41  \n4.6 Three Dimensional Turbulent Channel Flow .................. 46  \n4.7 Chapter Summary And Outlook ......................... 53  \n5 Challenges With Modeling Turbulence 56  \n5.1 Properties Of Turbulence ............................. 56  \n5.2 DNS, RANS And LES .............................. 58  \n5.2.1 Reynolds Averaged Equations ...................... 58  \n5.2.2 Large Eddy Simulations ......................... 59  \n5.3 The Kolmogorov K41 Hypothesis ........................ 60  \n5.4 Filtering ...................................... 62  \n5.5 Subgrid Scale Stress Tensor Models ....................... 66  \n5.5.1 Tests Of Model Performance ....................... 68  \n5.6 Turbulence Closure With Data-Driven Models ................. 70  \n5.7 Chapter Summary And Outlook ......................... 71  \n6 Machine Learning Assisted Mimetic Framework For Turbulence Modeling 72  \n6.1","cbCaip5ZlUvPFlqs","https://ap.wps.com/l/cbCaip5ZlUvPFlqs","pdf",8327449,1,238,"English","en",105,"# Introduction\n## Organization Of This Dissertation\n# Mimetic Difference Methods And Spatial Discretization\n## Mimetic Methods\n## Identities\n## High Order Mimetic Operators\n## Numerical Examples\n## Chapter Summary And Outlook\n# Fluid Flows And Navier Stokes Equations\n## Navier Stokes Equations\n## Mimetic Formulation Of The NS-Equations\n## Semi-Discrete Numerical Integration Of The NS-Equations\n## Semi-Discrete Mimetic Pseudo Symplectic Implementation\n## Chapter Summary And Outlook\n# Numerical Simulation Of Incompressible NS-Equations\n## Two Dimensional Lid Driven Cavity Problem\n## Three Dimensional Lid Driven Cavity Problem\n## Two Dimensional Taylor Green Vortex\n## Two dimensional Turbulent Taylor Green Problem\n## Three dimensional Taylor-Green Vortex\n## Three Dimensional Turbulent Channel Flow\n## Chapter Summary And Outlook\n# Challenges With Modeling Turbulence\n## Properties Of Turbulence\n## DNS, RANS And LES\n## The Kolmogorov K41 Hypothesis\n## Filtering\n## Subgrid Scale Stress Tensor Models\n## Turbulence Closure With Data-Driven Models\n## Chapter Summary And Outlook\n# Machine Learning Assisted Mimetic Framework For Turbulence Modeling\n## Burgers Equation And Filtering\n## SGS Closure Models Using Neural Networks\n## Numerical Example 1\n## Numerical Example 2\n## Numerical Example 3\n## Chapter Summary And Outlook\n# Thesis Conclusion And Outlook\n## Outlook For Future Research\n# Bibliography\n# Appendices","[{\"question\":\"What are mimetic difference methods in this dissertation, and why are they used?\",\"answer\":\"The dissertation develops mimetic difference methods to create spatial discretizations that preserve key mathematical structure. This helps maintain accuracy and conservation properties when solving PDEs and fluid equations.\"},{\"question\":\"How does the work treat Navier–Stokes equations numerically?\",\"answer\":\"It presents a mimetic formulation of the Navier–Stokes equations and uses semi-discrete numerical integration. The approach includes pseudo symplectic Runge Kutta methods and a semi-discrete mimetic pseudo symplectic implementation.\"},{\"question\":\"How are machine learning techniques applied to turbulence modeling here?\",\"answer\":\"The dissertation uses neural networks to build data-driven SGS closure models. It motivates the setting via filtering and examines performance through multiple numerical examples for turbulent flows.\"}]","Mimetic Methods And Machine Learning For Turbulent Flows - Dissertation | PDF",1785729926,600,{"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},"mimetic-methods-and-machine-learning-for-turbulent-flows-dissertation","",{"@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/mimetic-methods-and-machine-learning-for-turbulent-flows-dissertation/120414/",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","2026-08-03",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What are mimetic difference methods in this dissertation, and why are they used?","Question",{"text":75,"@type":76},"The dissertation develops mimetic difference methods to create spatial discretizations that preserve key mathematical structure. This helps maintain accuracy and conservation properties when solving PDEs and fluid equations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the work treat Navier–Stokes equations numerically?",{"text":80,"@type":76},"It presents a mimetic formulation of the Navier–Stokes equations and uses semi-discrete numerical integration. The approach includes pseudo symplectic Runge Kutta methods and a semi-discrete mimetic pseudo symplectic implementation.",{"name":82,"@type":73,"acceptedAnswer":83},"How are machine learning techniques applied to turbulence modeling here?",{"text":84,"@type":76},"The dissertation uses neural networks to build data-driven SGS closure models. It motivates the setting via filtering and examines performance through multiple numerical examples for turbulent flows.","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"]