TN-05_TechniquesCouplingContinuumFluidParticlePlasmaNeptune
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Techniques,and,software,relevant,to,the,coupling,of,continuum,(fluid),and,particle,models,of,plasma,for,NEPTUNE,Technical,Report,2068625-TN-05,Deliverable,3.1,Hussam,Al,Daas*,Niall,Bootland*,Tyrone,Rees*,Andrew,Sunderland†,Philippa,Rubin†,Sue,Thorne‡,Josh,Williams§,March,2023,(Revised,version,of,2060049-TN-02),1,Introduction,The,aim,of,the,“Fusion,Modelling”,use,case,within,ExCALIBUR,is,the,development,of,new,algorithms,,software,and,related,infrastructure,that,will,allow,for,the,efficient,use,of,current,Petascale,and,future,Exascale,supercom-,puting,hardware,to,draw,insights,for,ITER,,and,guide,and,optimise,the,design,of,STEP,,the,UK,demonstration,nuclear,fusion,power,plant,,and,related,fusion,technology.,With,existing,legacy,codes,not,scaling,well,and,not,containing,all,of,the,required,latest,physics,,significant,investment,is,needed.,However,,it,is,important,that,the,different,pieces,of,the,modelling,and,simulation,strategy,must,not,only,scale,well,in,isolation,,these,pieces,need,to,couple,together,and,limit,any,losses,in,scalability.,1.1,The,limitations,of,existing,legacy,codes,Figure,1,highlights,the,areas,of,the,tokamak,plasma,simulations,that,are,being,targeted,by,the,NEPTUNE,project.,Within,the,UK,,researchers,currently,make,extensive,use,of,fluid-based,codes,when,modelling,the,edge-plasma,region,of,fusion,devices.,However,,the,electrically,charged,nature,of,the,plasma,adds,significant,complications,when,using,a,fluid,approach,and,adds,significant,uncertainty,to,the,models,,particularly,,when,close,to,the,wall.,In,these,regions,,a,particle-based,(kinetic),method,such,as,particle-in-cell,(PIC),is,preferable.,It,is,therefore,necessary,to,couple,together,the,two,different,approaches,for,different,regions,of,the,plasma,and,this,is,the,focus,of,this,report.,In,Section,2,,we,review,some,of,the,methods,available,within,the,literature,for,performing,this,coupled,approach.,We,then,review,some,of,the,available,code,coupling,libraries,in,Section,3,to,try,to,identify,“off,the,shelf”,solutions,for,these,problems.,We,draw,our,conclusions,in,Section,4.,2,Methodologies,for,coupling,the,fluid,and,particle,simulations,Borodin,et,al.,[4],have,considered,a,number,of,methods,for,hybridising,the,fluid,and,particle,(concentrating,on,the,use,of,EIRENE,[37]),approaches.,The,fluid,approach,is,,in,general,,used,to,simulate,plasma,ions,and,electrons;,kinetic,(particle),or,hybrid,approaches,are,used,for,the,neutrals,including,molecular,species.,The,authors,do,review,the,possibility,of,using,a,purely,fluid,treatment,of,the,neutral,atoms,(taking,moments,of,the,*The,authors,are,with,the,Scientific,Computing,Department,,STFC,Rutherford,Appleton,Laboratory,,Harwell,Campus,,Didcot,,OX11,0QX,,UK.,†The,authors,are,with,the,Hartree,Centre,,STFC,Daresbury,Laboratory,,Sci-Tech,Daresbury,,Keckwick,,Daresbury,,Warrington,,WA4,4AD,,UK.,‡Sue,Thorne,is,with,the,Hartree,Centre,,STFC,Rutherford,Appleton,Laboratory,,Harwell,Campus,,Didcot,,OX11,0QX,,UK.,Email,contact:,sue.thorne@stfc.ac.uk,§Josh,Williams,is,with,the,Hartree,Centre,,Edinburgh,Royal,Observatory,,Blackford,Hill,,Edinburgh,,EH9,3HJ,,UK.,1,Figure,1:,Schematic,diagram,of,a,generic,tokamak,“poloidal,cross,section”.,The,shaded,circles,highlight,the,areas,of,plasma,and,first,wall,that,are,being,targeted,by,the,NEPTUNE,project.,Attribution:,G.,Federici,et,al.,[CC,BY,3.0,(,https://creativecommons.org/licenses/by/3.0),,minor,modifications,to,figure].,kinetic,equation),,which,is,known,as,the,advanced,fluid,neutral,(AFN),model:,they,conclude,that,whilst,there,are,benefits,in,terms,of,computational,costs,,the,modelling,error,can,be,quite,significant,,particularly,in,lower,recycling,regimes.,In,the,following,,it,will,help,to,define,Kn,,the,Knudsen,number.,In,fusion-relevant,plasmas,,let,λ,be,the,mean,free,path,for,neutrals,(expressed,in,length,units),and,L,be,the,characteristic,linear,dimension,(expressed,in,length,units),,then,the,Knudsen,number,is,defined,as,Kn,=,λ/L,and,is,a,dimensionless,value.,For,large,values,of,Kn,,there,is,no,accurate,fluid,closure,available,for,the,neutrals,,which,is,why,a,particle,approach,is,used.,In,high-collision,regions,,Kn,becomes,low,and,there,is,very,strong,coupling,of,the,neutrals,with,the,background,plasma.,We,note,that,different,authors,may,use,different,values,for,L,and,they,often,relate,to,properties,of,the,domain,under,consideration,and,,in,the,cases,of,gases,,the,compressibility,also,needs,factoring,in.,Thus,,the,exact,definition,of,L,will,need,careful,consideration,for,the,simulations,of,interest,to,the,NEPTUNE,Programme.,2.1,Spatial,Hybridization,(SpH),Approach,The,regions,where,Kn,is,sufficiently,small,to,allow,the,use,of,the,fluid,model,typically,occur,in,only,a,small,part,of,a,dense,divertor.,A,number,of,spatially,hybrid,approaches,have,been,proposed,in,literature,and,usually,dis-,tinguish,between,the,particle,and,fluid,regions,,coupling,the,regions,together,by,using,appropriate,boundary,conditions,at,the,interfaces:,how,this,is,done,varies,between,the,different,methods.,The,choice,of,interface,between,the,two,regions,poses,interesting,questions.,It,is,reported,that,it,must,be,such,that,the,boundary,conditions,can,be,defined,based,on,fluid-like,distributions,,which,is,where,the,Knudsen,number,is,required,[4],,but,if,a,naive,method,is,used,for,coupling,the,regions,,we,could,lose,too,much,computational,speed.,When,considering,Exascale,simulations,,it,will,be,important,to,spread,the,work,for,the,coupling,activity,,and,particle,and,fluid,approaches,across,an,HPC,system,to,optimally,load,balance,the,whole,simulation.,We,discuss,this,further,in,Section,3.,SpH,methods,are,not,just,applicable,to,fusion,problems.,For,example,,the,space,craft,re-entry,problem,is,a,hot,topic,at,the,moment.,The,modelling,of,the,hypersonic,flows,around,the,re-entry,vehicle,is,one,of,the,most,challenging,problems,within,aerospace,engineering.,In,[4],,the,plasma,domain,is,separated,into,two,regions,with,the,boundary,conditions,being,used,to,couple,within,the,interface.,In,the,space,craft,re-entry,problem,,there,are,three,different,regions,[16]:,(i),for,Kn,<,0.001,,the,gas,can,be,regarded,as,a,continuum;,(ii),2,for,Kn,>,10,,there,is,free-molecule,flow,,and,(iii),for,intermediary,values,,there,is,a,slip-transitional,flow,region,,where,both,molecular,transports,and,collisions,are,just,as,important.,Thus,,in,this,slip-transitional,flow,region,,there,are,two,possibilities:,(i),perform,both,continuum,and,free-molecule,flow,simulations,in,this,region,and,then,set,this,region,as,the,coupling,interface,with,the,coupler,combining,the,two,simulations,,or,(ii),explicitly,do,a,Micro-Macro,Hybrid,method,(Section,2.2),in,this,region,and,then,use,the,coupler,to,transfer,informa-,tion,between,the,different,regions.,The,former,is,considered,in,[40],,which,is,encompassed,in,the,Modular,Particle,Continuum,(MPC),hybrid,approach,and,demonstrated,for,a,number,of,test,examples,including,the,simulation,of,hypersonic,nitrogen,flow,over,a,cylinder.,The,MPC,approach,is,also,used,for,examples,without,a,slip-transitional,flow,regions.,2.2,Micro-Macro,Hybrid,(mMH),Approach,δ,δ,such,that,f,=,f,f,+,f,In,[12],,Horsten,et,al.,propose,splitting,the,(complete),neutral,distribution,function,f,into,a,fluid,part,f,f,and,a,kinetic,correction,f,holds,across,the,entire,simulation,domain.,For,the,fluid-part,,the,approach,leads,to,the,AFN,equations,but,the,kinetic,correction,leads,to,additional,corrections,on,source,and,transport,terms.,A,modified,kinetic,simulation,is,used,to,obtain,the,kinetic,correction:,positive,and,negative,correction,particles,are,used,with,net,zero,density,and,momentum,,which,provide,exact,closure,for,the,AFN,model.,This,approach,has,benefits,,namely,,the,method,has,been,shown,to,be,produce,solutions,that,are,equivalent,to,solving,the,fully,kinetic,equations,and,is,independent,of,the,recycling,regime,used.,However,,the,method,requires,a,significant,amount,of,developmental,effort,and,the,fluid,method,will,need,to,act,across,the,whole,of,the,domain,instead,of,just,a,subdomain.,The,use,of,such,an,approach,would,require,significant,changes,in,the,approach,currently,being,used,by,some,of,the,NEPTUNE,projects,but,,given,the,interesting,nature,of,this,methodology,,it,is,being,explored,as,part,of,one,of,the,other,NEPTUNE,Projects,(Oxford),,[3,,28–,30].,2.3,Kinetic-Diffusion,Monte,Carlo,Method,(KDMC),The,Kinetic-Diffusion,Monte,Carlo,(KDMC),scheme,is,an,asymptotic-preserving,scheme,that,is,fully,Monte,Carlo.,Each,Monte,Carlo,particle,alternates,between,acting,according,to,a,fluid,limit,(moving,via,a,random,walk,that,incorporates,a,Monte,Carlo,discretization,of,the,limiting,fluid,equation),and,acting,in,a,kinetic,manner.,Whilst,this,method,has,merit,in,that,it,does,not,require,intricate,couplings,between,fluid,and,kinetic,neutral,sub-domains,,it,has,so,far,been,only,demonstrated,on,simplified,problems,involving,single-species,scattering,or,absorption,,for,example,,[2].,The,decision,to,use,such,a,method,would,result,in,a,significant,change,of,steer,for,the,NEPTUNE,project.,3,Software,libraries,for,code,coupling,In,his,2015,paper,on,coupling,,Tang,[43],neatly,summarised,a,dilemma,for,code,developers,wishing,to,cre-,ate,coupled,multi-physics,models:,“Despite,existing,theoretical,developments,,implementing,concurrently,coupled,simulations,remains,difficult.,On,one,hand,,hard-coding,remains,commonplace,in,projects,that,em-,ploy,ad,hoc,coupling,approaches.,Such,practice,can,quickly,become,an,obstacle,when,further,development,is,needed.,On,the,other,hand,,despite,the,richness,of,available,coupling,schemes,and,tools,,adapting,exist-,ing,code,to,meet,the,programming,interface,specification,of,a,coupling,framework,frequently,leads,to,code,refactoring,that,consumes,a,substantial,amount,of,man-hours”.,Since,2015,,a,wide,range,of,new,software,coupling,libraries,have,been,developed,to,largely,mitigate,these,difficulties.,Many,coupling,libraries,are,now,minimally,invasive,to,the,underlying,computational,models.,Many,also,include,high-level,Application,Pro-,gramming,Interfaces,(APIs),with,support,for,a,range,of,programming,languages,and,are,based,on,MPI,(the,ubiquitous,message-passing,standard),for,data,exchange,management.,Given,the,potential,disruption,of,applying,the,coupling,approaches,described,in,Section,2.2,and,2.3,to,the,existing,code,base,,the,SpH,(Section,2.1),approach,may,be,favourable.,If,SpH,is,to,be,used,,there,are,a,range,of,code,coupling,libraries,already,available,,therefore,rendering,it,unnecessary,for,the,NEPTUNE,project,to,develop,its,own.,A,preferable,solution,is,a,generalised,approach,using,code,coupling,middleware,or,libraries.,In,this,section,,we,review,some,of,the,available,libraries,and,note,that,the,Software,Outlook,Project,[42],performed,an,extensive,review,of,a,number,of,code,coupling,libraries,[38],and,refer,the,reader,to,performance,comparisons,within,their,report,for,further,details.,3,3.1,The,advantages,of,using,Coupling,libraries,with,a,partitioned,approach,The,main,advantage,of,using,third-party,coupling,libraries,is,that,they,provide,a,framework,for,a,separation,of,concerns,for,complex,workflows,,where,individual,application,codes,can,remain,separate,entities.,With,the,provision,that,data,provided,to,the,coupling,middleware,remains,consistent,,each,application,model,can,be,developed,in,isolation,of,the,other.,This,also,results,in,increased,potential,for,HPC,optimisations.,For,example,,load-balancing,algorithms,can,be,applied,separately,to,each,application,domain,,individual,computational,grids,can,be,redefined,,coarsened,or,refined,,and,the,different,applications,can,even,be,run,on,separate,plat-,forms,if,appropriate.,It,should,be,noted,that,where,heterogeneous,CPU/GPU,coupling,schemes,are,imple-,mented,using,the,current,class,of,code,coupling,libraries,,the,coupling,framework,software,itself,resides,on,the,CPU,platform.,Most,coupling,libraries,provide,high-level,APIs,which,ensure,ease,of,use,and,facilitate,high,degrees,of,flexibility.,The,data,exchange,between,the,coupled,applications,usually,takes,place,within,standard-,ized,tools,for,message,passing,e.g.,MPI,,thereby,minimizing,the,invasiveness,of,the,integration.,Moreover,,the,library,approach,usually,ensures,that,the,data,exchange,is,undertaken,in,an,efficient,manner.,These,proper-,ties,lead,to,high-performance,and,portability.,We,note,that,within,the,NEPTUNE,Programme,,the,multiple,domains,are,planned,to,use,the,same,underlying,mesh,structure,at,the,coupling,interfaces.,Other,features,of,code-coupling,libraries,include:,•,Dynamic,load,balancing,of,the,coupling,interface,across,processors.,This,may,become,especially,impor-,tant,for,high-performance,computing,at,scale.,•,Variable,overlapping,of,domains.,•,Support,for,dynamic,meshes,(vs,static,meshes).,•,Multi-language,APIs.,•,Support,for,multiple,communication,methods,(MPI,,TCP/IP).,•,Multi-platform,,heterogeneous,HPC,environment,coupling,(e.g.,CPU/GPU).,•,Support,for,coupling,multiple,applications.,•,Open,source,or,free-to-use,software.,Presentations,on,many,of,the,coupling,libraries,discussed,in,this,report,are,available,on,recordings,from,the,Excalibur,Online,Workshop,The,State,of,the,Art,in,Scientific,Coupling,Technology,for,HPC,[45].,3.2,MUI,The,Multiscale,Universal,Interface,(MUI),is,an,open,source,code-coupling,library,,which,was,originally,devel-,oped,by,Brown,University,[43].,Originally,designed,for,multiscale,coupling,,the,software,is,also,applicable,to,multi-physics,coupling,of,problems,at,the,same,scale.,At,present,MUI’s,primary,developers,and,maintainers,are,UKRI-STFC,[11].,The,MUI,project,aims,to,create,“,.,.,.,a,light,weight,plugin,library,that,can,glue,together,essentially,all,numerical,methods,including,,but,not,limited,to,,Finite,Difference,,Finite,Volume,,Finite,Element,,Spectral,Method,,Spectral,Element,Method,,Lattice,Boltzmann,Method,,Molecular,Dynamics,,Dissipative,Particle,Dynamics,and,Smoothed,Particle,Hydrodynam-,ics”,[43].,MUI,developers,claim,that,the,coupling,process,is,so,lightweight,and,minimally,invasive,that,MUI,can,be,integrated,into,a,solver,using,only,ten,lines,of,code.,MUI,provides,a,small,set,of,programming,interfaces,to,conduct,send,and,receive,messages,between,do-,mains.,As,such,,it,does,not,put,restrictions,on,the,multi-physics,solvers,themselves;,“MUI,also,follows,PLE’s,philosophy,of,not,prescribing,how,the,physics,of,a,problem,should,be,coupled,,only,that,coupling,should,be,achieved,by,passing,data,through,an,interface.,Assuming,the,data,in,question,is,associated,with,a,point,struc-,ture,then,the,only,requirement,is,that,the,data,can,be,associated,with,a,single,point,in,space”,[17].,Following,its,original,design,targeting,multi-scale,problems,,MUI,does,not,rely,on,a,computational,mesh,approach,,in-,stead,using,a,particle,paradigm,for,its,data,transport,layer.,In,[43],,the,author,demonstrates,the,use,of,MUI,applied,to,three,test,problems,where,the,analytical,solution,is,known:,(i),Couette,flow:,Smoothed,Particle,Hy-,drodynamics–Smoothed,Particle,Hydrodynamics,coupling;,(ii),Soft,matter:,Smoothed,Particle,Hydrodynam-,ics–Dissipative,Particle,Dynamics,coupling,,and,(iii),Conjugate,heat,transfer:,energy-conserving,Dissipative,Particle,Dynamics-Finite,Element,coupling.,Whilst,no,values,are,given,that,compare,the,error,of,the,simula-,tions,with,the,analytical,solutions,,visually,,there,is,a,good,match.,4,Figure,2:,The,exchange,of,information,across,solvers,in,MUI,via,push,and,fetch,data,points,[43].,The,MUI,software,is,written,in,C++11,with,wrappers,for,C,,Fortran,and,Python.,A,header-based,approach,is,used,for,the,entire,library,and,the,only,external,library,is,the,Message,Passing,Interface,(MPI).,As,such,,it,can,be,used,in,the,same,way,any,other,C++,standard,library,would,be,used,,without,the,need,for,pre-compilation.,However,,it,has,the,bonus,advantage,of,not,interfering,with,pre-existing,MPI,communications,within,the,pre-,existing,solver.,MUI,is,open-source,software,,dual,licensed,as,either,GPLv3,or,Apache,2.0.,The,library,employs,techniques,such,as,dynamic,typing,,MPI,MPMD,execution,,asynchronous,I/O,,generic,programming,and,tem-,plate,metaprogramming,to,improve,both,performance,and,flexibility.,As,shown,in,Fig.,2,,MUI,assumes,a,push–fetch,workflow,and,serves,as,the,data,exchange,and,interpretation,layer,between,solvers.,A,data,sam-,pling,construct,is,provided,for,the,coupling,interface.,For,example,,this,may,be,used,where,there,exists,no,one-,to-one,correspondence,between,data,points,at,the,interface,of,the,coupled,applications,and,therefore,some,sort,of,weighted,interpolation,technique,is,required.,Using,the,flexible,data,interpretation,engine,provided,,users,can,plug,in,the,most,appropriate,interpolation,algorithm,with,minimal,effort.,MUI,has,a,well,maintained,website,with,documentation,,example,applications,,demonstrations,and,tuto-,rials,[21].,MUI,also,provides,a,testing,framework,which,allows,a,wide-range,of,complex,coupling,scenarios,to,be,simulated,via,artificial,benchmarking,[20].,MUI,is,currently,under,development,as,part,of,the,ExCALIBUR,projects.,The,software,optimisation,is,focusing,on,memory,overhead,reductions,,improved,MPI,usage,and,better,GPU,integration.,At,the,time,of,writing,it,is,also,planned,that,MUI,will,be,made,available,as,part,of,the,Nektar++,Spectral/HP,framework,[24].,3.3,OpenPALM,OpenPALM,(Projet,d’Assimilation,par,Logiciel,Multimethodes),is,another,coupling,library,that,enables,a,user,to,execute,components,of,code,concurrently,with,communication,between,them.,There,are,two,parts,to,Open-,PALM:,PrePALM,and,PALM.,PrePALM,is,the,graphical,user,interface,,and,PALM,is,the,driver,of,coupling,frame-,work,itself.,PALM,uses,MPI,communication,to,handle,the,exchange,of,data,for,the,coupling,algorithm.,On,the,OpenPALM,website,,it,states,they,have,had,simulations,of,130,000,cores,on,Titan,,130,000,cores,on,Turing,and,12,000,cores,on,Curie,[27].,Keyes,et,al.,[13],include,OpenPALM,as,one,of,the,successes,in,multi-,physics,software.,OpenPALM,does,not,appear,to,be,restricted,to,particular,scientific,fields,and,it,has,a,lengthy,user,guide,[19].,Therefore,,OpenPALM,maybe,of,interest,to,the,NEPTUNE,Programme.,The,OpenPALM,team,is,joint,between,CERFACS,and,ONERA.,CERFACS,have,also,created,another,coupler,called,OASIS,[25],but,it,is,dedicated,to,geophysical,applications.,In,contrast,to,OASIS,,OpenPALM,provides,a,more,generic,interpolation,framework,based,on,an,unstructured,mesh,formalism,[6],,provided,by,the,CWIPI,library,[44].,CWIPI,can,be,used,independently,of,the,OpenPALM,interface,,see,Section,3.6,for,further,informa-,tion.,5,Figure,3:,The,PrePALM,Interface.,This,example,was,sourced,from,OpenPALM’s,website,[27].,OpenPALM,applications,are,implemented,via,a,user,interface,called,PrePALM.,The,user,designs,their,cou-,pling,algorithm,into,sequential,and,parallel,sections,,loops,,conditional,executions,,and,communication,be-,tween,components.,The,designed,algorithm,is,presented,to,the,user,clearly,in,a,window,as,seen,in,Fig.,3.,OpenPALM,stress,you,can,create,parallel,code,“.,.,.,without,anything,to,know,about,MPI,,only,by,drawing!,It,is,one,of,the,PALM,features:,one,can,make,parallel,computing,without,any,further,specific,knowledge”,[19].,3.4,preCICE,The,Precise,Code,Interaction,Coupling,Environment,(preCICE),[34],is,a,coupling,library,developed,by,the,Uni-,versity,of,Stuttgart,and,the,Technical,University,of,Munich.,It,is,another,available,open,source,coupling,library,that,aims,to,couple,existing,solvers,together,,creating,what,is,known,as,‘partitioned’,simulations.,In,this,way,,they,have,similar,motivations,to,MUI,(Section,3.2),and,aim,for,the,highest,flexibility,possible,in,reusing,exist-,ing,components.,Their,team,have,particular,interests,in,fluid-structure,interaction,and,conjugate,heat,transfer,simulations,,but,they,stress,that,they,are,not,limited,to,such,fields.,The,preCICE,API,has,wrappers,for,C++,,C,,Fortran,,Python,,Matlab,and,Julia,and,the,project,used,a,policy,of,continuous,integration,with,automatic,testing,undertaken,at,all,levels.,The,software,supports,coupling,of,CFD,,FEM,,Particle,(with,background,meshes),and,in-house,solvers,us-,ing,an,adapter,to,interface,with,the,preCICE,coupling,library,,as,shown,in,Fig.,4.,This,adapter,is,a,stand-alone,software,package,that,may,either,be,provided,by,preCICE,(for,commonly,used,solvers),or,may,be,user-defined,(e.g.,for,in-house,solver,methods).,The,preCICE,library,provides,software,for,communication,,data,mapping,,coupling,schemes,and,time,interpolation.,Coupling,meshes,are,defined,only,once,during,initialization,,so,preCISE,is,not,suitable,for,problems,where,the,coupling,mesh,may,be,modified,during,the,simulation.,To,couple,your,code,with,preCICE,,an,input,file,must,be,developed.,preCICE,is,configured,with,an,XML,file:,a,reference,guide,is,available,[35].,One,particular,difference,between,preCICE,and,the,other,coupling,libraries,that,we,discuss,is,that,in,this,XML,file,,you,can,establish,an,m2n,communication,channel,(i.e.,from,m,processes,of,Solver1,to,n,processes,of,the,Solver2),based,on,TCP/IP,sockets.,It,is,possible,to,configure,preCICE,to,use,MPI,ports,if,you,wish,,but,the,preCICE,team,recommend,using,sockets.,Once,this,XML,configuration,is,complete,,the,user,can,then,insert,calls,to,the,preCICE,API,in,original,solvers,and,,at,this,stage,,preCICE,is,very,similar,to,MUI.,In,[38],,Rubin,documents,the,steps,that,she,had,to,go,through,to,install,preCISE,on,ARCHER2,[1],and,reports,that,it,was,not,straightforward.,preCICE,has,extensive,user,documentation,available,with,an,active,community,exchange,chat,page,and,forum.,The,website,also,has,articles,on,many,coupling,projects,and,includes,detailed,performance,analyses,6,Figure,4:,The,preCICE,Coupling,Methodology,[33].,from,HPC,systems.,It,is,used,by,over,one,hundred,research,groups,in,academia,and,industry.,Ongoing,and,fu-,ture,planned,developments,include,support,for,dynamic-adaptive,meshes,(i.e.,re-initialization),,higher-order,data,mapping,and,additional,support,for,mesh-particle,coupling.,3.5,PLE,The,Point,Location,Exchange,library,,PLE,,is,part,of,Code_Saturne,[8]:,an,open-source,CFD,software,released,by,EDF,,available,under,an,LGPL,licence.,PLE,was,specifically,designed,to,simplify,parallel,couplings,using,a,minimalist,API,and,and,minimal,dependencies.,Both,volume,and,surface-based,multiple,couplings,(with,overlap),are,supported.,Data,is,transferred,between,the,coupled,solvers,at,specific,spatial,points,[17].,The,library,has,much,in,common,with,other,coupling,libraries,,such,as,CWIPI,,MUI,and,preCICE,[10].,It,is,used,to,couple,Code_Saturne,to,other,EDF,codebases,,such,as,EDF’s,thermal,software,SYRTHES,[9].,Code_Saturne,is,available,on,GitHub,[7],,with,PLE,included,in,this,repository,[32].,The,PLE,developers,have,developed,a,coupling,framework,through,which,data,can,be,exchanged,between,different,solvers.,To,do,this,,PLE,creates,an,interface,between,the,solvers,and,an,MPI,intra-communicator,is,created,for,each,interface,,thus,integrating,with,pre-existing,MPI,functionality,within,the,original,solvers.,Although,MPI,is,currently,required,,the,library,could,easily,be,extended,to,other,communication,libraries,with,only,minor,changes.,Each,coupled,code,provides,their,own,set,of,local,points,in,a,mesh,location,algorithm.,The,mapping,of,data,from,one,mesh,to,another,is,done,independently,for,each,coupling,,within,the,associated,MPI,intra-communicator.,In,this,way,,PLE,works,in,a,very,similar,way,to,MUI,(Section,3.2),and,CWIPI,(Section,3.6).,A,PLE,locator,object,tracks,this,mapping.,In,cases,of,partial,overlap,,different,variables,may,be,exchanged,either,both,ways,or,one,way,only,on,some,part,of,the,computational,domain.,A,lightweight,coupling,set,object,is,defined,which,is,used,to,synchronize,time,stepping,status,across,multiple,codes.,Time,stepping,can,involve,both,locators,object,types,and,coupling,sets,object,types,for,field,data,exchange,and,global,synchronization,respectively.,Meshes,can,have,any,type,of,elements,,which,do,not,have,to,match,each,side,of,the,interface.,Data,points,at,the,interface,could,be,mesh,vertices,,face-centred,or,cell-centred,elements,,or,a,representation,of,independent,particles.,Each,code,defines,its,own,interpolation,algorithms.,Aside,from,the,Doxygen,documentation,,PLE,does,not,have,any,extensive,documentation,or,user,guide.,However,,there,is,a,brief,description,of,the,software,at,[31].,With,other,coupling,libraries,having,much,in,common,in,terms,of,technical,specification,,PLE’s,limited,documentation,means,that,it,is,not,one,of,our,rec-,ommended,libraries,for,use,within,the,NEPTUNE,Programme.,3.6,CWIPI,The,CWIPI,(Coupling,With,Interpolation,Parallel,Interface),library,can,be,used,for,either,chaining,and,cou-,pling,application,codes,in,a,massively,parallel,distributed,computing,environment,(chaining,is,defined,as,be-,ing,when,the,characteristic,times,of,the,physics,studied,in,the,individual,solvers,are,very,different,and,the,physics,must,therefore,be,processed,consecutively).,It,ensures,the,exchange,of,interpolated,fields,through,a,geometric,coupling,interface,and,allows,the,control,of,the,coupling,algorithm,using,control,parameters.,The,7,development,of,CWIPI,started,in,2009,,based,on,the,FVM,library,at,EDF,,now,developed,into,PLE,[32],,also,de-,scribed,here.,It,therefore,shares,many,common,approaches,and,features,with,PLE.,Call,interfaces,are,provided,to,C/C++,,Fortran,,Python/Numpy,and,Python/CGNS,and,the,software,is,freely,available,under,an,LGPL3,li-,cense.,The,main,CWIPI,website,[44],currently,has,only,limited,documentation,available,in,French,only.,CWIPI,is,currently,the,only,coupling,software,available,in,the,Spectral/HP,element,framework,Nektar++,[41].,There,are,two,alternative,operating,modes,for,CWIPI,-,via,direct,calls,or,via,the,OpenPALM,coupler.,When,using,the,direct,call,mode,,the,coupling,algorithm,is,defined,by,the,different,codes,,with,no,dedicated,cou-,pling,processes.,This,solution,is,less,flexible,than,the,use,of,a,coupling,manager,but,it,has,the,advantage,of,directly,processing,the,MPI-based,data,exchanges,between,the,codes,without,going,through,another,interme-,diate,code,,which,limits,the,memory,copies,and,therefore,ensures,better,performance,,especially,massively,parallel,computing,environment.,When,using,the,OpenPALM,route,,the,coupling,algorithm,is,defined,using,the,OpenPALM,GUI,and,driven,using,the,OpenPALM,coupler.,Both,MPI-based,communications,and,TCP/IP,communications,are,available,for,use,in,this,mode.,When,using,CWIPI,,both,coupled,codes,are,run,under,the,same,MPI,environment:,the,library,creates,MPI,intra-communicators,for,each,coupled,code.,Multiple,parallel,codes,are,executed,within,a,single,MPI,run,using,the,same,MPI,implementation,(this,is,a,constraint,that,the,CWIPI,developers,are,currently,attempting,to,eliminate).,No,predefined,coupling,schemes,are,provided.,Instead,users,define,their,own,coupling,scheme,using,CWIPI,control,parameters.,These,are,global,variables,that,are,shared,and,synchronised,between,the,codes.,CWIPI,constructs,a,point-to-point,communication,graph,between,the,multiple,codes.,This,graph,is,then,used,to,exchange,interpolated,fields,using,either,blocking,or,non-blocking,MPI,communications.,Elements,of,any,geometric,order,are,supported,(line,,surface,,volume).,In,advanced,use,,the,geometric,order,and,the,order,of,the,numerical,method,can,be,disassociated.,As,with,other,coupling,libraries,,meshes,can,have,any,type,of,elements,which,do,not,have,to,match,each,side,of,the,interface.,Data,points,at,the,interface,could,be,mesh,vertices,,face-centred,or,cell-centred,elements,,or,a,representation,of,independent,particles.,Recently,,the,geometric,localization,algorithm,has,been,redesigned,to,use,a,parallel,distributed,octree,structure,for,dy-,namic,load-balancing,of,the,coupling,interface,across,processors.,this,has,resulted,in,much,improved,parallel,performance,,particularly,on,large-scale,processing,platforms.,In,[15],,Langenais,et,al.,consider,an,example,that,couples,the,Navier-Stokes,equations,with,the,Euler,equa-,tions.,They,solve,the,Navier-Stokes,equations,by,using,a,cell-centered,finite,volume,method,on,generalized,unstructured,grids,,solve,the,nonlinear,Euler,equations,by,using,a,nodal,discontinuous,Galerkin,method,(DG),on,unstructured,grids,,and,use,CWIPI,to,couple,the,regions.,Each,region,uses,the,same,spatial,discretisations,within,the,interface,region.,Good,accuracy,of,solution,is,demonstrated,for,a,number,of,test,problems,includ-,ing,pulsating,sphere,,wave,guide,,standing,wave,in,cavity,,and,shock,tube,examples.,Lackhove,[14],provides,a,detailed,explanation,around,the,use,of,Nektar++,and,CWIPI,for,aeroacoustic,problems,where,the,two,re-,gions,have,different,time,steps,and,the,additional,algorithmic,steps,used,to,reduce,the,induced,error,from,the,coupling.,Both,of,CWIPI’s,operating,modes,are,currently,being,used,in,coupling,projects,by,engineers,,researchers,and,developers,primarily,in,the,aerospace,domain.,CWIPI,is,notably,used,at,ONERA,[26],in,unifying,“lightning”,and,“plasma”,research,projects,,in,the,“,elsA,–,CEDRE,synergy”,research,project,[5],,for,post-processing,of,the,CEDRE,code,,and,for,aeroacoustic,couplings,(CEDRE,/,CEDRE,coupling).,Current,users,also,include,Safran,,Siemens,,ArianeGroup,and,and,Airbus,CERFACS,,CNES,Meteo,France,and,the,University,of,Surrey.,A,major,new,version,of,CWIPI,is,expected,to,be,released,in,late-2022,or,early-2023,,which,will,contain,new,features,including,(i),non-blocking,synchronization,of,control,parameters,using,MPI,RMA,(Remote,Memory,Access),,(ii),access,to,multiple,types,of,spatial,interpolation,methods,,(iii),arbitrary,distributions,of,the,coupled,codes,to,processes,,i.e.,processes,will,be,able,to,run,multiple,applications.,In,Appendix,A,,we,provide,observations,and,results,from,preliminary,experiments,that,couple,Nektar++,and,a,simple,particle-style,code,with,an,interface,that,involves,CWIPI.,In,[47],,further,observations,and,results,are,provided,for,a,test,case,depicting,a,ball,of,hot,gas,that,is,ini-,tialised,in,the,centre,of,the,domain,and,rises,upwards,based,on,the,Grashof,number.,The,source,term,for,velocity,is,Fu,=,Gr,T,,,where,T,is,the,temperature.,The,NESO-Particles,[39],solver,advects,the,particles,with,a,random,velocity,(N,(0,,1)),and,is,coupled,with,the,Nektar++,simulation,to,provide,a,source,term,for,tempera-,ture.,For,this,test,case,,the,coupling,with,CWIPI,is,shown,to,minimally,impact,the,scalability,of,the,simulation,versus,using,a,non-coupled,version,of,the,Nektar++,simulation.,8,3.7,MUSCLE3,MUSCLE3,is,the,third,version,of,the,Multiscale,Coupling,Library,and,Environment,,developed,by,the,University,of,Amsterdam,[22].,Most,of,the,libraries,discussed,here,target,tightly-coupled,scale-overlapping,multiphysics,simulations,and,emphasise,efficient,execution,on,high-performance,computers.,According,to,its,principal,reference,[46],“The,MUSCLE3,framework,takes,a,somewhat,different,approach,,focusing,on,scale-separated,coupled,simulation.,These,types,of,coupled,simulations,have,specific,communication,patterns,which,occupy,a,space,in-between,tightly-coupled,,high,communication,intensity,multiphysics,simulations,,and,highly,parallel,computations,in,which,there,is,no,communication,between,components,at,all”.,MUSCLE3,connects,simulta-,neously,running,instances,of,different,sub-models,together,based,on,an,MMSL,(Multiscale,Modelling,and,Sim-,ulation,Language),description,of,how,to,do,so,,which,can,be,expressed,in,the,form,of,a,diagram.,The,software,is,particularly,suitable,for,undertaking,efficient,VVUQ,(Verification,,Validation,,Uncertainty,and,Quantification),analyses,of,ensemble,multiscale,simulations.,MUSCLE,3,consist,of,three,components:,libmuscle,,ymmsl-python,,and,muscle-manager.,libmuscle,is,a,library,that,is,used,to,connect,compute,element,implementations,(e.g.,new,or,existing,models),to,a,coupled,simulation.,It,offers,functions,for,sending,and,receiving,messages,to,and,from,the,outside,world,,determining,whether,to,restart,the,model,at,the,end,of,its,run,,and,various,utilities,like,centralised,settings,(for,convenience,and,UQ),,centralised,logging,(to,make,debugging,easier),and,basic,profiling.,ymmsl-python,is,a,Python,library,that,contains,class,definitions,to,represent,an,MMSL,model,description.,muscle-manager,is,the,central,run-,time,component,of,MUSCLE,3.,It,is,started,together,with,the,compute,element,instances,,and,provides,a,central,coordination,point,that,the,instances,use,to,find,each,other.,MUSCLE3,can,be,used,with,sockets-based,communication,or,MPI,communication.,It,can,be,built,as,a,C++,library,,with,wrappers,to,Python,,or,a,Fortran,library.,The,documentation,provided,[22],is,quite,exten-,sive,,with,several,tutorials,and,examples,provided,for,different,configurations.,MUSCLE3,allows,peer,instances,to,find,each,other,,and,then,transmit,messages,between,themselves,in,a,peer-to-peer,fashion.,Communica-,tion,between,the,models,therefore,does,not,suffer,from,typical,bottlenecks,created,by,a,central,component.,MUSCLE3,also,supports,time-domain,adjacency.,4,Conclusions,To,conclude,,of,the,three,algorithmic,approaches,considered,within,Section,2,,the,spatial,hybridization,(SpH),and,micro-macro,hybridization,(mMH),approaches,are,of,the,most,interest.,The,latter,approach,would,in-,volve,significantly,larger,software,development,time,within,the,NEPTUNE,Programme,,with,the,current,set-up,of,NEPTUNE,more,closely,aligning,to,the,SpH,approach.,Additionally,,the,open,source,libraries,considered,in,Section,3,,align,with,the,SpH,approach,,which,should,also,reduce,the,software,development,efforts,required,so,long,as,the,fluid,and,kinetic/particle,projects,are,scoped,in,such,a,manner,that,enables,the,use,of,one,of,these,libraries.,Many,relevant,general,features,of,the,available,coupling,libraries,have,been,discussed,in,this,report,,however,problem-specific,coupling,questions,,such,as,the,required,depth,of,overlapping,regions,required,for,stable,,accurate,simulations,when,coupling,fluid,and,kinetic,fusion-based,models,will,require,further,analysis,and,experimentation,[36].,The,general,attributes,of,most,appeal,for,this,project,are,that,the,coupling,software,used,is,(i),lightweight,and,minimally,invasive;,(ii),provides,APIs,for,several,programming,languages;,(iii),sup-,ports,coupling,fluid,and,kinetic/particle,models,and,(iv),performs,well,at,scale.,Of,all,of,the,libraries,discussed,here,,we,find,the,attributes,of,MUI,and,CWIPI,to,be,the,most,favourable,for,NEPTUNE.,With,the,major,new,ver-,sion,of,CWIPI,on,the,horizon,and,it,already,being,the,favoured,coupler,within,Nektar++,,we,will,be,building,a,proxyapp,that,uses,CWIPI,to,couple,together,fluid,and,kinetic,approaches,within,the,Nektar++,framework.,We,will,then,use,this,proxyapp,to,investigate,how,large,the,overlap,of,the,domains,needs,to,be.,In,Appendix,A,,we,provide,our,initial,experiences,and,results,from,successfully,coupling,a,simple,particl-style,code,to,Nektar++,,where,the,coupling,platform,uses,CWIPI.,A,Coupling,implementation,with,CWIPI,We,have,created,a,coupled,‘dummy’,solver,executable,to,send,information,from,an,external,solver,to,Nektar++,using,CWIPI.,To,later,be,replaced,by,NESO-Particles,(in,development,by,UKAEA),,we,have,created,two,‘dummy’,solvers,which,simply,create,a,mesh,and,sends/receives,cell,values,to/from,Nektar++,using,CWIPI.,This,aims,to,demonstrate,that,Nektar++,can,be,successfully,be,coupled,to,an,arbitrary,external,solver.,We,have,used,this,approach,to,develop,the,coupling,platform,and,show,its,application,to,two,cases:,(i),writing,global,and,spatially-varying,diffusion,coefficients,(using,dummyDiffusionSolver),,(ii),computing,a,source,term,for,fluid,velocity,based,on,received,temperature,field,(using,dummyNavierStokesSolver).,9,(a),D01,=,D00,(b),D01,=,0,(c),D01,=,−D00,Visualisation,showing,Figure,5:,from,dummyDiffusionSolver,to,Nektar++,on,the,fluid,velocity,in,Nektar++.,The,diffusion,coefficients,are,spatially,uniform,in,all,three,cases.,the,diffusion,coefficient,effect,of,varying,sent,the,A.1,Implementation,Coupling,an,external,solver,to,Nektar++,requires,the,addition,of,five,functions,to,the,solver.,The,first,function,is,an,initialisation,of,the,coupler,that,defines,the,mesh,and,relevant,simulation,control,parameters,(cwipi_coupling),,a,function,to,send,cell,values,to,Nektar++,(cwipi_send),,as,well,as,a,function,to,wait,for,sending,to,finish,(cwipi_wait).,Similarly,,we,defined,a,function,for,receiving,data,(cwipi_receive),as,well,as,a,function,to,wait,for,the,receiving,of,data,to,have,completed,(cwipi_receive_wait).,Finally,,there,is,a,function,to,terminate,the,coupling,once,the,both,simulations,have,finished,(cwipi_exit).,This,is,similar,to,the,OpenFOAM-Nektar++,one-way,coupling,by,Moratilla-Vega,et,al.,[18].,Our,source,code,for,this,is,available,on,Github,[23].,We,provide,a,separate,solver,for,each,example:,dummyDiffusionSolver,and,dummyNavierStokesSolver.,A.2,Coupling,results,In,our,first,example,,we,illustrate,that,Nektar++,can,receive,data,from,our,external,solver,by,varying,the,anisotropic,components,of,the,(2D),diffusion,tensor,D,=,(cid:182),(cid:181)D00,D01,D01,D11,.,(1),−3,and,the,ratio,D01/D00,was,varied,from,1,Specifically,,the,two,isotropic,components,are,equal,D00,=,D11,=,10,to,-1.,The,value,was,applied,uniformly,across,the,domain.,In,Figure,5,,we,observe,that,the,diffusion,coefficients,were,successfully,sent,from,dummyDiffusionSolver,to,Nektar++.,When,D01,=,D00,,the,velocity,field,follows,a,45°,angle,(Figure,5a).,When,D01,=,−D00,,the,flow,has,a,-45°,angle,(Figure,5c).,When,D01,=,0,,the,flow,is,symmetrical,due,to,no,anisotropic,component,(Figure,5b).,In,our,second,diffusion,example,,we,define,a,spatially,varying,D01,value.,As,a,simple,representation,of,the,interfacial,region,discussed,in,Section,2,,we,define,an,interfacial,region,between,xi,0,and,xi,1,,over,which,D01,varies,linearly,from,D01,=,D00,to,D01,=,0,(Figure,6).,Therefore,,near,the,end,of,the,interface,and,downstream,the,flow,should,appear,much,more,blurred,(similar,to,Figure,5b).,This,is,observed,in,Figure,7,,as,we,observe,that,the,flow,becomes,significantly,more,blurred,as,the,size,of,the,interface,grows.,In,our,third,case,,we,illustrate,that,the,coupling,platform,can,send,and,receive,information,throughout,the,simulation.,This,is,shown,for,the,Navier-Stokes,equation,solver.,We,provide,a,source,term,to,the,solver,from,CWIPI.,This,requires,defining,a,dummy,variable,which,is,used,to,store,the,information,sent,to,Nektar++.,The,source,term,is,then,found,by,evaluating,the,symbolic,relationship,for,the,source,term,defined,in,the,Nektar++,simulation,configuration,file.,In,our,case,,this,simply,evaluates,Fu,=,αcwi,pi,where,αcwi,pi,is,a,dummy,variable.,This,must,be,prefixed,with,“dummy”,in,the,Nektar++,configuration,file,to,avoid,being,treated,as,a,normal,variable,and,therefore,integrated,by,the,advection,solver.,This,check,for,the,“dummy”,string,is,implemented,in,VelocityCorrectionScheme.cpp.,Our,simulation,aims,to,replicate,a,case,provided,by,UKAEA,,where,the,equivalent,of,a,ball,of,hot,gas,is,initialised,and,rises,upwards,based,on,the,Grashof,number,,Gr,=,5,×,109.,The,source,term,for,velocity,is,Fu,=,10,Figure,6:,Schematic,of,diffusion,example,test,case.,This,shows,the,boundary,conditions,,and,interface,region,(between,xi,0,and,xi,1).,The,angle,of,the,high,velocity,region,from,the,horizontal,depends,on,the,diffusion,coefficient,(Figure,5).,(a),xi,0,=,xi,1,=,x1,(b),xi,0,=,x1/2,(middle,of,domain),(c),xi,0,=,0,(starts,at,inlet),Figure,7:,Visualisation,showing,the,effect,of,spatially,varying,the,diffusion,coefficient,,where,the,diffusion,co-,efficient,is,change,based,on,the,cell,x,coordinate.,In,all,cases,,the,interface,end,(xi,1),is,at,the,simulation,outlet,(right,boundary).,Panels,show,varying,interface,start,point,,xi,0.,11,Figure,8:,Schematic,of,Navier-Stokes,example,case.,This,shows,that,we,initialise,a,‘blob’,with,higher,tempera-,ture,than,the,surrounding,fluid,in,Nektar++.,The,temperature,is,sent,to,dummyNavierStokesSolver,and,the,velocity,source,term,(Fu),is,computed,based,on,T,and,returned,to,Nektar++.,.,Gr,T,,,where,T,is,the,temperature.,In,dummyNavierStokesSolver,,we,receive,T,,,multiply,it,by,Gr,and,send,it,back,as,a,source,term,Fu,(Figure,8).,In,Figure,9,,we,quantify,the,influence,of,the,dummyNavierStokesSolver,mesh,resolution,on,the,temper-,ature,field,computed,by,Nektar++.,The,error,is,computed,by,comparing,the,coupled,simulation,solution,to,a,simulation,where,the,source,term,is,computed,within,Nektar++,(i.e.,we,define,Fu,in,the,XML,file,as,Fu,=,Gr,T,).,The,Nektar++,mesh,had,N,=,102400,,where,N,is,the,total,number,of,cells.,This,gave,Nx,=,320,,where,Nx,is,the,number,of,cells,per,axis.,The,dummyNavierStokesSolver,resolution,was,then,varied,from,Nx,=,10,to,300.,At,the,coarsest,resolution,,Nx,=,10,,the,maximum,error,in,the,Nektar++,temperature,field,was,31.6%,and,the,root-,mean-squared,(RMS),error,was,3%.,At,Nx,=,100,(3.2,times,coarser,than,the,Nektar++,mesh),,the,maximum,error,reduced,to,9.7%,(RMS,was,0.32,%).,The,maximum,error,when,Nx,=,300,was,2.7%,(RMS,0.092%).,When,we,computed,the,source,term,in,Nektar++,,it,is,based,on,the,temperature,which,is,a,6th,order,polynomial.,When,we,send,the,temperature,from,Nektar++,to,dummyNavierStokesSolver,,this,high-order,information,is,lost,and,we,compute,the,source,term,as,a,cell-average,which,is,the,reason,for,the,error,being,non-zero,as,the,mesh,is,refined.,To,visualise,the,influence,of,the,dummyNavierStokesSolver,mesh,resolution,on,the,temperature,field,,we,show,the,temperature,and,source,term,for,a,fine,(Figure,10a,c),and,coarse,mesh,(Figure,10b,d).,The,hot,gas,rises,following,a,classic,plume,structure,in,the,fine,mesh,simulation,(Figure,10a).,On,the,coarse,mesh,,the,plume,structure,appears,very,different,(Figure,10b),due,to,inaccuracies,in,the,source,term,provided,to,Nektar++,(Figure,10d).,The,maximum,relative,temperature,error,on,the,coarse,mesh,is,31.6%,as,shown,in,Figure,9.,References,1.,ARCHER2,Website,https://www.archer2.ac.uk/.,2.,Arter,,W.,&,Eastwood,,J.,Particle-mesh,schemes,for,advection,dominated,flows.,Journal,of,Computational,Physics,117,,194–204,(1995).,3.,Barnes,,M.,,Parra,,F.,I.,,et,al.,Numerical,study,of,1D,drift,kinetic,models,with,periodic,boundary,conditions,tech.,rep.,2047357-TN-02-02,(UKAEA,Project,Neptune,,2021).,4.,Borodin,,D.,V.,,Schluck,,F.,,et,al.,Fluid,,kinetic,and,hybrid,approaches,for,neutral,and,trace,ion,edge,trans-,port,modelling,in,fusion,devices.,Nuclear,Fusion,(2021).,5.,CEDRE,France,,Research,Institute,http://wwz.cedre.fr/CEDRE.,6.,CERFACS,Research,Areas:,Code,Coupling,and,User,Interface,https://cerfacs.fr/en/code-coupling-,and-user-interface/.,12,Figure,9:,Maximum,and,mean-square,error,for,temperature,compared,to,baseline,simulation,provided,by,UKAEA,(where,source,term,is,explicitly,declared,in,Nektar++,XML,file,as,Fu,=,Gr,T,).,If,the,mesh,resolution,of,the,external,solver,is,too,coarse,the,temperature,field,will,have,high,maximum,error.,Error,is,evaluated,at,t,=,20,µs,(1000,iterations).,7.,Code,Saturne,GitHub,Repository,https://github.com/code-saturne/code_saturne.,8.,Code_Saturne,Website,https://www.code-saturne.org/cms/.,9.,EDF,R&D,Simulation,Software,Webpage,EDF,France.,https,:/,/,www.,edf,.,fr,/en,/,the-,edf,-,group,/,world,-,s,-,largest,-,power,-,company,/,activities,/,research,-,and,-,development,/,scientific,-,communities/simulation-softwares.,10.,Fournier,,Y.,Massively,Parallel,Location,and,Exchange,Tools,for,Unstructured,Meshes.,International,Jour-,nal,of,Computational,Fluid,Dynamics,34,,549–568,(Sept.,13,,2020).,11.,Hartree,Centre,-,Multiphysics,and,Multiphase,Code,Coupler,|,Scalable,and,flexible,code,coupling,https:,//www.hartree.stfc.ac.uk/Pages/scalable-and-flexible-code-coupling-.aspx.,12.,Horsten,,N.,,Samaey,,G.,,et,al.,A,hybrid,fluid-kinetic,model,for,hydrogenic,atoms,in,the,plasma,edge,of,tokamaks,based,on,a,micro-macro,decomposition,of,the,kinetic,equation.,Journal,of,Computational,Physics,409,,109308,(2020).,13.,Keyes,,D.,E.,,McInnes,,L.,C.,,et,al.,Multiphysics,simulations:,Challenges,and,opportunities.,The,Interna-,tional,Journal,of,High,Performance,Computing,Applications,27,,4–83,(Feb.,1,,2013).,14.,Lackhove,,K.,Hybrid,Noise,Simulation,for,Enclosed,Configurations,PhD,thesis,(2018).,15.,Langenais,,A.,,Vuillot,,F.,,et,al.,Assessment,of,a,Two-Way,Coupling,Methodology,Between,a,Flow,and,a,High-Order,Nonlinear,Acoustic,Unstructured,Solvers.,Flow,,Turbulence,and,Combustion,101,,681–703.,https://doi.org/10.1007/s10494-018-9928-0,(Oct.,2018).,16.,Li,,J.,,Jiang,,D.,,et,al.,Kinetic,comparative,study,on,aerodynamic,characteristics,of,hypersonic,reentry,vehicle,from,near-continuous,flow,to,free,molecular,flow.,Advances,in,Aerodynamics,3,,10.,https,:,/,/,doi.org/10.1186/s42774-021-00063-0,(May,2021).,17.,Longshaw,,S.,,Skillen,,A.,,et,al.,in,,28,(May,30,,2017).,ISBN:,978-1-874672-72-2.,18.,Moratilla-Vega,,M.,A.,,Angelino,,M.,,et,al.,An,open-source,coupled,method,for,aeroacoustics,modelling.,Computer,Physics,Communications,278,,108420,(2022).,19.,Morel,,T.,,Duchaine,,F.,,et,al.,O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