CD-EXCALIBUR-FMS0054-TS-1_ExcaliburD31SoftwareRequirementsSpecification
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   :description: technical note

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ExCALIBUR,D3.1,Software,Requirements,Specification,TS/1,Response,to,Tokamak,Science,Requirements,Specification,Abstract,This,document,provides,a,response,to,Tokamak,Science’s,exhaust,code,specification,document.,It,forms,part,of,the,technical,specification,(TS).,UKAEA,REFERENCE,AND,APPROVAL,SHEET,Client,Reference:,UKAEA,Reference:,Issue:,Date:,CD/EXCALIBUR-,FMS/0042/TS/1,1.00,26,October,2021,Project,Name:,ExCALIBUR,Fusion,Modelling,System,Prepared,By:,Name,and,Department,Joseph,Parker,Wayne,Arter,Signature,N/A,N/A,Date,26,October,2021,26,October,2021,BD,Reviewed,By:,Rob,Akers,26,October,2021,Advanced,Dept.,Manager,Computing,Approved,By:,Rob,Akers,26,October,2021,Advanced,Dept.,Manager,Computing,2,1,Introduction,This,document,is,Project,NEPTUNE’s,response,to,Tokamak,Science’s,Requirements,Specifica-,tion,document.,This,specification,was,received,by,Wayne,Arter,on,5/11/20,via,Rob,Akers,and,its,authorship,was,confirmed,to,be,Fulvio,Militello,and,James,Harrison,at,the,NEPTUNE,Project,Board,It,is,intended,that,this,document,helps,to,frame,expectations,of,the,capabilities,of,NEP-,TUNE,code,,as,well,as,highlighting,challenges,and,areas,of,potential,collaboration.,The,requirements,are,summarized,as:,“The,new,UKAEA,Exhaust,code,needs,to,be,able,to,capture,parallel,and,perpendicular,transport,of,charged,and,neutral,particles,in,3D,,full,geometry,and,in,a,time,depen-,dent,way.,Turbulence,should,be,self-consistently,modelled,,as,well,as,energy,transfer,physics,between,charged,particles,,neutrals,and,photons,(radiation).,While,perturba-,tions,need,to,be,3D,,a,minimal,requirement,for,the,code,is,that,it,can,simulate,realistic,axisymmetric,equilibrium,configurations,with,complex,topologies,and,wall,designs.,The,aim,of,the,code,should,be,to:,1.,Efficiently,and,reliably,model,exhaust,in,next,generation,experiments,,like,e.g.,MAST-U,,JT60-SA,,and,especially,ITER,(the,latter,is,a,stringent,requirement,for,the,code).,2.,Allow,predictive,exhaust,capability,for,future,reactor,relevant,machines,like,STEP,or,DEMO.”,More,detailed,specifications,are,given,in,the,following,sections,either,as,block,quotations,or,as,bold,paragraph,headers.,1.1,NEPTUNE,Science,Plan,The,Science,Plan,for,NEPTUNE,[1],is,available,online.,The,stated,goal,of,the,project,is,to:,“develop,new,algorithms,,software,and,related,e-Infrastructure,that,will,result,in,the,efficient,use,of,current,Petascale,and,future,Exascale,supercomputing,hardware,in,order,to,1.,draw,insights,from,ITER,“Big,Data”,2.,to,guide,and,optimise,the,design,of,the,UK,demonstration,nuclear,fusion,power,plant,STEP,and,related,fusion,technology,in,the,approach,to,the,Exascale.,The,aims,of,the,work,are,to,deliver,expertise,in,,and,tools,for,,“in-silico”,reactor,interpretation,and,design.”,The,Science,Plan,also,describes,the,software,development,and,theory,development,that,is,being,and,will,be,undertaken,under,NEPTUNE.,3,Software,development.,The,aim,of,NEPTUNE,software,development,is,to,provide,a,flexible,framework,for,implementing,different,physical,models,in,an,Exascale-targeted,manner.,In,partic-,ular,,the,project,does,not,envisage,a,“NEPTUNE,system,of,equations”,so,much,as,NEPTUNE,providing,the,ability,to,solve,a,class,of,relevant,equations,,with,models,described,relatively,simply,using,a,Domain-Specific,Language,(DSL).,This,flexibility,enables,the,hierarchy,of,models,of,vary-,ing,fidelity,and,computational,costs.,It,also,allows,engagement,from,different,classes,of,user,with,different,levels,of,physics,and,software,expertise.,Theory,development.,The,above,framework,approach,notwithstanding,,NEPTUNE,is,also,sup-,porting,theory,development,in,two,of,its,four,work,packages:,FM-WP2,Plasma,Multiphysics,Model,and,FM-WP3,Neutral,Gas,and,Impurity,Model.,These,will,develop,two,close,coupled,models,,with,FM-WP2,seeking,to,include,kinetic,effects,in,existing,and,new,edge,plasma,models,,and,FM-WP3,developing,particle-based,models,for,describing,the,region,outside,and,just,inside,the,plasma,(neutral,atoms/molecules,and,partially,ionized,impurities).,Another,work,package,,FM-WP1,Numerical,Representation,,is,addressing,related,numerical,is-,sues,,such,as,the,accurate,modelling,of,highly,anisotropic,dynamics,,the,accurate,representation,of,first,wall,geometry,,and,the,numerical,preservation,of,conservation,laws,from,the,underlying,models.,As,such,the,NEPTUNE,plan,is,aligned,with,all,the,points,in,the,summary,requirements,quoted,above,,though,there,are,minor,issues,regarding,the,details,as,discussed,in,the,following,sections.,It,should,be,noted,that,the,Science,Plan,outlines,a,five-year,programme,that,explicitly,requires,user,involvement,for,fuller,development,of,surrogate,models,(such,as,turbulent,friction),and,to,specify,the,detailed,physics,of,ionisation,and,excitation,reactions.,Indeed,,development,of,many,of,the,physics,capabilities,listed,below,will,benefit,greatly,from,a,strong,collaboration,between,Tokamak,Science,and,Advanced,Computing.,2,Overall,Capabilities,Hierarchical,approach,with,multiple,models,,going,from,low,fidelity,(e.g.,laminar,fluid,and,fluid-kinetic,runs,in,2D),to,medium,fidelity,(e.g.,fluid,runs,with,neutrals,and,turbulence,mul-,tispecies,,but,with,reduced,number,of,species),and,high,fidelity,(e.g.,full,kinetic,or,hybrid,kinetic/fluid,runs,with,turbulence,and,multispecies,approach).,The,plan,is,for,NEPTUNE,to,provide,a,framework,for,solving,relevant,physics,models,,and,a,user-friendly,Domain-Specific,Language,(DSL),for,doing,this.,This,allows,UKAEA,to,develop,its,own,physics,models,in,a,manner,significantly,independent,of,NEPTUNE,development,and,code,distribution,,see,Figure,1.,This,is,the,same,approach,as,currently,used,by,UKAEA,for,BOUT++,,where,UKAEA,has,ownership,of,physics,models,in,the,STORM,software,,while,other,organizations,have,ownership,of,the,BOUT++,framework.,Project,NEPTUNE,intends,to,provide,a,suite,of,examples,of,physics,models,as,part,of,the,code,distribution.,As,addressed,in,§3,,there,is,also,development,of,a,physics,model,under,NEPTUNE,that,could,be,adaptive,,displaying,a,range,of,fidelities,within,different,regions,of,the,domain,during,a,single,simulation.,4,Figure,1:,Development,of,NEPTUNE,software,via,a,sequence,of,proxyapps.,Numerically,efficiency,,obtained,for,example,through,scalability,to,large,number,of,cores,(given,the,expected,computational,resources,,the,code,should,be,designed,to,take:,∼1,week,for,low,fidelity,parametric,scans;,(cid:46)1,month,for,medium-high,fidelity,runs,for,ad-,vanced,design;,(cid:46)3,months,for,high,fidelity,physics,studies).,Order,of,magnitude,estimates,for,the,cost,of,code,execution,(see,Annex,Section,A),,indicate,that,these,timings,are,possible,but,challenging.,The,plan,is,to,target,Exascale,simulations,that,can,support,high-fidelity,physics,simulations.,Project,NEPTUNE,aims,to,do,this,in,a,performance,portable,fashion,using,abstraction,layers,to,separate,the,physics,from,the,computation,details.,However,,the,challenges,of,Exascale,mean,that,a,degree,of,specialization,of,the,code,towards,available,Exascale,machines,is,expected.,At,some,point,this,will,probably,entail,trade-offs,that,are,detrimental,to,performance,on,smaller,ma-,chines.,Despite,this,,we,still,anticipate,that,the,software,should,be,reasonably,performant,for,small-scale,runs.,Focus,on,stability,of,the,code,,using,(preferably),unconditionally,stable,numerical,schemes,and,capability,to,diagnose,and,re-start,failed,runs.,Ensure,a,small,failed,simulation,rate,for,common,configurations.,The,focus,will,be,on,accuracy,rather,than,stability.,An,accurate,so-,lution,will,be,a,stable,one,,whereas,the,converse,is,not,true.,The,use,of,bifurcation,tracking,techniques,is,expected,to,help,with,numerical,stability.,Moreover,,the,use,of,ensemble,techniques,(as,part,of,uncertainty,quantification),should,provide,information,on,stability,as,a,function,of,pa-,rameters,,as,well,as,making,it,likely,that,at,least,a,subset,of,calculations,produces,usable,results.,In,addition,,there,are,some,planned,technical,solutions,for,diagnosing,problems,with,runs.,The,simplest,functionality,is,to,allow,users,to,change,parameters,when,restarting,a,job,using,check-,point,files.,The,code,can,also,be,made,to,automatically,check,input,files,(to,catch,user,mis-,5,spellings),,and,to,output,a,file,containing,the,parameters,that,were,actually,used,in,a,simulation,(in,case,some,were,accidentally,overwritten).,Simulations,may,also,be,given,a,Universally,Unique,Identifier,(UUID),to,allow,provenance,tracking,of,simulations.,Provide,capability,to,model,exhaust,physics,all,the,way,from,sheath,limited,to,strongly,detached,regimes.,This,capability,follows,from,(1),the,implemented,physics,models/boundary,conditions,,and,(2),the,lengthscales,the,code,can,resolve,in,simulations,of,feasible,run,times.,Project,NEPTUNE,anticipates,that,this,will,be,feasible.,See,§3,for,further,details,for,the,physical,models.,Modern,software,design,with,modular,approach,(independent,and,efficient,libraries).,Project,NEPTUNE,is,certainly,adopting,a,modular,approach,to,software,design.,This,is,crucial,for,en-,abling,many,of,the,desired,features,,as,noted,below.,The,use,of,reliable,third-party,libraries,is,also,vital,for,enabling,a,small,team,of,developers,to,leverage,the,work,of,others,,and,to,allow,code,flexibility,and,ease,of,prototyping.,Ability,to,integrate,with,other,codes,(e.g.,with,IMAS).,This,feature,is,anticipated,,and,will,be,facilitated,by,writing,the,code,in,object-oriented,C++.,Integration,with,IMAS,(and,other,data,formats/standards),can,be,achieved,by,writing,a,module,to,translate,between,NEPTUNE’s,internal,data,structures,and,IMAS,format.,NEPTUNE,developers,are,involved,in,TSVV,software,which,will,also,integrate,with,IMAS,,so,will,have,experience,in,this,area.,Modern,visualization,tools,Integration,with,modern,visualization,tools,is,not,specifically,ad-,dressed,in,the,science,plan.,However,,this,is,enabled,by,using,standard,data,formats,such,as,netCDF/HDF5.,Auxiliary,tools,(similar,to,BOUT++’s,xBOUT,library),could,also,be,developed.,The,issue,of,in,situ,visualization,will,also,be,important,at,Exascale,,with,the,need,to,interrogate,large,quantities,of,data,without,moving,it,,perhaps,during,a,simulation.,Project,NEPTUNE,does,not,have,specific,plans,for,enabling,this.,However,,the,need,for,this,will,be,widespread,,and,we,expect,third-party,tools/libraries,to,become,available,to,support,this,,particularly,in,C++.,Accessibility,(output,easily,catalogued,and,interrogated,big,data),Given,the,constraint,of,producing,Exascale,volumes,of,data,,it,is,expected,that,NEPTUNE,will,default,to,using,the,Met,Office,practice,of,only,saving,the,files,necessary,for,repeating,a,simulation,,rather,than,full,outputs.,It,is,intended,that,key,aspects,will,be,captured,by,surrogates,,descriptions,of,which,will,be,saved,and,indexed.,Users,however,will,be,able,to,choose,to,output,more,data,and,to,define,custom,diagnostics.,A,modular,approach,to,software,design,and,the,use,of,standard,libraries,will,ease,the,implementation,of,these.,In,time,,there,will,likely,be,a,move,towards,creating,simulation,databases,in,preference,to,repeating,expensive,simulations.,Such,projects,are,nascent,,but,we,have,collaborators,who,are,working,in,6,this,area.,Again,,the,modular,approach,and,use,of,standard,data,structures,will,enable,interfacing,with,such,databases,as,the,technology,matures.,Version,control,and,user,support.,Version,control,is,a,fundamental,part,of,modern,software,development,,and,will,certainly,be,used,in,NEPTUNE.,More,generally,,the,project,will,use,best,software,practices,,including,protected,branches,,peer,reviewed,pull,requests,,issue,trackers,and,automated,testing.,The,main,code,contributors,are,familiar,with,such,practices;,we,have,heavy,involvement,from,the,projects,BOUT++,and,Nektar++,which,have,very,high,quality,software,prac-,tices.,Project,NEPTUNE,also,have,involvement,from,UKAEA,RSEs.,User,support,will,be,provided,through,issue,trackers,,a,project,Slack,channel,,and,where,relevant,,through,training,sessions.,Project,NEPTUNE,anticipates,supporting,several,classes,of,user,,from,those,with,limited,software,knowledge,,to,users,with,appreciation,of,different,numerical/algorithm,choices,,through,to,numerical/software,specialists,who,might,edit,the,code,on,a,granular,level.,Support,for,such,a,wide,range,of,uses,is,enabled,by,a,highly,modular,separation-of-concerns,approach.,7,3,Physics,model,3.1,General,requirements,Equations,need,to,be,applicable,to,arbitrary,aspect,ratio,devices.,The,equations,employed,will,not,generically,make,the,assumption,of,small,inverse,aspect,ratio.,The,collision,operators,between,plasma,components,,plasma,and,impurities,and,plasma,and,neutrals,have,to,be,sufficiently,accurate,to,properly,describe,the,radiation,generated,and,the,energy,transfer,between,species.,These,operators,may,be,included,in,the,model,being,derived,in,FM-WP2,,but,at,this,stage,simpler,model,operators,are,being,used.,Photon,opacity,effects,need,to,be,included,in,the,model.,The,treatment,of,effects,due,to,Initial,implementation,radiation,are,discussed,in,Annex,A,of,ref,[2],(“the,equations,document”).,will,account,only,for,usage,(1),the,calculation,of,source/loss,terms,,with,usage,(2),the,production,of,synthetic,spectra,,depending,very,much,on,input,from,experimentalists,,as,anticipated,in,the,science,plan,[1,,p˙,11].,The,equations,need,to,be,capable,of,dealing,with,multiple,species,in,non-trace,amounts,(at,least,D,,T,,He,and,seeding,impurities).,The,models,being,derived,support,distribution,functions,for,multiple,species.,The,equations,should,not,rely,on,the,Boussinesq,approximation.,The,model,derived,in,FM-,WP2,does,not,use,the,Boussinesq,approximation.,Technically,,this,means,NEPTUNE,will,need,to,be,able,to,invert,three-dimensional,elliptic,operators,with,non-constant,coefficients.,This,capability,will,be,available.,The,code,should,evolve,both,the,electron,and,ion,energy,(temperature).,This,is,the,case,with,the,FM-WP2,model.,It,would,be,acceptable,to,have,only,axisymmetric,equilibria,,potentially,corrected,through,small,perturbations.,This,is,answered,by,the,discussion,in,Section,5.,3.2,High,fidelity,simulations,“In,high,fidelity,simulations,,kinetic/fluid,transition,for,both,plasma,and,neutrals,has,to,be,properly,captured,,potentially,using,a,multi-region,approach,exploiting,different,models,in,different,parts,of,the,machine,could,be,considered,(for,both,neutrals,and,plasma);,Boundary,conditions,need,to,consider,improved,sheath,physics,(collisional,&,8,Figure,2:,NEPTUNE,software,will,use,finite,elements,and,particles,to,represent,different,atomic,species,as,needed.,shallow,angles);,Ideally,,the,model,should,be,able,to,treat,de-magnetized,ions,in,the,di-,vertor,region;,Electromagnetic,effects,should,be,included,,but,a,perturbation,approach,would,be,acceptable.”,The,Science,Plan,states,that,“FM-WP2,and,FM-WP3,will,concentrate,upon,development,of,the,two,close,coupled,models,of,the,NEPTUNE,programme,,specifically,FM-WP2,around,the,inclusion,of,kinetic,effects,into,existing,and,new,edge,plasma,models,,and,FM-WP3,of,particle,based,models,for,describing,the,region,outside,and,just,inside,the,plasma,(neutral,atoms/molecules,and,partially,ionized,impurities).”,See,Figure,2.,In,FM-WP2,,a,novel,“moment-based”,approach,is,being,developed,(for,both,plasma,species,and,neutrals).,This,approach,is,a,variant,on,gyrokinetics,(though,at,present,,the,derivation,exists,only,for,drift,kinetics).,Instead,of,the,stationary,background,Maxwellian,of,the,usual,gyrokinetics,,this,approach,uses,a,dynamically-varying,background,Maxwellian,,where,the,particle,density,,bulk,velocity,and,temperatures,are,allowed,to,vary,with,time.,The,result,is,a,hybrid,approach,,where,the,software,evolves,both,a,fluid,system,and,a,modified,kinetic,system.,One,of,the,benefits,of,this,approach,is,that,it,gives,a,natural,means,to,capture,the,fluid/kinetic,transition,,by,switching,between,the,fluid+kinetic,and,fluid-only,descriptions.,Moreover,this,approach,allows,the,software,to,detect,which,of,the,fluid,and,kinetic,descriptions,is,valid,in,any,region,based,on,the,properties,of,the,modified,distribution,function,,and,therefore,to,automatically,evolve,the,relevant,model.,The,favourable,properties,of,this,approach,are,valuable,,but,as,with,any,novel,approach,there,is,an,inherent,risk,of,the,scheme,not,working.,Thus,as,described,in,ref,[2,,§,1.1],,in,the,event,that,this,approach,is,not,feasible,,the,kinetic,calculations,will,use,a,Particle-in-Cell,(PIC),approach.,While,full,orbit,PIC,is,potentially,extremely,expensive,relative,to,gyrokinetics,,it,has,been,very,well-studied,both,in,terms,of,theory,and,numerical,implementation.,Moreover,the,issue,of,how,to,treat,the,transition,from,fluid,to,a,particles,in,a,coupled,model,is,well-understood,,at,least,in,classical,fluid,dynamics.,Relevant,sheath,physics,boundary,conditions,are,being,derived,as,part,of,this,work,,including,shallow,angles,and,collisions.,Ions,which,exit,the,domain,re-enter,as,neutrals,with,the,Knudsen,9,cosine,distribution.,While,the,current,derivation,is,electrostatic,,there,is,nothing,which,precludes,the,derivation,of,an,electromagnetic,model.,3.3,Neutrals,and,impurities,Different,levels,of,multispecies,capabilities,should,be,considered.,The,framework,nature,of,the,code,means,this,will,be,the,case.,In,medium,to,high,fidelity,models,,neutrals,and,heavy,species,should,be,treated,fully,kinet-,ically,(the,former,have,potentially,low,collisionality,and,they,are,not,bound,by,the,magnetic,field,,the,latter,have,a,large,Larmor,radius).,Development,of,a,neutral,gas,and,impurity,model,is,ongoing,under,FM-WP3.,Page,7,of,the,Science,Plan,states:,“Kinetic,levels,of,complexity,are,.,.,.,necessary,.,.,.,for,modelling,the,burning,plasma,regime,,due,to,the,inherent,uncertainty,in,the,fluid,codes.,The,plasma,in,a,fusion,reactor,may,well,behave,significantly,differently,to,plasma,in,existing,devices,because,it,will,in,general,contain,two,main,ionic,species,(Deuterium,and,Tritium),,neutral,fuel,particles,and,ionised,Helium,ash,(or,alpha,particles),,as,well,as,impurity,ions,originat-,ing,from,the,wall.”,That,is,,kinetic,models,will,be,derived,and,implemented,,though,it,is,hoped,that,this,will,facilitate,the,development,of,fluid,models.,In,high,fidelity,models,,dynamical,neutral,evolution,on,the,turbulence,time,scale,would,be,preferable,,if,possible.,High-fidelity,simulations,will,use,a,kinetic,model,for,neutrals,where,appropriate.,Ability,to,model,pumps,(either,directly,or,via,pumping,surfaces),should,be,included.,Pel-,lets:,the,code,should,enable,simulation,of,,or,coupling,to,models,that,can,model,,pellet,fuelling.,Models,for,these,aspects,are,not,included,in,the,Science,Plan.,As,we,will,use,an,unstructured,mesh,,it,will,be,possible,to,describe,arbitrary,pumping,surfaces.,The,role,of,sources,and,sinks,is,recognised,to,be,crucial,in,NEPTUNE,physics,so,that,modelling,of,pellets,as,a,source,will,be,possible.,The,tool,CWIPI,(Coupling,With,Interpolation,Parallel,Interface),may,be,used,for,coupling,to,more,complicated,pellet,models.,10,4,Physics,capabilities,“The,code,needs,to,be,able,to,give,reliable,predictions,of:,•,Divertor,loads:,•,Reliable,calculation,of,upstream,particle,and,heat,flux,profiles:,proper,drift,physics,and,upstream,turbulence;,•,Divertor,turbulence:,turbulence,spreading,in,the,divertor,region,,effect,of,magnetic,shear,next,to,the,X-point(s),to,understand,upstream/downstream,connection;,•,Multifluid,capacity,to,model,radiation,and,detachment,physics;,•,Reliable,calculation,of,the,electric,field,(collisionless,physics,near,the,separatrix,,proper,reflection,of,neutrals,at,the,target);,•,Able,to,capture,in/out,and,top/down,asymmetries,(geometry,,drifts,,radiation,and,de-,tachment),•,Wall,loads:,•,Should,be,able,to,predict,filamentary,transport,and,role,of,hot,ion,confinement,(wall,erosion),•,Should,calculate,radiation,and,neutral,loads,(may,require,dedicated,modules,,same,for,divertor,loads);,•,Impurity,transport,,pumping,and,fueling:,•,Ability,to,track,low,(He,Be),,medium,(C,,N,,Ne),and,high,Z,impurities,(W,,Ar,,Xe),with,multiple,charge,states;,•,Reliable,kinetic,modelling,of,neutrals,to,assess,fueling,and,pumping,capacity;,•,Ability,to,handle,non-trace,species,(D,,T,,He,,seeded,species),,which,requires,new,closures,for,the,equations,(if,fluid,,beyond,Braginskii,=⇒,Zhdanov,or,better);,•,Accurate,model,of,friction,forces,(turbulence,+,neoclassical,on,open,field,lines);,•,In,high,fidelity,models,,the,code,should,be,able,to,simulate,localized,gas,puffs,,via,injection,of,neutral,particles.,•,Dust,the,code,should,enable,coupling,to,codes,to,simulate,dust,generation,,transport,and,ablation,,via,exchange,of,fluxes,and,sources.”,Physics,models.,Many,points,in,this,section,relate,to,the,physics,model.,As,we,have,alluded,to,above,,the,actual,physics,model,used,is,the,responsibility,of,the,user;,so,,for,example,,it,will,necessary,for,users,to,derive,an,accurate,model,for,turbulent,friction.,Moreover,,as,NEPTUNE,will,initially,be,an,edge,code,,only,electromagnetic,radiation,from,the,edge,plasma,will,be,calculated,,and,an,additional,model,will,be,required,for,radiation,for,the,core,plasma.,Nonetheless,,we,plan,to,facilitate,models,which,have,the,listed,properties.,In,particular,,our,meshing,approach,will,allow,accurate,representation,of,the,walls,and,divertor.,Thus,powerful,and,flexible,source/sink,models,may,be,used,,for,both,volumes,and,surfaces.,11,Figure,3:,Project,software,will,integrate,a,range,of,models,of,different,complexity,,here,indicated,by,their,dimensionality.,NEPTUNE,code,will,also,be,capable,of,representing,scales,on,which,filamentary,transport,has,been,calculated,to,occur.,The,code,will,only,produce,fluxes,however,,and,it,will,be,up,to,the,user,to,calculate,wall,erosion.,Validation,,Verification,and,Uncertainty,Quantification,(VVUQ).,Naturally,,when,the,solution,of,a,problem,is,unknown,,it,is,difficult,to,assess,whether,the,provided,answer,is,reliable,as,re-,quested,in,the,first,line,of,the,current,section.,Therefore,we,are,integrating,NEPTUNE,with,a,suite,of,tools,for,VVUQ,to,enable,validation,of,code,outputs,against,experimental,results,,and,pro-,vide,a,error,bars,for,code,outputs,due,to,the,uncertainty,in,the,code,inputs.,Aa,allowed,by,error,estimates,,models,of,different,complexity,will,be,used,to,predict,key,properties,of,the,SOL,,see,Figure,3.,12,5,Geometry,“Ability,to,handle,complex,topologies,and,novel,geometries:,•,Capacity,to,treat,different,topologies,with,multiple,X-points,(>2),,possibly,in,a,dynamic,way,,or,at,least,implemented,in,a,way,that,does,not,preclude,time-varying,equilibria,being,modelled,in,future;,•,Ability,to,handle,singularities,in,the,grid,(null,points),or,to,develop,accurate,scheme(s),that,do,not,have,singularities;,•,Ability,to,interface,with,3D,CAD,designs,of,the,machine;,•,Capability,to,handle,conformal,grids,that,go,all,the,way,to,the,wall,for,both,neutrals,and,plasma;,•,Capability,to,treat,subdivertor,structures,(only,neutrals).”,NEPTUNE,will,use,a,spectral/hp,finite,element,approach.,This,allows,considerable,flexibility,in,meshing,,with,elemental,tetrahedra,,hexahedra,or,prisms,being,used,to,describe,complex,geome-,tries.,In,addition,to,refinement,of,the,elemental,grid,sizes,(h-adaptivity),,the,order,of,the,piecewise,polynomial,basis,functions,used,on,each,element,may,also,be,changed,(p-adaptivity).,The,produc-,tion,of,finite,element,griddings,conforming,to,CAD,descriptions,is,standard,for,virtually,all,meshing,packages.,Project,NEPTUNE,will,specially,aim,to,use,the,small,number,of,packages,that,may,produce,finite,elements,with,curved,edges,and,faces,to,exploit,fully,the,higher,order,basis.,This,gives,a,framework,which,can,achieve,spectral,convergence,on,complicated,,conforming,grids,,while,still,being,able,to,handle,discontinuities,in,the,solution.,Should,it,prove,necessary,to,produce,a,meshing,conforming,to,surfaces,of,an,equilibrium,magnetic,field,,then,because,the,finite,element,approach,does,not,require,a,structured,grid,,it,should,be,able,to,treat,arbitrary,geometries,and,topologies,,in,particular,including,multiple,X-points.,The,approach,could,be,extended,by,further,use,of,adaptive,meshing,to,allow,for,time-varying,equilibria.,A,Annex,A:,Order-of-magnitude,estimates,for,tokamak,edge,modelling,Suppose,plasma,number,density,n,≈,1018,m−3.,Order,of,magnitude,dimensions,are,L,≈,0.1,m,for,SOL,thickness,,reactor,minor,and,major,radii,say,a,=,3,m,and,R0,=,10,m,,so,the,volume,of,SOL,≈,4π2aR0L,≈,100,m3.,It,follows,that,the,total,number,of,electrons,≈,1020.,The,shortest,timescale,is,inverse,eB/me,,the,electron,cyclotron,frequency,,where,the,ratio,of,charge,to,mass,for,the,electron,is,|e|/me,=,1.76,×,1011,C,kg−1,,and,B,≈,10,T,,so,τBe,≈,10−12,s.,Hence,the,number,of,particle-steps,to,evolve,1,s,of,physical,time,is,1020+12+1,(assuming,of,order,10π,timesteps,per,orbit),,which,assuming,1000,flop,per,update,,needs,a,total,of,1036,flop.,Thus,to,complete,a,computation,in,1,s,on,Exascale,machine,,only,one,1,particle-step,in,1018,is,allowed.,This,implies,for,example,only,100,superparticles,in,the,volume,can,be,used,supposing,each,has,a,weight,1018,,which,is,unlikely,to,be,adequate,because,electrostatic,and,other,effects,will,produce,a,13,noise,level,that,swamps,any,physical,effects.,However,if,3,or,4,months,(approx.,107,s),are,allowed,,then,a,calculation,with,109,particles,may,be,performed,if,memory-access,bandwidth,constraints,can,be,satisfied,,when,the,noise,levels,may,be,manageable.,The,situation,may,be,shown,to,be,a,million,times,easier,for,neutrals,considered,separately,,as-,suming,neutral,density,n0,=,n,,particle,mass,mp,and,temperature,T0,=,10,eV,,for,a,timescale,of,τ0,=,Lmf,p/v0,where,the,mean,free,path,Lmf,p,≈,L,and,the,neutral,speed,typically,is,v0.,For,then,v0,=,(cid:112)|e|T0/mp,=,(cid:112)|e|/me,·,(cid:112)me/mp,10,≈,3,×,104.,Thus,T0,,ie.,v0,≈,4,×,105,×,(1/40),×,τ0,≈,10−6,s,,ie.,a,million,times,longer,than,the,electron,cyclotron,timescale.,√,√,Suppose,a,fluid,model,is,employed,instead,,ie.,the,electron,distribution,is,represented,by,its,first,3,If,the,electron,temperature,Te,≈,10,eV,,then,the,thermal,speed,VT,e,≈,40v0,≈,106,m,moments.,s−1.,Supposing,the,SOL,to,be,sampled,at,a,uniform,1,mm,interval,,then,the,number,of,sample-,points,≈,1011,,and,the,timestep,for,an,explicit,scheme,≈,(10−3/106),≈,10−9,s,,so,the,number,of,sample-point,updates,is,1011+9.,Assuming,1000,flop,each,update,,this,means,one,second,of,physical,time,needs,1023,flop,or,105,s≈,1,d,of,Exascale,machine,time,,if,memory-access,bandwidth,constraints,can,be,satisfied.,If,an,implicit,scheme,is,used,to,simulate,plasma,ions,as,a,fluid,on,a,drift,type,timescale≈,L/VT,i,,then,possibly,the,timestep,τi,≈,τ0,≈,10−6,s,,ie.,a,thousand,times,larger,,and,calculations,lasting,only,a,few,minutes,might,suffice.,Another,way,of,looking,at,this,is,to,suppose,that,numerical,problem,is,D-dimensional,,1000,flop,are,needed,for,each,sample,update,and,ND,samples,per,spatial,dimension,and,N,2,D,time,samples,are,allowed.,Then,to,update,such,a,model,in,1,s,requires,N,D+2,D,≈,1015.,Thus,if,D,=,3,,N3,≈,1,000,,and,N5,≈,100.,It,seems,that,accuracy,controlled,,unstructured,,implicit,fluid,models,should,be,possible,,although,for,the,more,complex,models,1000,flop,per,update,may,be,an,underestimate,by,orders,of,magnitude.,References,[1],W.,Arter,,L.,Anton,,D.,Samaddar,,and,R.,Akers.,ExCALIBUR,Fusion,Mod-,Technical,Report,CD/EXCALIBUR-FMS/0001,,UKAEA,,elling,System,Science,Plan.,2019.,https://www.metoffice.gov.uk/binaries/content/assets/metofficegovuk/pdf/,research/spf/ukaea-excalibur-fms-scienceplan.pdf.,[2],W.,Arter.,Equations,for,EXCALIBUR/NEPTUNE,Proxyapps.,Technical,Report,CD/EXCALIBUR-FMS/0021-1.01-M1.2.1,,UKAEA,,2021.,14

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