
thet sankhyatmak anukaran

thet sankhyatmak anukaran (dii. aine. ess.) heey sanganakeey drav gatishilatetil (see. eff. dii.) eka anukaran aahe jyamadhye navier-stokes samikarane konatyahi ashantatechya pratimanavina sankhyatmakaritya sodavali jaatat. yacha arth assa qee ashantatechya avkashiy aanee tatpuratya pramananchi sampoorn shreni sodavali jaane aavashyak aahe. sarvat lahan apvyaykari skelpasoon (kolmogorov microscale), avibhajya scale sootra _ 1 paryant, bahutek gatij urja asalelya halchalinshi sambandhit, ashantateche serve avkashiy scale sanganakeey jaalimadhye sodavale jaane aavashyak aahe. kolmogorov scale, sootra _ 2, dware dile jaate
jethe sootra 4 heey gatij snigdhata aahe aanee sootra 5 haah gatij urja apavyay darr aahe. dusarikade, avibhajya praman samanyatah seema atinchya avkashiy pramanavar avalambun asate. 
yaa sankalp aavashyakta purn karnyasathi, vadhiv sootra _ 7 saha dilelya jaalichya dishene sootra _ 6 gunanchi sankhya, asane aavashyak aahe
jenekarun avibhajya praman sanganakeey kshetrat samavisht asel, aanee
jenekarun kolmogorov scaleche nirakaran karata yeil.
tevhapasoon
jethe sootra _ 11 heey vegache mool sarasari varg (aar. emm. ess.) aahe, tethe mageel sambandh soochit karatat qee trimiteey dii. aine. ess. sathee anek jaalidar bindu sootra _ 12 chee aavashyakta asate.
jethe sootra _ 14 hii ashant reinolds sankhya aaheh
tyamule, dii. aine. ess. madheel smrutee sathavan aavashyaktemadhye, reynolds sankhyenusar khoop vegane vaadh hote. yavyatirikt, aavashyak asaleli khoop mothee smrutee pahata, velevar dravanache ektrikaran spasht paddhatidvare kele jaane aavashyak aahe. yacha arth assa qee achook honyasathi, bahutek vivechanachya paddhatinsathi, ektrikaran, sootra _ 16 yaa velechya tappyasah kele jaane aavashyak aahe, jeey itake lahan aahe qee drav kann pratyek tappyat jaali antar sootra _ 7 chaa keval eka ansh halvato. mhanje,
(sootra _ 19 yethe courant sankhya aahe). anukaran kelele ekoon vel antaral samanyatah dilelya ashantata vel praman sootra _ 20 chya pramanat asate
heey sambandh ekatra karane aanee sootra 7 heey sootra 2 chya kramanusar asane aavashyak aahe, vel-ektrikaran payanchi sankhya sootra 24 chya pramanat asane aavashyak aahe. dusarikade, varr dilelya sootra 14, sootra 2 aanee sootra 1 chya vyakhyanmadhun, teey asey aahe qee 
aanee parinami, reinolds kramankacha shakti niyam mhanoon velechya payanchi sankhya dekhil vadhate.
anukaran purn karnyasathi aavashyak asalelya floating-point operationschi sankhya hii jaalichya bindunchi sankhya aanee velechya payyanchya sankhyechya pramanat aahe aanee shevati, operationchi sankhya sootra _ 29 mhanoon vadhate assa andaj konihi lavu shakato.
tyamule, qamee reynold sankhyanvarhi, dii. aine. ess. chee sanganakeey kimmat khoop jaast aahe. bahutek audhyogik anuprayoganmadhye yenanya punarbharan sankhyansathi, dii. aine. ess. sathee aavashyak asaleli sanganakeey sansadhane sadhya upalabdh asalelya sarvat shaktishali sanganakanchya kshamatepeksha jaast asateel. tathapi, ashantatetil moolbhut sanshodhanat thet sankhyatmak anukaran heey eka upayukt sadhan aahe. dii. aine. ess. chaa vapar karoon "sankhyatmak prayog" karane shakya aahe aanee prayogshalet midvane katheen kinwa ashakya asaleli mahitee tyanchyakadun kadhane shakya aahe, jyamule ashantatechya bhautikshastrachi adhik changli samaj houu shakate. tasech, pratyaksh sankhyatmak anukarane vyavharik anuprayogansathi ashantata modelchya vikasat upayukt aahet, jase qee mothya edee anukaranasathi (leesa) up-grid scale models aanee reynolds-sarasari navier-stokes samikarane (rnd) sodavananya paddhatinsathi models. heey 'prayori' chachanyanchya madhyamatoon kele jaate, jyamadhye modelsathi input deta dii. aine. ess. simulationmadhun ghetala jaato kinwa 'postariori' chachanyandvare, jyamadhye modeldware tayar kelelya parinamanchi tulana dii. aine. ess. dware prapt kelelya parinamanshi kelee jaate.