▁Reyn olds ▁number . ▁ ▁One ▁can ▁estimate ▁that ▁the ▁number ▁of ▁floating - point ▁operations ▁required ▁to ▁complete ▁the ▁simulation ▁is ▁proportional ▁to ▁the ▁number ▁of ▁mesh ▁points ▁and ▁the ▁number ▁of ▁time ▁steps , ▁and ▁in ▁conclusion , ▁the ▁number ▁of ▁operations ▁grows ▁as ▁. ▁ ▁Therefore , ▁the ▁computational ▁cost ▁of ▁DNS ▁is ▁very ▁high , ▁even ▁at ▁low ▁Reyn olds ▁numbers . ▁For ▁the ▁Reyn olds ▁numbers ▁encountered ▁in ▁most ▁industrial ▁applications , ▁the ▁computational ▁resources ▁required ▁by ▁a ▁DNS ▁would ▁exceed ▁the ▁capacity ▁of ▁the ▁most ▁powerful ▁computers ▁currently ▁available . ▁However , ▁direct ▁numerical ▁simulation ▁is ▁a ▁useful ▁tool ▁in ▁fundamental ▁research ▁in ▁tur bul ence . ▁Using ▁DNS ▁it ▁is ▁possible ▁to ▁perform ▁" numer ical ▁experiments ", ▁and ▁extract ▁from ▁them ▁information ▁difficult ▁or ▁impossible ▁to ▁obtain ▁in ▁the ▁labor atory , ▁allowing ▁a ▁better ▁understanding ▁of ▁the ▁physics ▁of ▁tur bul ence . ▁Also , ▁direct ▁numerical ▁simulations ▁are ▁useful ▁in ▁the ▁development ▁of ▁tur bul ence ▁models ▁for ▁practical ▁applications , ▁such ▁as ▁sub - grid ▁scale ▁models ▁for ▁large ▁ed dy ▁simulation ▁( LES ) ▁and ▁models ▁for ▁methods ▁that ▁solve ▁the ▁Reyn olds - aver aged ▁Nav ier – Sto kes ▁equations ▁( R AN S ). ▁This ▁is ▁done ▁by ▁means ▁of ▁" a ▁pri ori " ▁tests , ▁in ▁which ▁the ▁input ▁data ▁for ▁the ▁model ▁is ▁taken ▁from ▁a ▁DNS ▁simulation , ▁or ▁by ▁" a ▁posterior i " ▁tests , ▁in ▁which ▁the ▁results ▁produced ▁by ▁the