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- Gerard Wilson
- 5 years ago
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1 , #*. ( )*. *,#, $.,.., - ( )*. *,#, &$C.,!. *. &$'.( )*.,*-( 9!!!"#$ %"#$"$ #!&"#' %$! %"!!' $!$(!#) #!& $##!&*# %# "$!"'..,... +,-.. / - -4 / $D%'EF("!E!&$!G &.- **E -.)*$H B( B(.+*$H B$ ' $ D* $DB *$%$ -.%'E,. $#D*$ B$I'.-!(" DB *J **E +.!' #.( - H-, &$-*E** D #'"#!(K, &$%*$D$-*, * $!*$- ( $H $DB*$!(. : &.#' -*E**E :- F- M($#! -#D*$ *$B,K+ - '.+.*., E# &.-$E(" -! #.( H $ - '.+.*., N$ $-*KF, N$ -*$!.- '"* $!E%* **K -($B$ '"*$!( &$ -!) #.( E), E# G,(",+!(", $D- ED** (Sh M(,)'E, Fr 8,, Eu 5S', Re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h M(,)'E, Fr 8,, Eu WS', Re S*$'"!). 9#D* -$DB$I*$!(" &$',+ *.E (#.) *$B.,KN.) - '.+.* * $!*$- $G$GN **$%$ D#$*!$)* *.E. E!',+ - - *$B.,KN. - '.- +.*V B$%,( * -)$.(" % $B (.+!#. DB V.!!', BV)!.!( B, +($,#DV- ( * -$DB$I*$!(" B$ '.$-*.E G D!$G'K *.E % $B (.+!#$%$ &$$G.E. : B$ '.$-*.,!*.I *. B *$!(., -($B$ '"*$!(",.!#I **$ B$ '.$-*.. A.I. Brunekin, M.V. Maimov. Reducing he dimension of he simulaion sace by bringing a mahemaical model o he self-similar, according o he crieria, form. The mehod of reducing he iniial mahemaical model o dimensionless form is considered. The ossibiliy of reducing he number of crieria, as comared wih he amoun rediced by he heory of dimension, is shown. On he eamle of he Navier-Sokes equaion he normalizing values, reducing all he crieria o he value of, which is equivalen o he achievemen of self-similariy a all involved in he decision crieria (Sh Srouhal, Fr Froude, Eu Euler, Re Reynolds number), are indicaed. The ossibiliy of normalizing hese values based on he generalized conservaion law is oined ou. In some cases, he normalizing values can eclude geomerical sizes of he sysems under sudy, which indicaes he ossibiliy of modeling wihou comlying wih geomeric similariy. Keywords: simulaion, reduced dimensions, self-similariy, disored simulaion. &#(.# &$ #(.$-*.E ( )*.+!#.)!.!( B (M) J.$#$.!&$'"D,K(!E.) B$ '. (B( B(.+!#.. C.D.+!#. ), i#!&.b *(V * #$($VB. &$D-$'EK( &$%*$D.$-(" )#- (.!(.#.!$D- B$%$ $Gj #(. k($gv &.B * *. B$ '. -'$ -V%$V, $* $'I* $G'(" E$B!-$S!(-, -I* S- J.B..D #$($V) E-'EK(!E &$!($(. #-(*$!(" $.%.*',..,!'$I* *.. M &$.!)$- <.7.,* (#.*, 6.. 6#!.B$-,
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9 47 5. A,(( 'D, M.M. <*'.D &$$G.E - ( &'$C.D.# / M.M. A,(( 'D. :$-$!.G.!#: :,#, 98. 8!. References. Sedov, L.I. Meody odobiya i razmernosi v mekhanike [Similariy and dimensionaliy mehods in mechanics] / L.I. Sedov. 9h ediion Moscow, Hunley, H.E. Dimensional analysis McDonald and comany / H.E. Hunley. London, Klayn, S.Dzh. Podobie: riblizhennye meody [Similariy: aroimae mehods] Transl. from English and edied by I.T. Alad'ev, K.D. Voskresenskiy. Moscow, Paankar, S.V. Numerical hea ransfer and fluid flow / S.V. Paankar. Hemishere, Washingon, Kuaeladze, S.S. Analiz odobiya v elofizike [Similariy analysis in hermal hysics] / S.S. Kuaeladze. Novosibirsk, *D *( - ( )*. *,#, &$C.!. *. &$'.( )*.,*-( :D *#$ <.8. $!(,&.' - #.K 6 $#(EGE %.
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