Lattice Boltzmann Method

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Adam Hill
6 years ago
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1 K K

2 K

3 K K K Q R S K UWV K K V _ K

4 hysis Kinti hory o ss hory o mny prtil systms oltzmnn ution ollision ruls isrt ynmil Systms llulr utomt m o i numr o prtils n init vloity sp linriztion o ollision intrl hpmn nsko xpnsion moii hpmn nsko xpnsion ontinuum hnis lui hnis vir Stoks ution symptoti nlysis hory o hyproli s Rlxtion shms tti s utomt Simultion o lows with oolns oolns rls tti oltzmnn tho

6 y x vloity vloity proils o osilltin wll t irnt tims visosity nu runy u iusiv slin t t t t nlyti silltin Wll on Uniorm ris ousti Slin im nos nos nos nos nos ximl solut ol rror in im ximl solut ol rror in silltin Wll on Uniorm ris iusiv Slin nos nos nos nos S R _ R _ R _

7 K Q R S UV W _ h ikj ikl m n o V W p K U o V W sr ut v tw yx z { }~ K ƒ Q i K Š K Œ ~ Ž š žœ Ÿ

8 R W K š žœ Ÿ { K K K K K K K K K K Q K K } { { o V K K K K K K K R

9 W K K Q W K K W K K Q W K K o o W K š žœ Ÿ

10 K Œ K K š žœ Ÿ

11 Ž { z z š žœ Ÿ

12 Œ z š žœ Ÿ

13 Œ } y y Œ y y š žœ Ÿ

14 K Q R S U VW S _ S S K S S h S S ji S _ S k l l S S h S S ji m nop r s t un v xp w zy o {p r s t un xp w zy o {p } p z t ~s n y t t tp t s S k S k ƒ ƒ K t r u o y s zt o zn o {p n { zr o s m Š ŒŽ Œ Š š Œ œš œ Š

15 šš Œ Œ Š Œ K Q R S UV W R K Q R W R K W V _ VU Q U VU Q U RV U h h i j k _ l m n _ l _ l ou _ l p r s K _ l U _ l t _ l p r s K Š ŒŽ Œ Š š Œ œš œ Š

16 Œ œš œ Œ Š Š ŒŽ Œ Š š Š R t s S u R t s S u R t s S u xy vloity lvl lins lur Vortiity mxrot u minrot u rssur mx min šš Œ Œ

17 Œ šš Œ Š Œ R t s S u R t s S u xy vloity lvl lins lur Vortiity mxrot u minrot u R t s S u R t s S u xy vloity lvl lins lur rot u mxrot u minrot u š K

18 š K K S K K K K K S K K K K K Q R S U V V W S h i _ jlk m m no p r s _ o j h m t m j u _ h v r o j m u m w h x u i v _v u o r yo m u v n z n v j yo _ i { h n h u m m _v u o m h} n h ~ h h x u i v _v u o r yo m j m h o v t ot h} u v n _v u _ u h n v p u t vm r u o z h} t i _ j h h n _ z m o n t _v u o h t j h i m _ j { m h š

19 S Q h S R S VU W S K ylor Vortx Strm ins t t R s S u t x R s S u t R s S u t numri nlyti numri nlyti numri nlyti numri nlyti ylor Vortx rosstion o v lon x xis throuh ntr ylor Vortx rosstion o prssur lon x xis throuh ntr ylor Vortx r lu _ S S š

20 h _ j m o i s h s yo m j h} o u v oh h t t h K Q _ K SRQ U hr V W W

21 h K K _ K SRQ U hr V W W

22 h K K _ K SRQ U hr V W W

23 h K K K SRQ U R V W W

24 W W K K SRQ U R V K K K

25 W W K olly Rin ri or ylor Vortx K K SRQ U R V

26 K K

27 V W K y y y y y y V y UV UV V VW U UV K Q R S Q Q UV VW VS UV outt on uniorm ri x vloity t nu u numri nlyti x rror o outt on uniorm ri t nu u numri u nlyti Uniorm ri nos trtions x rror o outt on rin ri t nu ors in u numri u nlyti ommon intr no no intrpoltion x rror o outt on rin ri t nu u numri u nlyti ors in ntrpoltion Splin x rror o outt on rin ri t nu u numri u nlyti x rror o outt on rin ri t nu ors in ntrpoltion ui ntrpoltion inr u numri u nlyti x rror o outt on rin ri t nu ors in ntrpoltion nrst u numri u nlyti ors in

28 rivn vity R s normliz vloity il rivn vity R sumshs rn s r s lu s rivn vity R ross Stion o x Vloity y oorint rn s r s lu s ross Stion o x Vloity U lon y xis throuh ntr x x x x x x x x x x x vloity

29 rivn vity R ri x vl ins o x rsp y vloitis lur rivn vity R vl ins o x rsp y vloity lur rivn vity R ri x vl ins o x rsp y vloity lur outr ri s mil ri s innr ri s rivn vity R ri x url o Vloity rivn vity R sumshs Vortiity rivn vity R ri x url o Vloity mxrot u minrot u

30 R t s S u R t s S n u S u R t s S u vloity il o th ylor vortx t t nu u ylor Vortx on Rin ri nu u t x uniorm ri x uniorm ri rin ri with splin intrpoltion rin ri with linr intrpoltion vloity il o th ylor vortx t t nu u rl rror o x vloity tim

31 R t s S u R t s n S u R t s S u R t s S u R t s n S u R t s S u

32 R t s S u R t s n S u R t s S u R t s S u R t s n S u R t s S u Stunt Vrsion o

33 rivn vity R ri x ivrn o Vloity rivn vity R ri x ivrn o Vloity rivn vity R ri x ivrn o Vloity

34 rivn vity R ri x vition rom uilirium rivn vity R ri x vition o uilirium rivn vity R ri x vition rom uilirium

An Example file... log.txt

An Example file... log.txt # ' ' Start of fie & %$ " 1 - : 5? ;., B - ( * * B - ( * * F I / 0. )- +, * ( ) 8 8 7 /. 6 )- +, 5 5 3 2( 7 7 +, 6 6 9( 3 5( ) 7-0 +, => - +< ( ) )- +, 7 / +, 5 9 (. 6 )- 0 * D>. C )- +, (A :, C 0 )- +,