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PART-A QUES TIO NS

(2 MARKS)

1. What are the important application o! "#$ in en%ineerin%&

2. $i tin%'i h et een conservation an* non-conservation !orm o! !l'i* !lo +

3. Write *o n the con er,ati,e !orm o! the contin'it e.'ation an* e/plain the term

in,ol,e*+

4. What i the ph ical i%ni!icance0meanin% o! the ,ario' term in con er,ation !orm

o! moment'm e.'ation&

5. Write *o n an e/pre ion !or ' tantial *eri,ati,e in "arte ian coor*inate +

6. 1i t o't a*,anta%e* o! panel metho*+

7. E/plain the *i!!ic'ltie o! e,al'atin% the in!l'ence o! a panel at it o n control point+8. What are limitation o! panel metho* &

9. $e!ine (a) "on,er%ence an* ( ) 1a/ e.'i,alence theorem

10. Ela orate the a ic a pect o! the !inite *i!!erence e.'ation +

11. Write *o n the i%ni!icance o! Taylor series expansion.

12. Write *o n the econ* or*er central mi/e* !inite *i!!erence e/pre ion !or

13. E/plain cell-centere* metho*+

14. $e!ine stability in n'merical ol'tion o! !l'i* !lo %o,ernin% e.'ation +

15. $e!ine convergence in n'merical ol'tion o! !l'i* !lo %o,ernin% e.'ation +

16. Write *o n the econ* or*er central mi/e* !inite *i!!erence e/pre ion !or $ heat

con*'ction e.'ation+

17. $i c' the nee* o! 'p in* t pe *i creti3ation+

18. Name the important error that commonl occ'r in n'merical ol'tion+

19. Tran !orm the tea* 4 incompre i le contin'it e.'ation !rom /4 ph ical plane to

26. What i the nece it !or ta%%ere* %ri* in control ,ol'me metho*&

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27. 1i t o't *i!!erence et een fini te volume an* fini te diference metho* +

28. $e!ine peclet number an* tate it importance&

29. What i the nece it o! tron% an* ea5 !orm'lation in o'n*ar ,al'e pro lem &

30. What t pe o! %ri* are %enerall ' e* in #inite 6ol'me Metho*&

PART-7 QUESTION S ( 8 MARK S)

1. (i) What i the nee* !or cla i!ication o! P$E an* ho *o o' cla i! econ* or*er

P$E& 9:;

(ii) What are the *i creti3ation techni.'e an* ho *o o' *i creti3e the e.'ation !or

' onic an* 'per onic !lo & 9:;

2. Write *o n the elliptic4 para olic an* h per olic partial *i!!erential e.'ation a

applica le to comp'tational !l'i* * namic +

3. (a) $eri,e the contin'it e.'ation in *i!!erential !orm !or in compre i le !lo + 9

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tran !ormation& 9:;

(ii) Ill' trate the a ic i*ea o! al%e raic tran !ormation o! t o *imen ional4 tea* 4

o'n*ar la er !lo o,er !lat plate ith 'ita le tran !ormation relation + 9:;

11. E/plain the %ri* %eneration techni.'e a e* on P$E an* 'mmari3e the a*,anta%e

o! the elliptic %ri* %eneration metho*+

2+ (i) What i the nee* !or %ri* %eneration& Mention the *i!!erent %ri* %eneration

techni.'e an* li t *o n their relati,e merit an* *emerit + 98;

(ii) E/plain ho %ri* %eneration i achie,e* n'merical ol'tion o! elliptic Poi on ?

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20. St'* the ta ilit eha,io'r o! econ* or*er a,e e.'ation 6on-Ne'man ta ilit

metho*+

21. (i) E/plain e/plicit 1a/-Wen*ro!! cheme o! time *epen*ent metho* + 9:;

(ii) $i c' cell centere* !orm'lation in #inite 6ol'me Techni.'e + 9:;

22. What are .'a*rilateral 1a%ran%e element an* i oparametric element in #EM&

23. $ra a !lo chart an* *e cri e SIMP1E al%orithm !or t o-*imen ional laminar

tea* !lo e.'ation in "arte ian co-or*inate +

24. Sol,e the impli!ie* St'rn-1io,ille e.'ation@

With o'n*ar con*ition (o characteri tic line are relate* to "o'rant n'm er !rom ta ilit ,ie & E/plain+

34. (a) $eri,e

9:;

( ) Write hort note on

(i) "on i tenc (ii) "on,er%ence (iii) Sta ilit 9:;

35. (a) $eri,e the !or ar* an* central *i!!erence4 appro/imation to the !ir t *eri,ati,e4

alon% ith the lea*in% error term+ 9:;

( ) $eri,e the ta ilit criterion ("#1 con*ition ) !or the I t or*er a,e e.'ation+ 9:;

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D + #or the !ollo in% e.'ation@

(a) O tain *i creti3e* !orm o! !inite *i!!erence .'otient+( ) U in% e/plicit metho*4 rite al%e raic e.'ation !or F G F %ri*+(c) E/plain an n'merical metho* to o tain ol'tion !or temperat're + 9 8;

D8+ E/plain the !ollo in% ith merit an* *emerit +

9 8;

a) E/plicit metho* ) Implicit metho*c) Semi-implicit metho*

DH+ $e cri e the Mac"orma5 ? techni.'e !or e,al'atin% the *en it at time tep (t J t)+

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CFD-AE2402