橡紙目次第１章1

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3 AstA A st t Q + = 0 Ast A st t y = bst ( y) t (1.1) (1.) y 1 Q + = 0 t b st q (1.3) (1.3) b st y Q + = q t (1.4)

4 Abbott(1979) Q Q y + ( β ) + ga + gas f = 0 t A q u (1.5) Q Q y + ( β ) + ga + Sf uq q = 0 t A β (1.6) b uhdz z z 0 β = (1.7) u A Q u = A u z 1 h z = uyzdy (, ) h z=z 0 z (1.3)(1.5) (1.4)(1.6) A st A (1.3)(1.5) (1.4)(1.6) b A st st q 1. ρ gas f 3

5 S f Q = K S f (1.8) K = Kh ( ) S Manning u = R S f ; Q AR S f n = n (1.9) n 13 ( s/ m ) Chezy) u = C RS ; Q = CA RS (1.10) f (Strickler) 3 3 Str f Str f f u = k R S ; Q= k AR S (1.11) 1 C k Str ( m / s) ( m 13 / s) R A R = (1.1) s s C 1 16 = R (1.13) n k Str 1 = (1.14) n f 4

6 S f i Qi = Q (1.15) i Ki S f = K S (1.16) f i (1.16) S f S f S f 5

7 (1.16) 1 5/3 K = bh (1.17) i i n i i K = Cbh (1.18) i 3 i i i 1.3 (1.5) (1.6) β β (1.7) β uz (1.7) β (1.7) u (1.17)(1.18) S f b i 1 1 h b A h b i n β = = K A 1 53 hi bi i n i i i i i i i ni (1.19) 6

8 Chb A Chb i i i i i i i i β = = K A 3 Cbh i i i i (1.0) (1.19)(1.0) β y 1.4 Q3 = Q1 + Q (1.1) 7

9 y1 = y = y3 (1.) u1 u u3 y1+ = y + = y3 + (1.3) g g g Q1 1 Q3 3 Q Qt () Qt () ( Qt) yt () Qt () A Q = f( y ) A A A 8

10 Q = Q B A A yt () QA( t+ t) Q ( t+ t) = Q ( t+ t) B A Q b 3 = µ g( yu yw) (1.4) Q 1 = µ 1 g( yd yw)( y u y d) (1.5) b 9

11 yu yd b y w µµ, 1 Q = ϕεab g( y y εa) (1.6) u w ϕ ε a h b y, y (1.6) c ( ) hc htest > hd; htest = 1+ 8Fc 1 h = εa c F Q = gb h 3 c u w (1.7) h test h c F c h c ( a) htest > hd y u h a hc = εa y d h d y w y u h a h d y d ( b) htest < hd y w i i+1 10

12 h < h test d ( ) Q= µ ba g y y (1.8) u d µ ( )y d ( ) Q= ψby ( y ) g y y (1.9) d w u d y u h y d h d y w i i+1 11

13 .1 h h u + u + h = 0 t (.1) u u h z + u + g + g + gs = 0 (.) t z G (1 nb ) + = 0 (.3) t G = Guh (, ) (.4) u, Q G h y b b A z t h u z S G 1

14 b b n z (.1) (.3) ht (, ), ut (, ), zt (,) (.4) (.3) (.1)(.4) z A (a) (b) y 13

15 (c) (.1)(.4) S S Manning-Strickler u S = k R (.5) 43 str k Strickler R str (.5) ϕ ( Suhd,,,,...) = 0 (.6) d Einstein(1950)Engelund and Hansen(1967) S (.6) (.1)(.4) (.4) G Q B q B 14

16 Einstein(1950). (1) G ( = 0) = f (); t Q ( = 0) = f () t (.7) 1 () y ( = L) = f () t (.8) = L (3) h ( = L) = f ( Q) (.9) (4) z ( = L) = f () t z ( = 0) = f () t (.10) (5) (a) ui+ 1 ui Qi+ 1 = Qi; Gi+ 1 = Gi; yi H = yi + (.11) g g H (6) (b) Qt () ( Gt) Gt () < 0, Qt () = 0 15

17 Q = Q + Qt (); G = G + Gt (); i+ 1 i i+ 1 i ui+ 1 ui yi H = yi + g g (.1) (7) (c) Q = Q + Q ; G = G + G ; c a b c a b uc ua ub yc + + H = ya + = yb + g g g (.13) (8) (d) Q = Q; G = f( G) (.14) i+ 1 i i+ 1 i 16

18 yi = f () t (.15) (1)(4) (5)(8).3 (.1)(.3) (.1) (.) (.3).3.1 t = t t (.1)(.) 1 0 t= t 1 t z ( ) ht (, 1) ut (, 1 ) (.4) (.3) (.3) zt (, ) (0 L) 0 z h z (.1)(.) (.3) 17

19 .3. Preissmann n+ 1 n (.1)(.3) f = f f (.1)(.3) i i i f f y, u, z [ A]{ w } [ B]{ w} { C} + + = (.16) [ ] [ ] i+ 1 i 0 A, B t 33 C n { } w { wi} ui = yi z i (.17) (.16) Q u u i Q i N (.16) 3( N 1) { } Q, y, z (i=1,,...,n) 3N i i i Double Sweep Method { } 18

20 3.1 Fick C C C = ε C m + εm + ε m t y y z z -1 C ε ms m ms 4 1m 000 point source)p (3.1) 19

21 P P P C C C C C C C + u + v + w = ε m + ε m ε + m t y z y y z z (3.) u, v, w, y, z 0

22 ( u, v, w) ( u', v', w') u = u + u'; v = v+ v'; w = w + w ' (3.3) C = C+ C' (3.4) (3.3) (3.4) (3.) yz,, i C C C ' + ui = εm uc i ' t i i i, y, z (3.5) uc ' ' i (3.5) ' ' C uc i = ε (3.6) i i ε i 1

23 -1-1 cm s 10 cm s, y, z C C C C u v w C C ε C = + εy + εz (3.7) t y z y y z z 3.7) (3.7) Cyzt (,,, ) (3.7) Holley, 1971) (3.7) Holly, 1975) C C C h ( huc) ( hwc) hε hε + + = + z t z z z u, w, C z ε, ε (3.7) ε, ε z (3.8) z

24 ε, ε ε, ε z z 3

25 (a) (b) (c) ε, ε ε, ε Elder(1959) z z ε ε z = 0.3uh * = 5.93uh * (3.9) ε ε ε z 3. Taylor(1954) Fick Ca ( ACa) + ( AUCa) = AK t (3.10) Ca U A K K ε K ε U, A, K 4

26 C CV ( Ut ) = A( Kt) 4Kt 0 0 a ( t, ) ep 1 π (3.11) C, V 0 0 (1) U, K, A ()Nordin and Sabol(1974) Fick (3) (3.10) L = 1.8l U R U * (3.1) l R U 3.10) L * 3.3 (3.10) (3.10) 5

27 C a t Ca + U = 0 (3.13) (3.13) C C C t a a a + U = Kn (3.14) K n K n K K K n Dobbins and Bella(1968) (3.13) ( i+ 1, n+ 1) ( n+ 1) ( i + 1) n ξ C ( i+ 1, n+ 1) = C ( ξ, n) (3.15) a a n n ξ 6

28 = U t U t ξ ξ i U t = (3.16) C ( i+ 1, n+ 1) = C (, i n) (3.17) a a (, in) ( i+ 1, n+ 1) (a) U, t U t (b) C ( ξ, n) C ( i 1, n) C (, in) Dobbins and a a Bella U a 7

29 ( α) Ca(, in) + αca( i 1, n) Ca( i+ 1, n+ 1) = Ca( ξ, n) = (3.18) α (b) ξ i (3.18) C ( i+ 1, n+ 1), C (, in), C ( i 1, n) ( i+ 1, n) a a a Taylor Ca C Ca( i+ 1, n+ 1) Ca( i+ 1, n) + t+ t t a ( t ) (3.19) Ca C Ca(, in) Ca( i+ 1, n) + a ( ) Ca Ca Ca( i 1, n) Ca( i+ 1, n) + ( ) (3.0) (3.1) (3.18) + α = U t U C C a a = U t (3.) C C α( α) C t t a a a + U = (3.3) K n α( α) = t (3.4) U t Cr = (3.5) (3.4) K n ( ) (1 Cr)( Cr ) = t (3.6) 8

30 Cr = 1 Cr = 0 K n = ( ) Cr = 1.5 Kn = 8 t 0 Cr 1 i 1 i + K n ( ) (1 Cr) Cr = t (3.7) Cr = 0 Cr = 1 K = 0 Cr = 0.5 n U = 1m/s h = 5m = 1km 3.7) Cr = 0.5 t = 500s K n ( ) 1000 = = = 50m s 8 t (3.8) Fischer(1973) K 50 RU = (3.9) * U -1 R h= 5m U* = 0.05ms 0-1 K = 6.5m s (3.30) K K n Dobbins and Bella (3.18) m 1m 0.1% Strickler 5 1m 3 /s 0.5m/s 10km = 00m 50 9

31 30

32 Leendertse(1970)) Holly and Cunge(1975) t=9,600s Cr = 0.5, Cr = 0.5, Cr = 0.75, Cr =

33 Holly-Preissmann(1977) "-point 4th order method" Dobbins and Bella ( i+ 1, n+ 1) i 1 ξ i ξ C ( ξ, n) a Dobbins-Bella C ( i 1, n), C (, in) a a Ca Ca Holly-Preissmann ( i 1, n), (, in) Holly-Preissmann C ( i+ 1, n+ 1) = C ( ξ, n) = ac ( i 1, n) + ac (, in) a a 1 a a Ca Ca + a3 ( i 1, n) + a4 (, in) (3.31) a1 = Cr Cr a = 1 a 1 (3 ) a = Cr (1 Cr)( ) 3 i i 1 a = Cr(1 Cr)( ) 4 i i 1 (3.3) C a ' Ca U (3.13) C ' a t ' Ca + U = 0 (3.33) 3

34 C ( i+ 1, n+ 1) = C ( ξ, n) = bc ( i 1, n) + bc (, in) ' ' a a 1 a a b = 6 Cr( Cr 1)/( ) 1 i i+ 1 b = b1 b = Cr(3Cr ) 3 b = ( Cr 1)(3Cr 1) 4 + bc i n + bc in ' ' 3 a( 1, ) 4 a(, ) (3.34) (3.35) Holly-Preissmann t=9,600s Cr =1.0 Cr = 0.5, Cr = 0.50, Cr = 0.75 Holly-Preissmann (1) 6-point scheme Komatsu, Holly, Nakashiki and Ohgushi, 1985) Holly-Preissmann 33

35 scheme H-P H-P H-P 6-point scheme C (, in+ 1) = bc ( i 3, n) + bc ( i, n) + bc ( i 1, n) a 1 a a 3 a + bc (, in) + bc ( i+ 1, n) + bc ( i+, n) 4 a 5 a 6 a (3.36) b Cr Cr Cr 3 1 = b Cr Cr Cr 3 = b Cr Cr Cr 3 3 = b Cr Cr Cr 3 4 = b Cr Cr Cr 3 5 = b Cr Cr Cr 3 6 = / Cr = U t 6-point scheme H-P 8-point scheme(holly and Komatsu, 1983) 6-point scheme 6-point scheme H-P 34

36 FORTRAN CBASIC 35

37 Cunge, J.A., F.M.Holly, Jr., and A. Verwey:Practical Aspects of Computational River Hydraulics, Institute of Hydraulic Research, College of Engineering, The University of Iowa, Iowa City, USA, II : 60, Komatsu, T., F.M.Holly Jr., N.Nakashiki, K.Ohgushi: Numerical Calculation of Pollutant Transport in One and Two Dimensions, Journal of Hydroscience and Hydraulic Engineering, Vol.3, No., pp.15-30,

38 Dobbins and Bella 3.18) Taylor 37

3/4/8:9 { } { } β β β α β α β β

α β : α β β α β α, [ ] [ ] V, [ ] α α β [ ] β 3/4/8:9 3/4/8:9 { } { } β β β α β α β β [] β [] β β β β α ( ( ( ( ( ( [ ] [ ] [ β ] [ α β β ] [ α ( β β ] [ α] [ ( β β ] [] α [ β β ] ( / α α [ β β ] [ ] 3

橡紙目次第１章1

橡紙目次第１章1