2 С BURG SOLVES BURGERS EQUATION FOR A PROPAGATING SHOCK*

4 DIMENSION R(6S),U(65),UD(6S);UE(65),A(S,65)

5 1,EF(4) Д(б5) ,AA(2) ,BB(2) ,CC(2)

6 OPEN(1,FILE= BURG.DAT)

7 OPEN(6,FILE= BURG.OUT )

8 READ(1,1)ME,JMAX,NTIH,XMAX,AD

9 READ(i;2)C,S,Q,EM

10 1 FORMAT(315.2E10.3)

11 2 FORMAT(F5.2,3E10.3)

12 С

13 JMAF JMAX 2

14 JMAP JMAX - 1

15 АИР JMAP

16 DX 2ЛХМАХ/АНР

17 DT C*DX

18 SA AD*C*C

19 ALPH = S*DX*DX/DT

20 IF(ALPH .LT. l.OE-10)ALPH = l.OE-10

21 RCEL = DX/ALPH

22 QQ Q*C/3.

23 IF(HE .LT. 3)QQ = 0.

24 HQ 0

25 ir(ABS(QQ) .GT. O.OOODMQ = 1 2S ATIH = NTIM

27 TIM = 0.

28 TIMAX = DT*ATIM

29 PI > 3.141592654

30 С

31 VRITE(6,3)

32 3 FORMAT(* PROPAGATING SHOCK WAVE(BURGERS EQUATION)*)

33 1Г(ИЕ .EQ. 1)VRITE(6,4)ME

34 ir(ME .EQ. 2)WRITE(6,5)ME

35 ir(HE .EQ. 3)WRITE(6,6)ME зе 1Г(МЕ .GE. 4)WRITE(6,7)ME

37 4 F0RMAT(5H ME ,I2,3X,18H FTCS DIFFERENCING)

38 5 F0RMAT(5H HE ,I2,3X,13H LAX-WENDROFF)

39 б F0RHAT(5H HE .I2,3X,20H EXPLICIT 4PT UPWIND)

40 7 rORHAT(5H HE ,I2,3X,23H GENERAL CRANK-NICOLSON)

41 WRITE(6,8)JHAX,NTIH,C,DX,DT,XMAX

42 8 FORMATC JHAX M3, NTIH M3/ C 4F5.2,

43 V DX \r5.3, DT 4r5.3/ XHAX=\F5.2)

44 WRITE(6,9)S,ALPH.RCEL,Q,EM,SA

45 9 FORMATC 8 ЧГ5.2/ ALPH \E10.3/ RCEL \r6.1, Q \F5.2,

46 1 EH \F6.3, SA=\E10.3)

47 С

48 IF(HE .GT. 3)G0T0 10

49 AA(1) 0.5*C + 3.*QQ

50 BB(1) - 3.*QQ

51 CC(1) -0.5*C + QQ

52 IF(ME .NE. 2)GOTO H

53 AA(1) = 0.

54 BB(1) = 0.5*C

55 CC(1) = -0.5*C

56 AA(2) = С

57 BB(2) = -C

58 CC(2) * 0.

59 GOTO 11

60 10 AA(1) EH + 0.5*S

61 BB(1) 1.0 - 2.0*EM - S

62 CC(1) EM + 0.5*S

63 11 WRITE(6,12)AA,BB,CC

64 12 FORMATC AA \2F8.5/ BB \2F8.5/ CC .2F8.5,/)

65 С

66 С INITIALISE и AND EVALUATE UEX

67 С

68 CALL EXSH(JMAX,X,U,UE,DX,XMAX,ALPB,TIMAX)

69 с

70 UD(1) U(l)

71 UD(JMAX) = и(JMAX)

72 DO 14 J 1,JMAX

73 DO 13 К = 1,5

74 13 A(K,J) 0.

75 14 CONTINUE

76 WRITE(6.15)TIM

77 15 FORMATC INITIAL SOLUTION, TIH ЧГ5;3)

78 VRITE(6,16)(X(J),J l,JHAX)

79 WRITE(6,17)(U(J),J 1,JMAX) BO 16 FORMATC X M2F6.3)

BI 17 FORMATC U-M2F6.3) 82 с

S3 с MARCH SOLUTION IN TIME 84 С

tS DO 27 N 1,NTIM

86 IF (ME .GT. 3)GOT0 21

t7 С

tZ с EXPLICIT SCHEMES

89 С

90 IP 1

91 18 IFdP .EQ. DEFd) 0.5*U(1)*0(1) 2 IFdP .EQ. 2)ЕГ(1) 0.5*UD(l)*UDd)

93 ЕГ(2) EF(l)

94 EF(3) ЕГ(2)

95 IFdP .EQ. 1)ЕГ(4) 0.5*U(2)*U(2)

96 IFdP .EQ. 2)ЕГ(4) 0.5*UD(2)*UD(2)

97 DO 20 J 2,JMAP

98 IF(ME .EQ. 3)EFd) EF(2)

99 ЕГ(2) ЕГ(3)

100 EF(3) EF(4)

101 IFdP .EQ. 1)ЕГ(4) 0.5*U(J+1)*U(J+1)

102 IFdP .EQ. 2)ЕГ(4) 0.5*UD(J+1)*UD(J+1)

103 DUM S*(U(J-1) - 2.*U(J) + U(J+1))

104 IF(ME .NE. 2 .OR. IP .EQ. 2)GOTO 19

105 JP J+1

106 ir(J .EQ. JMAP)JP * J

107 DUM 0.5*DUM+0.5*S*(U(J)-2.*U(J+1)+U(JP+1))+0.5*(U(JP)-U(J))

108 19 UD(J) U(J) + AA(IP)*EF(2) + BB(IP)*EF(3) + CCdP)*EF(4) + DU!t

109 ir(ME .EQ. 3)UD(J) UD(J) - QQ*Er(l)

110 20 CONTINUE

111 IF(ME .NE. 2 .OR. IP .EQ. 2)C0T0 25

112 IP IP + 1

113 GOTO 18

Рис. 10.4 (продолжение).