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 epsilon=1, t=100, N= 800.

epsilon=1, t=100, N= 800.

3.5

-1.5 MC RB upwind RB MUSCL (N=200) NS

MC RB upwind RB MUSCL (N=200) NS

-2

3 -2.5 2.5

u(x,t)

rho(x t)

-3

2

-3.5

-4 1.5 -4.5 1 -5

0.5

-5.5 0

10

20

30

40

50

60

70

80

90

0

10

20

30

40

x

50

60

70

80

90

x

epsilon=1, t=100, N= 800.

epsilon=1, t=100, N= 800.

6

4.5 MC RB upwind RB MUSCL (N=200) NS

5.5

MC RB upwind RB MUSCL (N=200) NS

4

5

3.5

4.5

3

4 sigma(x,t)

theta(x,t)

2.5 3.5 3

2 1.5

2.5 1

2

0.5

1.5 1

0

0.5

-0.5 0

10

20

30

40

50

60

70

80

90

x epsilon=1, t=100, N= 800. MC RB upwind RB MUSCL (N=200) NS

16 14 12

q(x,t)

10 8 6 4 2 0 -2 10

20

30

40

50 x

10

20

30

40

50 x

18

0

0

60

70

80

90

60

70

80

90



 epsilon=1, t=100, N= 800 .

epsilon=1, t=100, N= 800 .

4

-3 MC RB NS

MC RB NS

-4

3.5 -5 3

-6 -7 u(x,t)

rho(x t)

2.5

2

-8 -9 -10

1.5

-11 1 -12 0.5

-13 0

50

100

150

200

250

0

50

100

x

150

200

250

x

epsilon=1, t=100, N= 800 .

epsilon=1, t=100, N= 800 .

35

35 MC RB NS

MC RB NS

30

30

25 25

sigma(x,t)

theta(x,t)

20 20

15

15

10 10 5 5

0

0

-5 0

50

100

150

200

250

x epsilon=1, t=100, N= 800 . MC RB NS 250

200

q(x,t)

150

100

50

0

-50 50

100

150 x

50

100

150 x

300

0

0

200

250

200

250