Pcatut 5472 Presentation

7/28/2019 Pcatut 5472 Presentation

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Pyroclastic flows Montserrat


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dAdt

=A

t+ v

A = F(A,A)


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= (1 r2)

m = (x)2


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AI(r) =

A(r)W(r r, h)dr

A(r) =

A(r)(r r)dr


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limh0

W(r, h) = (r)

W(r, h)dr = 1

W(r, h) =er

2/h2

h33/2


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A(r)

(r

)

W(r r, h)(r)dr b

mbAb

b

W(r rb)

A(r) =

b

mbAb

b

W(r rb)


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(r

) =b

mbW(r rb, h

)

(r)dr =

b

mb

W(r, h)dr =b

mb


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As(r)

b

mbAb

b

W(r rb)

As(r)

b

mbAb

b

W(r rb)

A = 1((A)A)

(A)a =1

a

mbb

b(Ab Aa)W(ra rb, h)


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d

dt= v

d

dt=

( (v) v )

d

dt

=

a

a

b

mbb

b

(vb va) Wab

d

dt

a

= a

b

mb

b

vab aWab

= 1

aWab = rabFab


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mbvab

rabFab

ddta

=b

mbvab aWab

=


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AI(x) =

A(x)W(x x, h)dx

AI(x) =

A(x) + (x x)dA/dx +

1

2(x x)2d2A/dx2 + ......

W(xx)dx

O(h2)d2A/dx2

AI(x) = A(x) +1

2h2d2A/dx2 + ...


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M1(q) = 1

M1(q) = 0

M2(q) = 1 q

M2(q) = 0


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M4(q) =2

3 q2 +

1

2q3

M4(q) =1

6(2 q)

3

M4(q) = 0


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A =

hK(W(0, h) + 2W(, h) + 2W(2, h) + ....)

h =

h = 1.2

h = 1.5


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0 1 2-2

-1

0


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