A modified Lagrange Galerkin method for a fluid rigid system
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- rigid body
- discrete formulation
- has given
- stokes equations
- lagrange-galerkin method
- semi-discretization scheme
- characteristic function
- domain has
- ?0 ?
Publié par
Nombre de lectures
34
y z
t tk+1 k
2OR
t; (t)
( t) =OnB((t)) t u(x;t) p(x;t)
(t) !(t)
@u
+ (ur)u u +rp = f; x2 ( t);t2 [0;T ];f f
@t
u = 0; x2 ( t);t2 [0;T ];
u = 0; x2@O;t2 [0;T ];
0 ?
u = (t) +!(t)(x (t)) ; x2@B((t));t2 [0;T ];
Z Z
00
m (t) = nd + f(x;t)dx;t2 [0;T ];s
@B((t)) B((t))
Z Z
0 ? ?J! (t) = (x (t)) nd + (x (t)) f(x;t)dx;t2 [0;T ]:s
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= pId + 2D(u) D(u) =
T T(ru+ru )=2 ru ru
m J
y
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0;1s> 0 C (O) O
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Z
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O
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B() O
bK() = u2K()j u = 0 O ;
2M() = p2L (O)jp = 0 B() :0
K()
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2u2K() l 2R ! 2Ru u
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OnB()
u
0 ?u(x;t) = (t) +!(t)(x (t)) 8x2B((t));
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u
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p(;t)2M((t)) (u;p)
h i
d e u (t);’ +a(u;’) +b(’;p) = (f(t);’) 8’2K((t));
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Z
1 2a(u;v) = 2 D(u) : D(v) dx 8u;v2H (O)
O
Z
1 2 2b(u;p) = div(u)p dx 8u2H (O) ; 8p2L (O):0
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k kk 0 2b(u ; )2K( )\C (O) O
t =tk
e eX(x) = (t ;t ;x)
