] 1 1 u (1) = G 1 ( 1 ) u (1) a s UC Irvine Geometric - - PowerPoint PPT Presentation

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1 1 u 1 g 1 1 u 1 a s uc irvine geometric conservation

Jan 10, 2024 136 likes •179 views

u (1) = G 1 u (1) u (2) = G 2 u (2) u a = Gu s a s a s u a = 1 u (1) + 2 u (2) = 1 G 1 u (1) + 2 G 2 u (2) a a s s UC Irvine G 1 ( 1 ) = 0 . 5 [(1 1 ) G ( ) + (1 + 1 ) G (+) ] 1 1 u (1) = G 1 ( 1 ) u

SLIDE 1

ua = Gus u(1)

a

= G1u(1)

s

u(2)

a

= G2u(2)

s

ua = η1u(1)

a

+ η2u(2)

a

= η1G1u(1)

s

+ η2G2u(2)

s UC Irvine

SLIDE 2

G1(η1) = 0.5 ∗ [(1 − η1)G(−)

1

+ (1 + η1)G(+)

1

] u(1)

a

= G1(η1)u(1)

s UC Irvine

SLIDE 3

] 1 1 u (1) = G 1 ( 1 ) u (1) a s UC Irvine Geometric - - PowerPoint PPT Presentation

ua = Gus u(1)

a

= G1u(1)

s

u(2)

a

= G2u(2)

s

ua = η1u(1)

a

+ η2u(2)

a

= η1G1u(1)

s

+ η2G2u(2)

s UC Irvine

G1(η1) = 0.5 ∗ [(1 − η1)G(−)

1

+ (1 + η1)G(+)

1

] u(1)

a

= G1(η1)u(1)

s UC Irvine

Geometric Conservation Law

For deforming grids the folowing relation has to be satisfied in order to avoid influence of the grid motion on the flow solution: ∂ ∂t

Ω

dΩ −

S

V g · n dS = 0

UC Irvine