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Corrected $n * \sigma$ in fsi_tutorial.jl #25

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Merged
merged 2 commits into from
Jun 11, 2020
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Corrected $n * \sigma$ in fsi_tutorial.jl #25

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670394a
Corrected $n * \sigma$ in fsi_tutorial.jl
oriolcg Jun 10, 2020
dae0cb2
Fixed a typo in fsi_tutorial.jl
oriolcg Jun 10, 2020
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14 changes: 7 additions & 7 deletions src/fsi_tutorial.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -44,7 +44,7 @@
# \left\lbrace
# \begin{aligned}
# u_{\rm F} = g_{\rm F} &\text{ on } \Gamma_{\rm F,D},\\
# \boldsymbol{\sigma}_{\rm F}\cdot n_{\rm F} = 0 &\text{ on } \Gamma_{\rm F,N},\\
# n_{\rm F} \cdot \boldsymbol{\sigma}_{\rm F} = 0 &\text{ on } \Gamma_{\rm F,N},\\
# u_{\rm S} = g_{\rm S} &\text{ on } \Gamma_{\rm S,D},\\
# \end{aligned}
# \right.
Expand All @@ -55,7 +55,7 @@
# \left\lbrace
# \begin{aligned}
# u_{\rm F} = u_{\rm S} &\text{ on } \Gamma_{\rm FS},\\
# \boldsymbol{\sigma}_{\rm F}\cdot n_{\rm F} + \boldsymbol{\sigma}_{\rm S}\cdot n_{\rm S} = 0 &\text{ on } \Gamma_{\rm FS}.\\
# n_{\rm F} \cdot \boldsymbol{\sigma}_{\rm F} + n_{\rm S} \cdot \boldsymbol{\sigma}_{\rm S} = 0 &\text{ on } \Gamma_{\rm FS}.\\
# \end{aligned}
# \right.
# ```
Expand Down Expand Up @@ -118,7 +118,7 @@ us_0(x) = VectorValue( 0.0, 0.0 )

# We consider a free tranction condition at the channel outlet
# ```math
# \boldsymbol{\sigma}_{\rm F}\cdot n_{\rm F} = \mathbf{0}\quad\textrm{on }\Gamma_{\rm F,N}
# n_{\rm F} \cdot \boldsymbol{\sigma}_{\rm F} = \mathbf{0}\quad\textrm{on }\Gamma_{\rm F,N}
# ```
hN(x) = VectorValue( 0.0, 0.0 )
p_jump(x) = 0.0
Expand Down Expand Up @@ -252,9 +252,9 @@ end
# ```math
# \begin{aligned}
# a_{fs}(\mathbf{x}^h,\mathbf{y}^h)=&\langle\gamma\frac{\mu_f}{h}(\mathbf{v}^h_{\rm F}-\mathbf{v}^h_{\rm S}),(\mathbf{u}^h_{\rm F}-\mathbf{u}^h_{\rm S})\rangle_{\Gamma_{\rm FS}}\\
# &- \langle(\mathbf{v}^h_{\rm F}-\mathbf{v}^h_{\rm S}),\boldsymbol{\sigma}^{dev}_f(\mathbf{u}^h_{\rm F})\cdot\mathbf{n}_{\rm FS}\rangle_{\Gamma_{\rm FS}}
# &- \langle(\mathbf{v}^h_{\rm F}-\mathbf{v}^h_{\rm S}),\mathbf{n}_{\rm FS}\cdot\boldsymbol{\sigma}^{dev}_f(\mathbf{u}^h_{\rm F})\rangle_{\Gamma_{\rm FS}}
# + \langle(\mathbf{v}^h_{\rm F}-\mathbf{v}^h_{\rm S}),p^h_{\rm F}\mathbf{n}_{\rm FS}\rangle_{\Gamma_{\rm FS}}\\
# &- \chi\langle\boldsymbol{\sigma}^{dev}_f(\mathbf{v}^h_{\rm F})\cdot\mathbf{n}_{\rm FS},(\mathbf{u}^h_{\rm F}-\mathbf{u}^h_{\rm S})\rangle_{\Gamma_{\rm FS}}
# &- \chi\langle\mathbf{n}_{\rm FS}\cdot\boldsymbol{\sigma}^{dev}_f(\mathbf{v}^h_{\rm F}),(\mathbf{u}^h_{\rm F}-\mathbf{u}^h_{\rm S})\rangle_{\Gamma_{\rm FS}}
# + \langle q^h_{\rm F}\mathbf{n}_{\rm FS},(\mathbf{u}^h_{\rm F}-\mathbf{u}^h_{\rm S})\rangle_{\Gamma_{\rm FS}}\\
# \end{aligned}
# ```
Expand All @@ -273,8 +273,8 @@ function a_fs(x,y)
εuf = jump(ε(uf_Γ))
εvf = jump(ε(vf_Γ))
penaltyTerms = α*vf*uf - α*vf*us - α*vs*uf + α*vs*us
integrationByParts = ( vf*(p*n_Γfs) - vf*(σ_dev_f(εuf)*n_Γfs) ) - ( vs*(p*n_Γfs) - vs*(σ_dev_f(εuf)*n_Γfs) )
symmetricTerms = ( q*(n_Γfs*uf) - χ*(σ_dev_f(εvf)*n_Γfs)*uf ) - ( q*(n_Γfs*us) - χ*(σ_dev_f(εvf)*n_Γfs)*us )
integrationByParts = ( vf*(p*n_Γfs) - vf*(n_Γfs*σ_dev_f(εuf)) ) - ( vs*(p*n_Γfs) - vs*(n_Γfs*σ_dev_f(εuf)) )
symmetricTerms = ( q*(n_Γfs*uf) - χ*(n_Γfs*σ_dev_f(εvf))*uf ) - ( q*(n_Γfs*us) - χ*(n_Γfs*σ_dev_f(εvf))*us )
penaltyTerms + integrationByParts + symmetricTerms
end

Expand Down