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A DG method for Stokes and Darcy flow
4 years 5 months ago #2775
by dong
A DG method for Stokes and Darcy flow was created by dong
I tried to implement a DG method for Stokes and Darcy problem on a square with two rectangle subdomains.
[tex]a_D(u,v)+a_S(u,v)+a_I(u,v)+b(v,p)+b(u,q)=\int_{\Omega_S}f_Svdx+\int_{\Omega_D}f_Dqdx[/tex]
with
[tex]a_{S}(u,v)=\sum_{T\in \mathcal{T_S}}2\mu\int_T\epsilon(u):\epsilon(v)dx-\sum_{F\in\mathcal{F^i_S}}\int_{F}2\mu\{\{\epsilon(u)\}\}n\cdotvds-\sum_{F\in\mathcal{F^i_S}}\int_{F}2\mu\{\{\epsilon(v)\}\}n\cdotuds
+\sum_{F\in \mathcal{F}^i_S}\frac{\sigma k^2}{h}\int_{F}uvds+\sum_{F\in\mathcal{F_S}}\frac{2\sigma k^2}{h}\int_{F}uvds[/tex]
where $\mathcal{F^i_S$ is the set of faces that are interior to Stokes region.
Please see the attached file for more details.
When I run the code, there was a traceback error as follows.
Could you please tell me what the mistake I made is?
Thank you so much.
[tex]a_D(u,v)+a_S(u,v)+a_I(u,v)+b(v,p)+b(u,q)=\int_{\Omega_S}f_Svdx+\int_{\Omega_D}f_Dqdx[/tex]
with
[tex]a_{S}(u,v)=\sum_{T\in \mathcal{T_S}}2\mu\int_T\epsilon(u):\epsilon(v)dx-\sum_{F\in\mathcal{F^i_S}}\int_{F}2\mu\{\{\epsilon(u)\}\}n\cdotvds-\sum_{F\in\mathcal{F^i_S}}\int_{F}2\mu\{\{\epsilon(v)\}\}n\cdotuds
+\sum_{F\in \mathcal{F}^i_S}\frac{\sigma k^2}{h}\int_{F}uvds+\sum_{F\in\mathcal{F_S}}\frac{2\sigma k^2}{h}\int_{F}uvds[/tex]
where $\mathcal{F^i_S$ is the set of faces that are interior to Stokes region.
Please see the attached file for more details.
When I run the code, there was a traceback error as follows.
Code:
NgException Traceback (most recent call last)
<ipython-input-8-4a91a1ef6207> in <module>
139
140 #Solve
--> 141 inv = a.mat.Inverse(freedofs=X.FreeDofs(), inverse="umfpack")
142 res = f.vec.CreateVector()
143 res.data = f.vec - a.mat*gfu.vec
NgException: UmfpackInverse: Numeric factorization failed.
Could you please tell me what the mistake I made is?
Thank you so much.
Attachments:
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