From 619f43105fa8f5ef3aa897b23d68f6becfffeb0a Mon Sep 17 00:00:00 2001 From: bangerth Date: Mon, 30 Oct 2006 17:50:11 +0000 Subject: [PATCH] Remove now unnecessary files git-svn-id: https://svn.dealii.org/trunk@14132 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-21/doc/perm.png | Bin 90806 -> 0 bytes deal.II/examples/step-21/doc/pr4meshes.png | Bin 20104 -> 0 bytes deal.II/examples/step-21/doc/solp4meshes.png | Bin 77427 -> 0 bytes deal.II/examples/step-21/doc/sols4meshes.png | Bin 82228 -> 0 bytes deal.II/examples/step-21/doc/solu14meshes.png | Bin 118452 -> 0 bytes deal.II/examples/step-21/doc/solu24meshes.png | Bin 108575 -> 0 bytes .../step-21/doc/yanli_project_result.tex | 42 ------------------ 7 files changed, 42 deletions(-) delete mode 100644 deal.II/examples/step-21/doc/perm.png delete mode 100644 deal.II/examples/step-21/doc/pr4meshes.png delete mode 100644 deal.II/examples/step-21/doc/solp4meshes.png delete mode 100644 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h_{4}=2^{-6}$$ - -Our permeability is $K(x,y)=\frac{1.0}{2+1.99*sin(2 \pi \frac{2x-y}{\epsilon})}$:\\ - -\includegraphics[width=6 in]{perm.eps} - -Because of heterogeneity in the medium, the solution for velocity and saturatio are periodic. -Compare the following pictures on four meshes at time $t=T$:\\ -Velocity-x:\\ -\includegraphics[width=5 in]{solu14meshes.eps} -\\ -Velocity-y:\\ -\includegraphics[width=5 in]{solu24meshes.eps} -\\ -Pressure:\\ -\includegraphics[width=5 in]{solp4meshes.eps} -\\ -Saturation:\\ -\includegraphics[width=5 in]{sols4meshes.eps} -\\ -From above comparation, we can see pressure is stable but velocity and saturation are not. -The reason is heterogeneity of the medium and some complexity fo the dynamic systems. -By our direct numerical computation, only fine mesh solution is able to catch the subgrid properties. -That means an accurate well-posed computation requires tremendous amount of computer memory and CPU time. -But usually ,it easily exceed the limit of today's computer resources.\\ -There are some alternative approaches have been developed. A common approach is to "scale up" a heterogeneous medium. -This method is to find an effective representation of permeablility on a coarse mesh so that the large scale flow can be correctly computed on this mesh.The computational cost is thus greatly reduced. -\\ -At last,let's see Oil Production Rate on the boundary $\Gamma_{2}$: -$$ PR(t)=1-\frac{\int_{\Gamma_{2}} (\mathbf{u}\cdot \mathbf{n})F(S)dx}{\int_{\Gamma_{2}} (\mathbf{u} \cdot \mathbf{n})dx}$$ - -\includegraphics[width=6 in]{pr4meshes.eps} - - -\end{document} \ No newline at end of file -- 2.39.5