From 6d0f4bff58fd0749d55b35700c4549670063c5f7 Mon Sep 17 00:00:00 2001 From: salgado Date: Tue, 22 Sep 2009 18:44:02 +0000 Subject: [PATCH] I changed the intro section to reflect the new treatment of the boundary conditions and what this implies for the weak formulation. git-svn-id: https://svn.dealii.org/trunk@19491 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-35/doc/Re100t0.png | Bin 0 -> 6712 bytes deal.II/examples/step-35/doc/Re100t1.png | Bin 0 -> 49426 bytes deal.II/examples/step-35/doc/Re100t10.png | Bin 0 -> 6745 bytes deal.II/examples/step-35/doc/Re100t3.png | Bin 0 -> 52876 bytes deal.II/examples/step-35/doc/Re100t5.png | Bin 0 -> 63294 bytes deal.II/examples/step-35/doc/Re100t8.png | Bin 0 -> 70766 bytes deal.II/examples/step-35/doc/geometry.gif | Bin 4350 -> 0 bytes deal.II/examples/step-35/doc/geometry.png | Bin 1613 -> 0 bytes deal.II/examples/step-35/doc/intro.dox | 100 ++++++++++++++++---- deal.II/examples/step-35/doc/visit0001.jpeg | Bin 130639 -> 0 bytes deal.II/examples/step-35/doc/visit0002.jpeg | Bin 130657 -> 0 bytes deal.II/examples/step-35/doc/visit0003.jpeg | Bin 105230 -> 0 bytes deal.II/examples/step-35/doc/visit0004.jpeg | Bin 116142 -> 0 bytes 13 files changed, 83 insertions(+), 17 deletions(-) create mode 100644 deal.II/examples/step-35/doc/Re100t0.png create mode 100644 deal.II/examples/step-35/doc/Re100t1.png create mode 100644 deal.II/examples/step-35/doc/Re100t10.png create mode 100644 deal.II/examples/step-35/doc/Re100t3.png create mode 100644 deal.II/examples/step-35/doc/Re100t5.png create mode 100644 deal.II/examples/step-35/doc/Re100t8.png delete mode 100644 deal.II/examples/step-35/doc/geometry.gif delete mode 100644 deal.II/examples/step-35/doc/geometry.png delete mode 100644 deal.II/examples/step-35/doc/visit0001.jpeg delete mode 100644 deal.II/examples/step-35/doc/visit0002.jpeg delete mode 100644 deal.II/examples/step-35/doc/visit0003.jpeg delete mode 100644 deal.II/examples/step-35/doc/visit0004.jpeg 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In the test case that we solve here the boundary is partitioned into two disjoint subsets $\partial\Omega = \Gamma_1 \cup \Gamma_2$ and we have @f[ - u|_{\Gamma_1} = u_b, \qquad u\times n|_{\Gamma_2} = 0. + u|_{\Gamma_1} = u_b, @f] -where $n$ is the outer unit normal. The boundary condition on $\Gamma_2$ is used to model outflow conditions. +and +@f[ + u\times n|_{\Gamma_2} = 0, \quad p|_{\Gamma_2} = 0 +@f] +where $n$ is the outer unit normal. The boundary conditions on $\Gamma_2$ are often +used to model outflow conditions. In previous tutorial programs (see for instance @ref step_20 "step-20" and @ref step_22 "step-22") we have seen @@ -63,8 +68,7 @@ Let us shortly describe how the projection methods look like in a semi-discrete obtain a sequence of velocities $\{u^k\}$ and pressures $\{p^k\}$. We will also obtain a sequence $\{\phi^k\}$ of auxiliary variables. Suppose that from the initial conditions, and an application of a first order method we have found -$(u^0,p^0,\phi^0=0)$ and $(u^1,p^1,\phi^1=p^1-p^0)$. Then the projection method consists of three steps: - +$(u^0,p^0,\phi^0=0)$ and $(u^1,p^1,\phi^1=p^1-p^0)$. Then the projection method consists of the following steps: