From: Abner J. Salgado Date: Tue, 22 Sep 2009 18:44:02 +0000 (+0000) Subject: I changed the intro section to reflect the new treatment of the boundary X-Git-Tag: v8.0.0~7084 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=f2ab2927b5efd63306729b908c9aabbc191ab76f;p=dealii.git 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 --- diff --git a/deal.II/examples/step-35/doc/intro.dox b/deal.II/examples/step-35/doc/intro.dox index 0dfe1b88c1..a79873627f 100644 --- a/deal.II/examples/step-35/doc/intro.dox +++ b/deal.II/examples/step-35/doc/intro.dox @@ -29,9 +29,14 @@ condition, is It is possible to prescribe other boundary conditions as well. 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: