From de3cd5a077baee85c147faffcecdb72dac734aa7 Mon Sep 17 00:00:00 2001 From: David Wells Date: Sun, 5 Jun 2016 17:54:54 -0400 Subject: [PATCH] Use I, not 1, in the traction term. When we multiply through by n we should end up with a `p n' term. Prefer I As 1 could be interpreted as a matrix of all ones. --- examples/step-22/doc/intro.dox | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/examples/step-22/doc/intro.dox b/examples/step-22/doc/intro.dox index be9ba4ae35..4d6fa27a26 100644 --- a/examples/step-22/doc/intro.dox +++ b/examples/step-22/doc/intro.dox @@ -238,16 +238,16 @@ possibilities for imposing boundary conditions: \\ &=& (\textbf{n} \otimes \textbf{v}, - p \textbf{1} - 2\; \varepsilon(\textbf{u}))_{\Gamma_N}. + p \textbf{I} - 2\; \varepsilon(\textbf{u}))_{\Gamma_N}. \\ &=& (\textbf{v}, - \textbf{n}\cdot [p \textbf{1} - 2\; \varepsilon(\textbf{u})])_{\Gamma_N}. + \textbf{n}\cdot [p \textbf{I} - 2\; \varepsilon(\textbf{u})])_{\Gamma_N}. @f} In other words, on the Neumann part of the boundary we can prescribe values for the total stress: @f{eqnarray*} - \textbf{n}\cdot [p \textbf{1} - 2\; \varepsilon(\textbf{u})] + \textbf{n}\cdot [p \textbf{I} - 2\; \varepsilon(\textbf{u})] = \textbf g_N \qquad\qquad \textrm{on}\ \Gamma_N. @f} @@ -268,7 +268,7 @@ possibilities for imposing boundary conditions:
  • Robin-type boundary conditions: Robin boundary conditions are a mixture of Dirichlet and Neumann boundary conditions. They would read @f{eqnarray*} - \textbf{n}\cdot [p \textbf{1} - 2\; \varepsilon(\textbf{u})] + \textbf{n}\cdot [p \textbf{I} - 2\; \varepsilon(\textbf{u})] = \textbf S \textbf u \qquad\qquad \textrm{on}\ \Gamma_R, @f} @@ -296,7 +296,7 @@ possibilities for imposing boundary conditions: @f{eqnarray*} \textbf u_{\textbf t} &=& 0, \\ - \textbf n \cdot \left(\textbf{n}\cdot [p \textbf{1} - 2\; + \textbf n \cdot \left(\textbf{n}\cdot [p \textbf{I} - 2\; \varepsilon(\textbf{u})] \right) &=& 0. @@ -317,7 +317,7 @@ possibilities for imposing boundary conditions: \textbf{n}\cdot\textbf u &=& 0, \\ (\textbf 1-\textbf n\otimes\textbf n) - \left(\textbf{n}\cdot [p \textbf{1} - 2\; + \left(\textbf{n}\cdot [p \textbf{I} - 2\; \varepsilon(\textbf{u})] \right) &=& 0, @@ -627,7 +627,7 @@ domain $\Omega=[-2,2]\times[0,1]\times[-1,0]$: \end{array}\right) \qquad\qquad \textrm{at}\ z=0, x=0, @f} -and using natural boundary conditions $\textbf{n}\cdot [p \textbf{1} - 2 +and using natural boundary conditions $\textbf{n}\cdot [p \textbf{I} - 2 \varepsilon(\textbf{u})] = 0$ everywhere else. In other words, at the left part of the top surface we prescribe that the fluid moves with the continental plate to the left at speed $-1$, that it moves to the right on the -- 2.39.5