From 6878155e99299a1025c26891de315fce9c2d192b Mon Sep 17 00:00:00 2001 From: bangerth Date: Sun, 21 Sep 2008 20:52:43 +0000 Subject: [PATCH] Discuss no normal flux-boundary conditions. git-svn-id: https://svn.dealii.org/trunk@16883 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-22/doc/intro.dox | 24 ++++++++++++++++++++++++ 1 file changed, 24 insertions(+) diff --git a/deal.II/examples/step-22/doc/intro.dox b/deal.II/examples/step-22/doc/intro.dox index 497433e459..c46fa90ad3 100644 --- a/deal.II/examples/step-22/doc/intro.dox +++ b/deal.II/examples/step-22/doc/intro.dox @@ -259,6 +259,30 @@ possibilities for imposing boundary conditions: &=& 0. @f} + + An alternative to this is when one wants the flow to be parallel + rather than perpendicular to the boundary (in deal.II, the + VectorTools::compute_no_normal_flux_constraints function can do this for + you). This is frequently the case for problems with a free boundary + (e.g. at the surface of a river or lake if vertical forces of the flow are + not large enough to actually deform the surface), or if no significant + friction is exerted by the boundary on the fluid (e.g. at the interface + between earth mantle and earth core where two fluids meet that are + stratified by different densities but that both have small enough + viscosities to not introduce much tangential stress on each other). + In formulas, this means that + @f{eqnarray*} + \textbf{n}\cdoy\textbf u &=& 0, + \\ + (\textbf 1-\textbf n\otimes\textbf n) + \left(\textbf{n}\cdot [p \textbf{1} - + \varepsilon(\textbf{u})] \right) + &=& + 0, + @f} + the first condition (which needs to be imposed strongly) fixing a single + component of the velocity, with the second (which would be enforced in the + weak form) fixing the remaining two components. Despite this wealth of possibilities, we will only use Dirichlet and -- 2.39.5