]> https://gitweb.dealii.org/ - dealii-svn.git/commitdiff
Discuss no normal flux-boundary conditions.
authorbangerth <bangerth@0785d39b-7218-0410-832d-ea1e28bc413d>
Sun, 21 Sep 2008 20:52:43 +0000 (20:52 +0000)
committerbangerth <bangerth@0785d39b-7218-0410-832d-ea1e28bc413d>
Sun, 21 Sep 2008 20:52:43 +0000 (20:52 +0000)
git-svn-id: https://svn.dealii.org/trunk@16883 0785d39b-7218-0410-832d-ea1e28bc413d

deal.II/examples/step-22/doc/intro.dox

index 497433e459972671de4eb85a86c4bd837a4fd966..c46fa90ad3a97502b1c386bd7067de373f1c65c3 100644 (file)
@@ -259,6 +259,30 @@ possibilities for imposing boundary conditions:
       &=& 
       0.
     @f}
+
+    An alternative to this is when one wants the flow to be <i>parallel</i>
+    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.
 </ol>
 
 Despite this wealth of possibilities, we will only use Dirichlet and

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