<a name="results"></a>
<h1>Results</h1>
+<a name="Re100"></a>
+<h2> $Re = 100$ <h2>
+
We run the code with the following <code>parameter-file.prm</code>, which can be found in the
same directory as the source:
@verbatim
If we we were to set it to <code>true</code> we would get information on what the program is doing and
how many steps each iterative process had to make to converge, etc.
-A plot of the obtained results for $t=0,1,5,10$ is the following
+A plot of the obtained results for $t=0,1,3,5,8,10$ is the following
-@image html visit0001.png
+@image html Re100t0.png
+@image html Re100t1.png
+@image html Re100t3.png
+@image html Re100t5.png
+@image html Re100t8.png
+@image html Re100t10.png
-@image html visit0002.png
+The contour lines correspond to the pressure, the color to the voriticity and the arrows to the velocity.
+Here we only show a zoom into a region near the obstacle which is, after all, where the interesting things happen.
-@image html visit0003.png
+<a name="Re500"></a>
+<h2> $Re = 500$ <h2>
-@image html visit0004.png
+Changing the Reynolds number, $Re$, to in the parameter file to a value of $500$ we obtain the following results.
+@image html Re500t0.png
+@image html Re500t1.png
+@image html Re500t3.png
+@image html Re500t5.png
+@image html Re500t8.png
+@image html Re500t10.png
-The contour lines correspond to the pressure, the color to the voriticity and the arrows to the velocity.
-Here we only show a zoom into a region near the obstacle which is, after all, where the interesting things happen.
<a name="extensions"></a>
<h2> Possible Extensions </h2>
projection methods with variable time step,
practice shows that they perform very well.
+ <li> High Reynolds numbers: As we can see from the results, increasing the Reynolds number changes significantly
+ the behavior of the flow. Using well-known stabilization techniques we could be able to
+ compute the flow in this, or many other problems, when the Reynolds number is very large.
+
<li> Variable density incompressible flows: There are projection-like methods for the case of incompressible
flows with variable density. Such flows play a role if fluids of different
density mix, for example fresh water and salt water, or alcohol and water.