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Results

+ +

$Re = 100$

+ We run the code with the following parameter-file.prm, which can be found in the same directory as the source: @verbatim @@ -52,18 +55,29 @@ Since the verbose parameter is set to false, we do not If we we were to set it to true 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 + +

$Re = 500$

-@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.

Possible Extensions

@@ -78,6 +92,10 @@ This program can be extended in the following directions: projection methods with variable time step, practice shows that they perform very well. +
  • 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. +
  • 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. -- 2.39.5
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