The testcase that we use for this program consists of the flow around a square obstacle. The geometry is
as follows:
-@image html geometry.gif
+@image html geometry.png
with $H=4.1$.
have the inflow boundary condition
@f[
u =
- \begin{array}{c} 4 U_m y (H-y)/H^2 \\ 0 \end{array},
+ \left( \begin{array}{c} 4 U_m y (H-y)/H^2 \\ 0 \end{array} \right),
@f]
with $U_m = 1.5$, i.e. the inflow boundary conditions correspond to Poiseuille flow for this configuration. Finally, on the right
vertical wall we impose the condition that the vertical component of the velocity should be zero.
A plot of the obtained results for $t=0,1,5,10$ is the following
-@image html visit0001.jpeg
+@image html visit0001.png
-@image html visit0002.jpeg
+@image html visit0002.png
-@image html visit0003.jpeg
+@image html visit0003.png
-@image html visit0004.jpeg
+@image html visit0004.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.
density mix, for example fresh water and salt water, or alcohol and water.
<li> Compressible Navier-Stokes equations: These equations are relevant for
- cases where
+ cases where
velocities are high enough so that the fluid becomes compressible, but not
fast enough that we get into a regime where viscosity becomes incompressible
and the Navier-Stokes equations need to be replaced by the hyperbolic Euler