12.2 PASS:
Transcritical flow over a bump
-
Author
- Stéphane Popinet
- Command
- sh shock.sh
- Version
- 120717
- Required files
- shock.gfs (view) (download)
shock.sh error.ref
- Running time
- 33 seconds
This is a classical test case for shallow-water solvers. Water
flowing over a bump goes from subcritical through supercritical over
the bump and back to subcritical. Figure 146 illustrates the
stationary solution with a shock. Figure 147 gives the
convergence with resolution. The analytical solution was obtained
thanks to the SWASHES library [12].
| Figure 146: Numerical and analytical solutions for
transcritical flow over a bump. |
| Figure 147: Convergence of the error between the numerical
and analytical solution with the spatial resolution. |
12.2.1 PASS:
Transcritical flow with multiple layers
-
Author
- Stéphane Popinet
- Command
- sh layered.sh
- Version
- 120717
- Required files
- layered.gfs (view) (download)
layered.sh uprof.awk field.awk prof.ref
- Running time
- 1 minutes 52 seconds
This is meant to replicate the multilayer test case of
[4, 5]. The vertical viscosity is set to
ν=0.01 m2/s and the Navier condition at the bottom is given
by the Strickler relation
with S=25 m1/3/s, the Strickler coefficient, h the
water depth and U the depth-averaged velocity.
The stationary solutions are summarised in the figures below. They
can be compared to Figure 9 of [5] and Figure 8 of
[4]. They agree more or less although our Strickler
coefficient is lower (i.e. we need a larger explicit friction to
match [4, 5]).
| Figure 148: Free surface and topograghy. |
| Figure 149: Horizontal velocity field (15 layers). |
| Figure 150: Velocity profiles at (a) x=10, (b) x=15, (c) x=20. |
