NTHMP Mapping and Modeling Benchmarking Workshop: Tsunami Currents
For a description of the workshop and all data provided, see the
workshop webpage.
For GeoClaw code, see the
GitHub
repository
Results for other problems
GeoClaw results for Benchmark problem 1
Results presented at workshop:
Notes:
- With Manning \(n = 0.025\) a steady vortex street develops. With smaller
values of n, the vortex pattern is less regular.
- The Manning coefficient is set to zero where the tank bottom is flat
and is only nonzero on the conical hill. With friction everywhere, the flow
slows down or the depth increases, depending on the boundary conditions
imposed on the left bounary. Note that flow is sub-critical (the Froude number
is less than 1 near the left boundary) and so information propagates upstream
and mathematically it is not correct to specify both an inflow depth and an
inflow velocity as is done in the problem description. The flow will slow down
due to friction as it flows down the channel, which should cause the depth to
increase and this increase will propagate back to the inflow.
When friction is set to zero except on the cone, there is minimal effect, but
with friction everywhere there is significant effect. Adding friction only near
the cone and downstream also has an effect in the case \(n = 0.01\) (see the
comparisons below).
- Constant velocity \(u = 0.115\) m/s is imposed at the left boundary.
- The results with unstable vortex shedding are very sensitive to
any changes in the code. For example, changing the target Courant number from
0.9 to 0.89 (resulting in slightly smaller time steps) gives very different
vortex shedding patterns.
-
Comparison plots with Manning 0.01 applied only on cone:
Plot index
... Gauge 1
... Gauge 2
(The two set of plots are Courant number 0.89 and 0.9.)
Note that at
40 seconds differences are
starting to appear, and by
80 seconds the patterns are
very different.
- Comparison plots with Manning 0.01 applied for \(x > 4.0\):
Plot index
... Gauge 1
... Gauge 2
(The two set of plots are Courant number 0.89 and 0.9.)
In this case, the Manning friction is applied not just on the cone
but for all \(x > 4.0\) in the wave tank. There is agreement of the results
with different Courant numbers for slightly longer, but they still diverge.
Also note that in
this case the increased friction leads to the fluid velocity falling at the
inflow boundary and a steady vortex shedding pattern develops as a result.
Work done after the workshop:
Convergence tests:
- Comparison plots with Manning coefficient n = 0.017
with two grid resolutions. Coarse: dx=dy=0.0095 (original),
Fine: dx=dy=0.00475.
Note that periodic vortex shedding is observed initially but the shedding
becomes non-periodic at later times.
The results agree fairly well for the periodic portiona
(after shifting one time series due to different transient phases).
- Comparison plots with Manning coefficient n = 0.02
with two grid resolutions. Coarse: dx=dy=0.0095 (original),
Fine: dx=dy=0.00475.
Note that periodic vortex shedding is observed in both
cases and the results agree fairly well (after shifting one time series due to
different transient phases).
First-order method:
Using the first order Godunov method (omitting the high-resolution
correction terms normally included in GeoClaw) gives more diffusive results.
In this case even with Manning coefficient n = 0.015, periodic shedding is
observed, and the amplitude matches the experimental results better than with
the high-resolution method.
