Tsunami#
Overview#
In this benchmark we model the propagation of the 2011 Tohoku tsunami by solving the shallow water equations. For the numerical solution of the PDE, we apply an ADER-DG method implemented in the ExaHyPE framework. The aim is to obtain the parameters describing the initial displacements from the data of two available buoys located near the Japanese coast.
Run#
docker run -it -p 4242:4242 linusseelinger/model-exahype-tsunami
Properties#
Model |
Description |
---|---|
forward |
Tsunami model |
forward#
Mapping |
Dimensions |
Description |
---|---|---|
inputSizes |
[2] |
x and y coordinates of a proposed tsunami origin |
outputSizes |
[4] |
Arrival time and maximum water height at two buoy points |
Feature |
Supported |
---|---|
Evaluate |
True |
Gradient |
False |
ApplyJacobian |
False |
ApplyHessian |
False |
Config |
Type |
Default |
Description |
---|---|---|---|
level |
int |
0 |
between 0 and 2, the model level to run (see below for further details) |
verbose |
bool |
false |
switches text output on/off |
vtk_output |
bool |
false |
switches vtk output to the /output directory on/off |
Mount directories#
Mount directory |
Purpose |
---|---|
/output |
VTK output for visualization |
Source code#
Description#
The underlying PDE model can be written in first-order hyperbolic form as
\( \frac{\partial}{\partial t} \begin{pmatrix} h\\hu\\hv\\ b \end{pmatrix} + \nabla \cdot \begin{pmatrix} hu & hv\\ hu^2 & huv\\ huv & hv^2 \\ 0 & 0\\ \end{pmatrix}+ \begin{pmatrix} 0\\ hg \, \partial_x (b+h)\\ hg \, \partial_y (b+h)\\ 0\\ \end{pmatrix}= 0, \)
where
\(h\) denotes the height of the water column,
\((u,v)\) the horizontal flow velocity,
\(g\) gravity
\(b\) denotes the bathymetry.
This benchmark creates a sequence of three models:
First model:
bathymetry is approximated only by a depth average over the entire domain
pure DG discretisation of order 2
The second model:
DG discretisation with a finite volume subcell limiter allowing for wetting and drying
smoothed bathymetry data (Gaussian filter)
The third model:
DG discretisation with a finite volume subcell limiter allowing for wetting and drying
full bathymetry data
The bathymetry data has been obtained from GEBCO
More details: Reference Paper