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