# 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