# 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](https://doi.org/10.1016/j.cpc.2020.107251). The aim is to obtain the parameters describing the initial displacements from the data of two available buoys located near the Japanese coast.

![Tsunami-Model](https://raw.githubusercontent.com/UM-Bridge/benchmarks/main/docs/source/images/tohoku_full.png "Level Hierarchy for Tohoku Tsunami Model")

## Authors
- [Anne Reinarz](mailto:anne.k.reinarz@durham.ac.uk)

## 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

[Model sources here.](https://github.com/UM-Bridge/benchmarks/tree/main/models/exahype-tsunami)

## 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:
1. First model:
    - bathymetry is approximated only by a depth average over the entire domain
    - pure DG discretisation of order 2
2. The second model:
    - DG discretisation with a finite volume subcell limiter allowing for wetting and drying
    - smoothed bathymetry data (Gaussian filter)
3. 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](https://www.gebco.net/)
- More details: [Reference Paper](https://doi.org/10.1145/3458817.3476150)