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.

Tsunami-Model

Authors#

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.

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